International workshop on next generation gamma-ray source

Understanding the emergence of hadron structure and the nuclear force in terms of QCD are key questions at the frontier of nuclear physics. These phenomena are a consequence of quarks and gluons interacting at confinement-scale distances, where color forces are strong. The beams at a medium-energy NGLCGS facility will enable measurements that uniquely probe hadron structure and hadronic interactions in this non-perturbative regime of QCD. The experimental program will investigate LEQCD phenomena with unprecedented precision in the photon energy range from about 60 MeV to the nucleon-to-delta(1232) transition. The initial research program at such a facility will two main components: (1) Compton scattering to investigate nucleon structure and (2) photopion production to investigate the QCD origins of isospin symmetry breaking in the strong nuclear force. Both program components will require high-density polarized targets.

• Low-energy QCD and nucleon structure: the beam capabilities at a medium-energy NGLCGS will enable high-precision measurements of the scalar and spin nucleon polarizabilities by Compton scattering from unpolarized and polarized targets. Such measurements, together with advances in calculations using lattice QCD (LQCD) and QCD-based effective field theories, will explore the QCD origin of nucleon structure associated with the collective response of nucleons to electromagnetic impulses with unprecedented sensitivity. For example, the experimental programs at the NGLCGS facility are proposed to improve the statistical accuracy of the nucleon spin polarizability measurements by more than a factor of 10 from current values and to impact the dynamical scaler polarizabilities of the neutron and proton with precision from energies below to above the pion production threshold.
• Low-energy QCD: photopion production: the high intensity and high energy resolution of beams at a medium-energy NGLCGS facility will enable determination of electromagnetic s-wave and p-wave amplitudes to the π⁰ production with sufficiently high precision to observe charge-symmetry violation. Photoproduction of pions at energies near the reaction threshold provides mechanisms for investigation of the QCD origin of breaking of isospin symmetry in strong nuclear interactions.

The beams at low-energy NGLCGS facilities will enable high-accuracy measurements in nuclear structure, nuclear astrophysics, fundamental symmetries, and γ-ray beam applications in nuclear and homeland security. The research opportunities in each area are summarized below:

• Nuclear structure: the beams at an advanced γ-ray source will enable systematic studies of weak collective dipole and quadrupole nuclear excitations with unprecedented precision. Such studies will provide nuclear structure details and information about the symmetry energy of the nuclear equation of state (EOS) that are difficult to obtain by other means. The high γ-ray beam intensities will enable mapping of states accessed through M1 transitions from the ground state in nuclei with a level of detail and breadth that will contribute to modeling of coherent neutrino-nucleus scattering and to calculating nuclear matrix elements for neutrinoless double-beta decay. Also, a next-generation γ-ray beam facility will enable new exclusive measurements of photodisintegration of few-nucleon systems with a precision that provides sensitivity to three-nucleon interactions.
• Nuclear astrophysics: new γ-ray beam capabilities will enable measurements that contribute broadly to open questions in nuclear astrophysics, questions such as big-bang nucleosynthesis, helium burning in massive stars, and synthesis of heavy nuclei. One of the most important reactions in stellar modeling is ¹²C(α, γ)¹⁶O. The rate of this reaction relative to the carbon forming reaction 3α → ¹²C determines the fate of massive stars. The measurement of the rate of the ¹⁶O(γ, α)¹²C reaction at energies approaching the temperatures at the core of stars is a grand challenge in nuclear astrophysics.
• Fundamental symmetries: the beams at an advanced low-energy γ-ray beam facility will enable measurements of parity violating photodisintegration of few-nucleon systems. In particular, a measurement of parity violation (PV) in deuteron photodisintegration near threshold is sensitive to a nucleon–nucleon (NN) PV amplitude that is not accessible using other systems. Such measurements sample the short-range part of the NN interaction, providing unique quantities for comparison with calculations using lattice gauge theory.
• Applications: the intense mono-energetic γ-ray beams at low-energy NGLCGS facilities will enable photonuclear reaction measurements important for technologies and techniques used in homeland security and nuclear safeguards. Programs to develop field-deployable system will benefit by having a target areas equipped for evaluating concepts for γ-ray beam interrogation of cargo, nuclear fuel, and special assemblies at these facilities. The new beam capabilities at advanced γ-ray sources will also create opportunities for applications in medicine.

The nuclear resonance fluorescence (NRF) reaction is one of the work horses in the investigation of the dipole response of atomic nuclei. The method enables the extraction of intrinsic properties of excited states such as spin, parity and transition widths in a model independent way. Furthermore, due to the low momentum transfer of photons, primary dipole transitions are induced, i.e., in even–even nuclei states with J = 1^± are populated. This makes NRF an excellent reaction to systematically study the phenomena in the dipole response of nuclei, such as the PDR and the scissors mode over a large range of nuclei.

Thus far, mostly the decay branch back to the ground state as been investigated with the NRF reaction. However, the detailed decay pattern of excited states is often connected to important details in its nuclear structure. The decay widths to the individual lower-lying excited states or the ground state are directly linked to the corresponding transition matrix elements. Thus, the individual decay channels are sensitive to different components of the nuclear-state wave function. For example, in the case of transitions to lower-lying excited states, the de-excitation takes place via a different component in the wave function than the excitation from the ground state. Therefore, the observation of these transitions and the determination of the branching ratios reveal important experimental information that tests modern nuclear-structure models.

The method of γγ coincidences in the spectroscopy of the decay of excited states has been proven to be a powerful tool for determining even small branching ratios to excited low-lying states [30, 31]. The principle is illustrated in the left part of figure 4. After excitation by photoabsorption, the high-lying state at excitation energy E_x may de-excite either directly to the ground state with width Γ₀ or via an intermediate state with width Γ_i. By detecting the two emitted γ rays in coincidence, even small branching ratios Γ_i/Γ₀ can be determined with good precision, since the background is strongly suppressed. This technique allows the branching of dipole-excited states to individual lower-lying levels to be determined, thus greatly aiding in building up complex level and decay schemes. An example is shown in figure 4. The right-hand side of the figure provide, the level structure for a measurement on ⁷⁶Ge, where the decay of the 1⁺ scissors mode has been investigated [32]. The 1⁺ state at 3.763 MeV is populated by photo-excitation. Gating on the decays of the ${\mathrm{2}}_{1}^{+}$ and ${\mathrm{2}}_{2}^{+}$ states, as shown on the left side of the figure, allows the order of the γ-ray transitions in the decay to be determined.

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The combination of large-volume LaBr₃ and high-resolution HPGe detectors opens the way for γγ-coincidence measurements with sufficient statistical accuracy to track γ-ray decay cascades. High-resolution HPGe detectors allow for a separation of individual γ-ray transitions from dipole excited states in regions where the level density is not yet too high. Even in regions with a high level density, individual states can sometimes have substantial excitation strength and are, thus, separable from the otherwise rather continuous spectrum. This provides a way to normalize spectra to complementary data sets obtained using bremsstrahlung beams. Nevertheless, most dipole-excitation strength in regions of high level density is so strongly fragmented that individual states cannot be resolved. In this case, the large-volume LaBr₃ detectors have a significant advantage over HPGe detectors because of their higher detection efficiency. This high efficiency allows the fragmented strength in the beam region to be separated from the background and enables integrated branching strengths to be determined. In deformed nuclei, where the first-excited-state energies are very low, decays to the ground state and the first excited state are close in energy, posing a challenge to the accelerator team to deliver beams with high intensity and low energy spread to the target. Deconvolution methods have recently been developed and applied to aid in extracting decays out of the detector response (figure 5), see e.g. [33, 34].

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With the combination of HPGe and LaBr₃ detectors, the high efficiency of the latter provides sufficient statistics to observe branching decays from higher-lying states, either in low-resolution LaBr₃ or even in high-resolution HPGe spectroscopy, as demonstrated in [30, 31]. Especially at low energies, electric quadrupole excitation probabilities can be sufficiently large for observation, and can be separated from the dipole strength making use of angular distribution and correlation measurements using arrays of HPGe and LaBr₃ detectors. In certain cases even the mixing ratio of M1/E2 transitions can be measured. This recently facilitated a first measurement of the isovector quadrupole strengths in ¹⁵⁶Gd [35], for example.

The capabilities of the next-generation laser Compton γ-ray source combined with modern γ-ray detectors will enable measurements that address a broad range of physics through photo-excitation studies. The topics include multi-phonon structures such as quadrupole–octupole coupled states and the search for rotational isovector scissors excitations; the investigation of the PDR along with its structural evolution and fingerprints in going from spherical to deformed regions; and detailed spectroscopic studies of the M1 spin-flip resonance. Therefore, the physics topics to be addressed embrace shape coexistence, octupole correlations, isovector excitations, neutron skins, and photon strength functions (PSFs), often with strong relevance for the fields of nuclear astrophysics and weak-interaction physics such as neutrinoless double-beta decay and neutrino scattering.

3.1.1.1. Shape coexistence and link with physics with radioactive beams

3.1.1.2. Multi-phonon and rotational low-lying states

At low energies, in spherical or near-spherical nuclei, excited states are often formed by phonon excitations. For example, the first 2⁺ state is identified with a quadrupole phonon, and the first 3⁻ state with an octupole phonon. Such phonons can be coupled, leading to multiplets of multi-phonon states built from like phonons, or from mixtures of, e.g., quadrupole and octupole phonons. As such, the quadrupole–octupole coupled quintuplet of states, 1⁻...5⁻ contains an E1-excited 1⁻ state which typically is the first excited 1⁻ state, located at roughly the sum energy of its constituents and carrying most of the E1 strength at low energies. (See the schematic diagram of γ-ray transitions associated with multiple-phonon de-excitation is given in figure 6.) In addition to excitations where protons and neutrons move in phase, there are so-called mixed-symmetry states where at least one pair of protons/neutrons has a different phase [39]. This leads to additional states, such as a quadrupole-excited one-phonon mixed-symmetric ${\mathrm{2}}_{\mathrm{m}\mathrm{s}}^{+}$ state. Again, the phonon coupling between the latter and the symmetric ${\mathrm{2}}_{1}^{+}$ phonon state leads to a multiplet of mixed-symmetry states, one of which is an M1-excited 1⁺ state, which is typically the strongest M1 excitation at low energies of roughly 3 to 4 MeV. In rotational nuclei, this state evolves into the well-known scissors mode, where valence protons and neutrons are counter-oscillating in a scissors-like fashion.

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Different mechanisms forming E1 and M1 excited states at such low energies can, however, compete with one another. For example, spin-flip excitations, where a nucleon is moved from an ℓ ± 1/2 orbital to its ℓ ∓ 1/2 partner, can generate M1 excitation strengths similar to those of the scissors mode. In the E1 sector, the generation of E1 strength in valence spaces containing either no or a very limited number of opposite-parity orbitals is under much discussion, and there are other possibilities, such as the formation of alpha clusters (see below). Therefore, it is not only important to locate those dipole excited states and to determine their parity and decay strengths, it is also crucial to measure their decay pattern, which contains important information on their underlying structure. These tasks are uniquely facilitated by the capabilities at a next-generation laser Compton γ-ray source for measuring decay branches, parities, and relative excitation strengths. Furthermore, in rotational nuclei, band structures are expected on J = 1 band-heads such as the scissors-mode state. Indeed, in recent work [35], a first candidate for the long-sought rotational ${\mathrm{2}}_{\mathrm{s}\mathrm{c}}^{+}$ member of the scissors-mode band has been discovered. In addition, measurements of angular correlations made possible by arrays of γ-ray detectors with large angle coverage, high detection efficiency, and high energy resolution used in combination with linearly polarized monoenergetic γ-ray beams will enable measurements of multipole-mixing ratios. These, in turn, can reveal absolute isovector E2 strengths. High quality data of this type are crucial in constraining effective charges in nuclear dynamics calculations.

Another aspect of dipole excited states has recently been found and is connected to weak-interaction physics. While the strong interaction dominates in nuclei, nuclei are also laboratories for studying the weak interaction through the possibility of β or ββ decay. Of special interest for many experiments, and for the characterization of neutrinos in general, is the search for neutrinoless double-beta (0νββ) decay. The existence of this decay mode would identify the neutrino as a Majorana particle, one which is its own anti-particle. It would provide information about the absolute mass of the neutrino involved in the decay through the ratio of the measured decay rate and the calculated nuclear matrix element for the decay. Since many candidate isotopes (mother and/or daughter) for 0νββ decay occur in mass regions near transitions from spherical to deformed shapes, their model description is challenging. Furthermore, isovector parameters are seldom known. NRF measurements can be used to extract information on phenomena such as shape coexistence and mixed-symmetry states from the observation of the scissors mode and its decays, especially its decays to the potentially mixed-configuration ${\mathrm{0}}_{1,2}^{+}$ states (see reference [40]).

3.1.1.3. The E1 pygmy dipole resonance.

3.1.1.4. Alpha-cluster excitations.

3.1.1.5. The M1 spin-flip resonance.

Nuclear fission is a highly exothermic and strongly collective nu clear process in which most of the energy is released through the kinetic energy of the ejected fission fragments. The evolution of a fissioning system proceeds from the initial impact of the incident particle through the intermediate saddle point(s), then through scission, and finally to the configuration of separated fission fragments. This evolution is governed by a multi-dimensional potential-energy surface (PES) and by the shell structure of the fragments. Development of reliable theoretical models of nuclear fission is important for basic research and for the development of nuclear energy and nuclear security technologies. For these purposes, data for different types of observables are needed, including fission product yields over wide ranges of masses and half lives, as well as the kinetic energy and angular distributions of the emitted fragments and neutrons.

To first approximation, the fission barrier of a heavy nucleus can be studied by measuring the fission probability as a function of the excitation energy. By comparing the experimentally determined fission probabilities to the results obtained with the WKB approximation, the shape of the fission barrier (its height and curvature parameter) can be determined.

Significant progress has been made in studying the multiple-humped fission barrier landscape of actinides, where a strongly deformed deep third minimum in the potential landscape was established [60, 61]. This is illustrated in figure 7, where horizontal dashed lines show transmission resonances in the superdeformed (SD) second minimum and in the hyperdeformed (HD) third minimum. One expects that the HD minimum in a cluster description consists of a rather spherical ¹³²Sn-like component with magic neutron and proton numbers N = 82 and Z = 50. Recent theoretical results [62, 63] highlight the role of shell corrections in the prominence of the third minima for thorium and light uranium isotopes. There is a clear trend suggesting that lower N values produce larger neutron shell corrections and, thus, more prominent third minima. This is in stark disagreement with experimental results. Using the ²³¹Pa(³He, df) reaction, Csige et al [64] studied sub-barrier fission in ²³²U and inferred a fission barrier with a well-formed third minimum that does not agree with the theoretical predictions. Pronounced third minima have also been inferred to exist through observation of fine structure in the cross section of transfer-reaction-induced fission or through sub-barrier photofission cross-section measurements. There is particular interest in identifying resonances in the third minimum, where very large deformations cause the GDR to split into two components with a low-lying oscillation along the long symmetry axis with a typical excitation energy of 4–5 MeV. It is expected that these resonances may have a significantly enhanced γ-ray width Γ_γ of about 100 eV in the population of the third minimum, while, for the second minimum, one expects a γ-ray width of only about 1 eV. E1 resonances excited from the ground state will have about the same absolute excitation strength as resonances in the third minimum, but resonances in the third minimum will be much broader, with a total width of about 1 keV.

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Photofission measurements enable the selective investigation of extremely deformed nuclear states in the light actinides and can be utilized to better understand the landscape of the multiple-humped PES of these nuclei. The selectivity of these measurements stems from the low and reasonably well-defined amount of angular momentum transferred during the photoabsorption process. High-resolution studies can be performed on the mass, atomic number, and kinetic energy distributions of the fission fragments following the decay of well-defined initial states in the first, second and third minima of the PES in the region of the light actinides. The beams available at the next-generation laser Compton source facilities will enable high fidelity studies of the PES using transmission resonance spectroscopy, as well as studies of heavy clusterization in the actinides, and of rare fission processes such as ternary fission. Each of these opportunities is discussed in this section.

3.1.2.1. Transmission resonance spectroscopy in photofission.

3.1.2.2. Photofission as a probe of heavy clusterization in the actinides.

3.1.2.3. Investigation of rare fission modes: ternary photofission.

Models of p-process and s-process nucleosynthesis require reliable (γ, n), (γ, p) and (γ, α) reaction cross sections on hundreds of stable and unstable nuclei. The proton-rich nuclei cannot be produced by neutron capture reactions. Complete network calculations on p-process nucleosynthesis include several hundred isotopes and the corresponding reaction rates. Theoretical predictions of the rates, normally in the framework of the Hauser–Feshbach (HF) theory, are necessary for modeling the nucleosynthesis reaction network. The reliability of these calculations should be tested experimentally, especially at rate-limiting paths in the network. Different approaches are available and necessary to improve the experimental data base for the p-process. The (γ, n) cross sections in the energy regime of the GDR have already been measured extensively (see, e.g., [65]). More recently, substantial effort has be devoted to using beams with a continuous bremsstrahlung spectrum to determine the reaction rates without any assumptions on the shape of the cross section's energy dependence in the astrophysically relevant energy region, close to the reaction threshold [66–68]. A determination of the reaction rates by an absolute cross section measurement is also possible using monoenergetic photon beams produced by a laser Compton γ-ray source [69]. The beam capabilities at next-generation laser Compton γ-ray sources will open the possibility of higher accuracy (γ, n) cross-section measurements and measurements on nuclei with low natural abundances, for which the amount of target material will be small.

In contrast, the experimental knowledge about the (γ, p) and (γ, α) reactions in the corresponding Gamow window is smaller. In fact, the experimental data is based on the observation of the time reversal (p, γ) and (α, γ) cross sections, respectively [70–74] for the proton-rich nuclei with mass numbers around 100. Due to the difficulties concerning the experimental accessibility of the (γ, α) reaction rates, a method using elastic α scattering has been established [75, 76]. It would be a tremendous improvement in the quality of the database to measure these rates directly using photon beams. Having a significant impact on this database will require a program of systematic measurements on a broad range of nuclei. This type of program would be made possible by a next-generation laser Compton γ-ray source.

The heavy elements above the so-called iron peak are mainly produced in neutron capture processes: the r process (r: rapid neutron capture) deals with high neutron densities, well above 10²⁰ cm⁻³, and temperatures of around 2 to 3 GK. It is thought to occur in explosive scenarios such as supernovae [78, 79] and was recently verified in neutron star merger via gravitational wave observations [80]. In contrast, the average neutron densities during s-process nucleosynthesis (s: slow neutron capture) are rather small (around 10⁸ cm⁻³), so that the neutron capture rate λ_n is normally well below the β-decay rate λ_β , and the reaction path is therefore close to the valley of β stability [81–83]. However, during the peak neutron densities, branching occurs at unstable isotopes with half-lives as low as several days. The half-lives of these branch points are normally known with high accuracy, at least under laboratory conditions, and rely on theory only for the extrapolation to stellar temperatures [84]. However, their neutron capture cross sections are accessible to direct experiments only in special cases. For this reason, nuclear astrophysics reaction-network simulations currently rely heavily on HF model calculations of the critical neutron capture cross sections. The difficulty is that there are many examples where the results of HF model calculations differ substantially from measurements (see, e.g., reference [85]). Thus, experimental constraints on the theoretical predictions of these branch points are needed. Laser Compton γ-ray sources enable measurements of the inverse (γ, n) reaction, which can also provide information about the stellar enhancement factors (SEFs). The SEF accounts for the difference in the neutron-capture cross section measured in the laboratory and the effective cross section in the stellar environment. Because nuclei in stars spend much of the time in excited states, capture reactions mostly occur on excited states, not the ground state. In addition to determining the cross sections and the SEFs directly from (γ, n) cross-section measurements, the SEFs can be calculated using PSFs determined from NRF measurements. The importance of each nucleus and reaction in the s-process network must be analyzed on its own merits. An example of the type of information that can be obtained using linearly polarized mono-energetic photon beams is illustrated in the proposed NRF measurement on ⁶⁴Ni at HIγS.

The ⁶⁴Ni nucleus is the product of neutron capture on ⁶³Ni, which is a branch-point nucleus. Figure 8 illustrates the situation during He-core burning (yellow) and C-shell burning (red) of a massive star, where the weak component of the s-process originates [86]. As the branching is very sensitive to the ⁶³Ni(n, γ) cross section, a measurement was performed at CERN using a radioactive ⁶³Ni target [77, 87]. However, the reaction rate in the hot environment of the stellar plasma differs significantly from the measured value because excited states are populated [88]. In the case of ^63gsNi(n, γ), the stellar rate is still around 90% at He-core burning temperatures, but it drops to around 40% at the higher temperature in the C-shell burning phase [77]. HF model calculations are required to account for the stellar enhancement [89]. These calculations rely on the PSF in ⁶⁴Ni, which can be deduced from photoabsorption cross sections and the decay properties of low-spin states. The linearly polarized monoenergetic beams available at laser Compton γ-ray sources enable model-independent determination of photoabsorption cross sections as a function of the excitation energy, and consequently, a determination of the PSFs (see, e.g., [30, 33, 34, 90, 91]).

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Late-stage red giant stars produce energy in their interiors via helium burning. In first generation stars, helium burning proceeds through the 3α process and then ¹²C(α, γ)¹⁶O, while in later generation stars, α captures also involve the various CNO seed nuclei. In both cases, the ¹²C(α, γ)¹⁶O reaction helps to regulate the efficiency of helium burning in massive stars (those with masses greater than the suns). It also determines core mass, temperature and density during the latter stages of stellar evolution, and ultimately the mass of the iron core in the incipient supernova. In addition, the carbon-to-oxygen ratio (C/O) influences the abundances of elements produced in the ensuing explosion. After several decades of effort, the uncertainty in the rate of the α-particle capture reaction on ¹²C is still large enough to substantially limit our understanding of the latter stages of stellar evolution. To resolve this problem, the astrophysical S factor for the ¹²C(α, γ)¹⁶O reaction must be determined to an accuracy better than about 10% in the Gamow window (E_cm = 300 keV), which is indicated by the vertical band in figure 9 [92, 93].

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As shown in figure 9, the cross section has been measured at various levels of precision down to a center-of-mass (cm) energy of 1.2 MeV; then it must be extrapolated down to 300 keV, the energy needed for stellar reaction-rate calculations. One of the major uncertainties in performing the extrapolation arises from the presence of several resonances which contribute to the cross section at energies around E_cm = 0.75 MeV. Above E_cm = 1 MeV, the elastic scattering and capture reactions are dominated by a broad 1⁻ resonance at an excitation energy in ¹⁶O of E_x = 9.59 MeV (E_cm = 2.43 MeV) and a narrow 2⁺ state at E_x = 9.85 MeV (E_cm = 2.70 MeV). However, a 1⁻ state at E_x = 7.12 MeV, just 42 keV below threshold, determines the capture cross section in the astrophysically relevant energy region, including its interference with the higher lying 1⁻ and 2⁺ states. In addition, broad high-lying states and direct processes produce a coherent background that affects the energy dependence of the cross section and thereby the extrapolation.

Direct measurements of the ¹²C(α, γ)¹⁶O cross section at energies below E_cm = 2 MeV have been attempted for over 30 years. The major difficulty encountered in these experiments is the intense neutron background arising from the ¹³C(α, n) reaction. This background tends to swamp the γ-ray detector. The γ-ray beams produced by laser Compton sources have a narrow energy spread and thus offer an alternative technique for measuring the cross section for α capture on ¹²C at energies important to astrophysics as discussed above. The principle of detailed balance allows the determination of the (α, γ) cross section from the measurement of the cross section for the time reversed (γ, α) reaction. An added advantage of using the (γ, α) reaction over the direct reaction is that the cross section in the gamma window is enhanced by about a factor of 50 due to detailed balance. This experimental concept has been demonstrated at HIγS using a CO₂ gas-filled optical TPC [99, 100]. The calculated cross section for the ¹⁶O(γ, α)¹² reaction is shown in figure 10. An upgrade of HIγS to increase the γ-ray beam flux on target by a factor of about fifty in the energy region important for this reaction, would enable meaningful measurements in the red shaded energy range (⟨E_cm⟩ = 1.3 MeV) in the figure. The next-generation laser Compton sources could potentially deliver more than an additional factor of 500 in beam flux on target relative to HIγS, thereby enabling measurements down to about ⟨E_cm⟩ = 700 keV. This measurement should be performed at next-generation laser Compton γ-ray source facilities using a variety of experimental techniques, such as gas TPCs (both optical and charge readout), silicon strip detectors with thin targets, and total cross-section measurements using super-heated high-purity water detectors (e.g., as in reference [101]).

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More than half of the heavy nuclei with A > 120 are produced by r-process nucleosynthesis. The r-process involves nuclear reactions driven by rapid neutron capture, where the neutron capture rate is faster than the competing beta decay. The likely environments for the r-process are type-II supernovae and merging neutron stars. Simulations of r-process nucleosynthesis require reliable (n, γ) reaction cross sections on hundreds of stable and unstable nuclei. Theoretical predictions of the rates, normally in the framework of HF theory, are necessary for modeling neutron capture on unstable nuclei. The reliability of these calculations should be tested experimentally, especially at rate-limiting paths in the network. The (γ, n) time-reversed photodisintegration reaction offers a mechanism for determining the neutron capture cross section and level density of radioactive nuclei. Next-generation laser Compton γ-ray sources will enable measurements on isotopes with low natural abundances and thus very limited sample sizes.

Obtaining information about the detailed structure of the crust of a neutron star is an important open challenge in astrophysics. The crust is composed of non-uniform neutron-rich solid matter that is about 1 km thick and located above a liquid core [102, 103]. The inner crust comprises the region from the density at which neutrons drip from nuclei to the inner edge separating the solid crust from the homogeneous liquid core. While the density at which neutrons drip from nuclei is well determined, the transition density at the inner edge is much less certain because of insufficient knowledge of the EOS of neutron-rich nuclear matter. Measurements of collective responses of neutron-rich nuclei provide constraints on the nuclear EOS. The monoenergetic and linearly polarized beams at laser Compton γ-ray sources enable unique measurements of dipole and quadrupole excitations. Those most relevant to exploring the EOS are studies of the PDR on nuclei at the neutron rich end of an isotope chain using NRF and determination of the centroid energy and width of the isovector giant quadrupole resonance (IVGQR) via Compton scattering [104]. The underlying structure of the PDR is often interpreted as an oscillation of less bound valence neutrons forming a neutron skin [105, 106]. However, the true nature of the PDR is a matter of ongoing discussion. Furthermore the PDR and the E1 strength in general have a direct connection to the neutron skin of nuclei and the symmetry energy of nuclear matter [107, 108] (figure 11).

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Weak NN amplitudes at low energy are suppressed by six to seven orders of magnitude compared to strong NN amplitudes and are therefore difficult to observe. While these effects can be amplified by several orders of magnitude by nuclear dynamics in complex systems, the unambiguous extraction of the weak interactions among nucleons requires parity violating measurements in very light nuclei, where theory is under good control. At the moment this includes the deuteron, the triton, and ³He, with the four-nucleon system in the pipeline. These very light systems can be calculated using two- and three-nucleon interactions, which in turn are understood in terms of effective field theories (EFTs) that systematically incorporate the symmetries of QCD. The EFT approach can consistently be applied to strong and weak nucleon interactions as well as to external currents. There is also growing optimism that parity-odd effects in A > 4 nuclei can be calculated. We are at a juncture in the development of theory where PV may soon be understood in terms of QCD dynamics even in many body nuclei. Ongoing programs [126] are pursuing the matching of LQCD to EFTs, which are used as input into many-body calculations of heavier nuclei. Both SM and beyond-the-SM physics can be treated in this way.

At leading order in the EFT power counting, and at very low photon energies (below 10 MeV), there are five parity violating low-energy constants (LECs) that parameterize the short-distance physics [127–129]. ³⁵ The values of these LECs cannot be determined within the EFT framework but have to be extracted from experiment or ultimately from calculations involving nonperturbative QCD. Recent work shows that upon combining the EFT approach with the large-N_c expansion of QCD, the number of independent parity-violating LECs reduces to two at leading order [134]. One of these is the ΔI = 2 isotensor coupling, which is poorly constrained from existing measurements. Combining the existing data for $\vec{p}+p$ scattering (which constrains the remaining leading-order isoscalar piece) with the results of a measurement of the ΔI = 2 contribution would therefore constrain all terms at leading order in this combined EFT and large-N_c expansion [135].

An important experimental constraint on the isovector parity violating interactions comes from the parity violating asymmetry from polarized neutron capture on the proton, $\vec{n}+p\to D+\gamma$, recently measured by the NPDGamma collaboration at the Spallation Neutron Source (SPS) at ORNL [136]. In the next few years we expect to possess two additional pieces of experimental information on the NN weak interaction in few-nucleon systems. The analysis of PV in $\vec{n}+{}^{3}\text{He}\to {}^{3}\text{H}+p$ completed recently at the SPS at ORNL will be published, and another experiment on PV in $\vec{n}+{}^{4}\text{He}$ spin rotation [137] will be performed at the new NG-C neutron beam line at the NIST Center for Neutron Research (NCNR). However, these will yield scant experimental information on the elusive ΔI = 2 component of the NN weak interaction. Fortunately the ΔI = 2 operator is the easiest target for a quantitative lattice calculation from the SM because it does not receive contributions from disconnected diagrams. The isotensor operator is scheduled to be calculated on the lattice in the next few years [138, 139]. Lattice constraints on other NN weak amplitudes are many years out, at least at physical quark masses.

The cleanest experimental channel for extracting the ΔI = 2 component in few-body PV is P-odd deuteron photodisintegration near threshold using the helicity-dependent photodisintegration cross section for circularly polarized photons. Limits from previous attempts exist from Chalk River [140] and from the reverse reaction [141], but did not resolve a nonzero value. Experiments to measure this observable have been proposed in the past at JLab [142, 143], SPRING-8, and the Shanghai Synchrotron, but they have not yet been realized. It was therefore listed in the last NSAC long-range plan as a priority NN weak interaction measurement for the future. In addition, it is possible to contemplate other PV experiments involving helicity-dependent reactions with circularly polarized photons in few-nucleon systems, such as the breakup of three-nucleon systems. We emphasize the importance of a $\vec{\gamma }d\to pn$ parity-violation measurement because of the unique information it will provide about the weak interaction in hadronic systems and the state of EFT and lattice calculations.

The parity-violating asymmetry in deuteron photodisintegration, including its energy dependence, has been considered in pionless EFT in references [144, 145]. The next-to-leading order results of reference [145] were combined with different model estimates for the LECs to determine the expected size of the parity-violating asymmetry ${A}_{L}^{\gamma }$, to estimate a figure of merit (FOM), and to extract the best energy regime for performing the experiment. ${A}_{L}^{\gamma }$ is computed as the ratio of the difference in the photodisintegration cross section measured with positive (h = +1) and negative (h = −1) beam helicity divided by the unpolarized cross section, which is the sum of the positive and negative helicity cross sections. The beam helicity is h = +1 when the polarization vector of the circularly polarized beam is in the direction of the beam momentum vector. ${A}_{L}^{\gamma }$ for the photodisintegration of the deuteron computed using various parameterizations of the hadronic weak coupling constants is plotted as a function of photon energy in figure 12. The FOM quantity that is optimized for obtaining the best statistical accuracy per hour of beam time is FOM = (${A}_{L}^{\gamma }$)² σ, where σ is the unpolarized photodisintegration cross section. The FOM computed for various parameterizations of the hadronic weak coupling constants are plotted as a function of photon energy in figure 13. This analysis indicates that the experiment should ideally be performed in the photon energy region between 2.26 and 2.30 MeV. In this energy window, the average cross section and ${A}_{L}^{\gamma }$ are 600 μb and 4 × 10⁻⁷, respectively.

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A schematic diagram of the concept for the experiment setup is shown in figure 14. The neutrons from the photodisintegration reaction in the liquid deuterium (LD) target are detected in an array of ³He ionization tubes embedded in a cylindrical polyethylene moderator that surrounds the target. The background due to interactions of scattered γ rays in the ³He ionization tubes is determined using an array of ⁴He ionization tubes located outside the inner layers of ³He ionization tubes. About 75% of the γ rays incident on the 21 cm long LD target are transmitted through the target. The γ-ray beam is collimated to a diameter of 10 mm, and the inner diameter of the ³He ionization tube array is 6 cm. The ionization tubes are 50 cm long and centered about the LD target. With this target thickness, detector geometry, and a γ-ray beam intensity of 10¹⁰ γ/s on target in the above energy window, a statistical accuracy of ±10⁻⁷ can be obtained with about 9000 h of beam time.

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The technical demands to minimize γ-ray helicity-dependent changes in the phase space of the γ-ray beam are comparable to those encountered at the polarized electron injector section at JLab in the parity violating electron scattering. Developing the capability for delivering polarized γ-ray beams to targets with the stability and precision required to perform 10⁻⁷ asymmetry measurements will demand focused and dedicated resources for R&D work and implementation of the supporting systems. Suggested beam parameters for studying PV in deuteron photodisintegration are shown in table 4.

The size of the expected parity violating asymmetries from reactions in few-nucleon systems induced with photons at MeV energies are generally around several times 10⁻⁷. For such experiments, achieving the required systematic accuracy is a formidable challenge, especially at the initial ramp-up stage of an NGLCGS facility. This motivates us to look for parity violating asymmetries that are larger, and therefore easier to measure, even if the interpretation is not as theoretically clean as in few-nucleon systems. Certain light nuclei possess doublets with narrow energy spacings in the 10 to 100 keV range between levels of opposite parity. Parity-odd asymmetries can be amplified by several orders of magnitude by the interference of such parity doublets states involved in photon-induced reactions. There are a half dozen such nuclei (some of which were investigated using charged-particle beams a few decades ago) [117] whose parity-odd asymmetries could be measured using the ultra-high intensity mono-energetic polarized photon beam at the NGLCGS. To develop the technical infrastructure and scientific expertise among the staff, a PV program at such facilities should start with an asymmetry measurement on parity doublets in nuclei, where the parity violating asymmetry is several orders of magnitude larger than that in few-nucleon systems. The experiment could measure either the helicity dependence in the total cross section using transmission or the asymmetry of the fluorescence from the doublet using a HPGe detector array. Examples of candidate nuclei and estimated amplification factors for parity violating asymmetries in nuclear resonance fluorescence are described by Titov et al [149].

Either parity-odd asymmetry can be calculated in a simple way in terms of the energies and widths of the states and the parity-odd matrix elements of interest. PV in states which are particle unstable will be difficult to handle theoretically. However, as the theoretical tools to calculate PV in these nuclei improve, we can identify one or more candidate nuclei for a focused effort involving both theory and experiment.

Although the parity violating asymmetry is enhanced in the parity doublet systems, the photonuclear cross section is small compared to Compton and pair production cross sections in the energy range of interest below the GDR. The beam requirements are therefore still challenging, as shown in table 5.

First though, we address how such measurements are related to QCD. Polarizabilities can be computed directly on the lattice. But since they are second-order in electromagnetic fields and furthermore diverge near the chiral limit, they provide a considerable challenge, and thereby a stringent test of lattice methods. Similar techniques can then be trusted for QCD input to double-beta decay, dark-matter detection, and beyond-the-standard-model currents in nucleons and nuclei.

The recent success of the background-field technique used for these calculations has led to a strong effort to refine computations of nucleons and nuclei in uniform electromagnetic fields [168–176]. Results from the NPLQCD collaboration shown in figure 21 even include the first computations of magnetic properties of light nuclei. There is also a pioneering computation of γ_E1E1 by Engelhardt [177]. Both show that lattice and experimental uncertainties on these quantities are commensurate, and have the opportunity to be reduced in parallel.

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Currently, the most significant systematic error is that computations are performed at unphysically large pion masses, altering the dynamical response to applied electromagnetic fields. However, recent cross-fertilization between LQCD and phenomenology furthers the goal of exposing the role of chiral symmetry in low-energy QCD [178]. For magnetic polarizabilities, the pion mass provides a dial that alters the relative weight of diamagnetic and paramagnetic contributions, leading to a deeper understanding of the underlying effective degrees of freedom. Analysis of LQCD results with χEFT, moreover, provides a consistency check that is independent of using Compton data. In turn, high-accuracy experiments in single and few-nucleon systems provide crucial constraints on LQCD computations.

Equation (4.1) shows that, near ω = 0, the effects of the scalar polarizabilities in cross sections are ∝ω², and ∝ω³ for spin polarizabilities. With increasing energy, polarizability contributions become more prominent. Resonances and particle-production thresholds lead to further enhancements. When inelastic channels are open, the dynamical polarizabilities become complex, and their imaginary parts are directly related to pion photoproduction. That allows, for example, an indirect exploration of some currently ill-determined nπ photoproduction multipoles [179].

Since data are taken at (ideally several) nonzero energies, the '(static) polarizabilities' α_E1(ω = 0) etc follow from an extrapolation of results at nonzero energies and compress the richness of such information into just a few numbers. A sophisticated and reliable understanding of the energy dependence of these functions is required, so that the static values can be extracted from data taken at energies from 70 to 250 MeV. A good understanding of the energy dependence induced by pion-production and the Δ(1232) resonance is therefore mandatory.

Recently, an open letter of theorists with backgrounds in several variants of dispersion relations and effective field theories summarized the theory status as follows [180]:

• (a)  
  Static scalar polarizabilities can be extracted from future data well below the pion-production threshold with high theoretical accuracy.
• (b)  
  Data around and above the pion production threshold show increased sensitivity to the spin polarizabilities and will help to understand and resolve some discrepancies between different approaches.
• (c)  
  All theoretical approaches resort to well-motivated but not fully controlled approximations around and above the Δ(1232) resonance. Concurrently, sensitivity to the static polarizabilities decreases substantially. Instead, one studies details of the Δ(1232) resonance, as well as the degrees of freedom exchanged between photons and the nucleon in the t-channel.

The transition from one regime to another is, of course, gradual rather than sudden.

Neutron polarizabilities are less well determined than proton ones, see equation (4.2). Since both are equal at leading order in χEFT, their precise measurement could reveal subtle differences in the pion dynamics around the neutron and proton.

Such effects have fundamental implications: reference [159] pointed out that the subtraction function in their dispersive treatment of the neutron–proton mass difference can be integrated to yield ${\alpha }_{E1}^{(\mathrm{p})}-{\alpha }_{E1}^{(\mathrm{n})}$. Accurate measurements of the differences of the electric polarizabilities will therefore illuminate the interplay of quark-mass and electromagnetic contributions to M_n − M_p.

The neutron dynamical polarizabilities can be determined from Compton scattering on light nuclei. For photon energies below 100 MeV, elastic scattering is favored. While the Compton response of the neutron itself is quite small there, it interferes constructively with large pieces of the nuclear amplitude, including the proton Thomson term and the sizable pion-exchange currents of bound systems. The importance of the latter for Compton scattering in light nuclei means that measurements of the elastic reaction also provide indirect, non-trivial benchmarks for the theoretical description of mesonic contributions to nuclear binding. The different systematics in theory calculations of elastic and quasi-free (QF) Compton scattering on light nuclei make experiments in neutron QF kinematics an attractive complement to measuring the coherent process.

In each case, χEFT provides the necessary, model-independent parameterizations of Compton scattering on the various targets described here, including consistency between single-nucleon and pion-exchange currents [16]. And crucially, it does so in a framework where the residual theoretical uncertainties can be reliably estimated. A χEFT that is well-matched to the experiments outlined below exists for the proton up to about 250 MeV; for the deuteron, up to 120 MeV; and for ³He, at 50 to 120 MeV. Accuracies are 2% or better up to ω ∼ m_π , and 20% or better around the Δ resonance. For each of these nuclei, comprehensive studies of the sensitivities of Compton observables with polarised beams and/or targets, and even for some recoil observables, are available in these regions [181–185]. With present efforts and new experiments on the horizon, a consistent χEFT description up to 250 MeV for all light nuclei, including ⁴He, is being pursued vigorously. Results can be expected within the next few years.

The 2015 US long range plan states: 'Great progress has been made in determining the electric and magnetic polarizabilities.' The 2018 Particle Data Group numbers for the proton and neutron scalar polarizabilities (in the canonical units of 10⁻⁴ fm³) are:

$$\begin{equation}\begin{aligned}\hfill {\alpha }_{E1}^{(\mathrm{p})}=11.2\pm 0.4& \qquad {\beta }_{M1}^{(\mathrm{p})}=2.5\pm 0.4;\hfill \\ \hfill {\alpha }_{E1}^{(\mathrm{n})}=11.8\pm 1.1& \qquad {\beta }_{M1}^{(\mathrm{n})}=3.7\pm 1.2;\hfill \end{aligned}\end{equation} \tag{ 4.2 }$$

see figure 22. The sums, ${\alpha }_{E1}^{(\mathrm{p})}+{\beta }_{M1}^{(\mathrm{p})}=13.8\pm 0.4$ and ${\alpha }_{E1}^{(\mathrm{n})}+{\beta }_{M1}^{(\mathrm{n})}=15.2\pm 0.4$ are quite accurately known from the Baldin sum rule and therefore used as constraints in scalar-polarizability determinations [187–189]. This implies that a portion of the error bars are anticorrelated. Particularly notable in the proton case is that efforts by several theory groups, in different frameworks, have led to compatible results, in each of which theory and experimental uncertainties are of similar size [190–192]. For example, the extraction of reference [190] quotes a theory error of ±0.3 while the uncertainty stemming from the γ-proton data itself is ±0.35. In spite of this positive development, there is a disconcerting residual dependence of extractions on the γ-proton data used [16, 190–193]. This has led to an ongoing discussion about the appropriate criteria for a statistically consistent database. Ultimately, this matter can only be definitively decided by additional high-quality γ-proton data. If NGLCGS were to start running tomorrow, this would be a pressing problem for it to address. But approved experiments at HIγS and MAMI will greatly expand the proton Compton database within the next few years; we expect they will resolve it.

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As for the neutron results, a US-led collaboration at MAX-IV added 22 points in 2015, effectively doubling the deuteron's world dataset and reducing the statistical error for the neutron values by 30% [194, 195]. Since HIγS is now adding precision data, we anticipate that proton and neutron errors will soon be small enough to enable quantitative exploration of the extent to which the proton and neutron deformations in electromagnetic fields differ.

Another US-led collaboration conducted the pioneering measurements of doubly polarized Compton-scattering observables at MAMI and provided the first extraction of proton spin polarizabilities [166, 167, 196–198]. They compare favorably with predictions from two different implementations of χEFT and from dilution refrigerator (DR); see figure 23. In units of 10⁻⁴ fm⁴:

$$\begin{equation}\begin{matrix}\hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill {\gamma }_{E1E1}\hfill & \hfill \hfill & \hfill {\gamma }_{M1M1}\hfill & \hfill \hfill & \hfill {\gamma }_{E1M2}\hfill & \hfill \hfill & \hfill {\gamma }_{M1E2}\hfill \\ \hfill \hfill & \hfill \mathrm{M}\mathrm{A}\mathrm{M}\mathrm{I}\enspace [170,171,200-202]\hfill & \hfill \hfill & \hfill -3.5\pm 1.2\hfill & \hfill \hfill & \hfill 3.2\pm 0.9\hfill & \hfill \hfill & \hfill -0.7\pm 1.2\hfill & \hfill \hfill & \hfill 2.0\pm 0.3\hfill \\ \hfill \hfill & \hfill \chi \mathrm{E}\mathrm{F}\mathrm{T}\mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{n}\mathrm{t}\enspace 1\enspace [182]\hfill & \hfill \hfill & \hfill -1.1\pm 1.{9}_{\mathrm{t}\mathrm{h}}\hfill & \hfill \hfill & \hfill 2.2\pm 0.{5}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm 0.{6}_{\mathrm{t}\mathrm{h}}\hfill & \hfill \hfill & \hfill -0.4\pm 0.{6}_{\mathrm{t}\mathrm{h}}\hfill & \hfill \hfill & \hfill 1.9\pm 0.{5}_{\mathrm{t}\mathrm{h}}\hfill \\ \hfill \hfill & \hfill \chi \mathrm{E}\mathrm{F}\mathrm{T}\mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{n}\mathrm{t}\enspace 2\enspace [203]\hfill & \hfill \hfill & \hfill -3.3\pm 0.{8}_{\mathrm{t}\mathrm{h}}\hfill & \hfill \hfill & \hfill 2.9\pm 1.{5}_{\mathrm{t}\mathrm{h}}\hfill & \hfill \hfill & \hfill +0.2\pm 0.{2}_{\mathrm{t}\mathrm{h}}\hfill & \hfill \hfill & \hfill 1.1\pm 0.{3}_{\mathrm{t}\mathrm{h}}\hfill \\ \hfill \hfill & \hfill \mathrm{D}\mathrm{R}\enspace [162,185,204]\hfill & \hfill \hfill & \hfill -[3.4\dots 4.5]\hfill & \hfill \hfill & \hfill [2.7\dots 3.0]\hfill & \hfill \hfill & \hfill [-0.1\dots 0.3]\hfill & \hfill \hfill & \hfill [1.9\dots 2.3]\hfill \end{matrix}\end{equation} \tag{ 4.3 }$$

But more work is clearly needed to reduce the experimental uncertainties of 20%–170% and obtain more accurate information on the low-energy response of the nucleon's spin degrees of freedom to electromagnetic fields.

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The existing unpolarized proton database, while large in size, is noisy, and the data between 190 MeV and 250 MeV are not of particularly high quality [16]. The deuteron data were markedly improved by Myers et al [194, 195], but the uncertainties are not on a par with the proton ones. Spin polarizabilities are best extracted from data with both polarized beams and polarized targets. For the proton, pioneering double-polarization data are now available [166, 167, 196–198]; but there is no corresponding data set for a light-nuclear target from which neutron values can be inferred. Indeed, no data, polarized or unpolarized, have been published for ³He, which seems to be a promising target in this regard.

Further progress in our understanding of the nucleon's electromagnetic response will thus come on three fronts:

• Very accurate extractions of neutron scalar polarisabilities that will illuminate differences in neutron and proton internal structure;
• Measurements of the largely unexplored neutron spin polarizabilities;
• Marked improvement of the proton spin-polarizability values, enabling issues requiring precision knowledge of low-energy spin structure to be addressed.

We therefore propose a suite of high-accuracy experiments on protons and light nuclei that, together, will determine the static polarizabilities and map out the dynamical polarizabilities of the neutron and proton over a broad energy range. The result will be an understanding of the role that different QCD effects play in nucleon structure. The experiments are described in section 4.1.5, where each has its own subsection, with individual specifications of beam parameters. We close with sections on the target (section 4.1.6) and beam (section 4.1.7) technology needed to make these experiments a reality.

Several interrelated experiments are necessary since it is unlikely that a single experiment will determine a particular static polarizability with the requisite precision. The program is designed to provide a coherent data set which will dramatically improve extractions and enable unprecedented checks of both experimental systematics and theoretical bias. For all targets, high-quality data with carefully formulated correlated and point-to-point systematic errors are needed.

The scalar polarizabilities are best extracted from both unpolarized and polarized experiments where the effect of spin polarizabilities is small, namely at photon energies below 100 MeV. Proton targets provide a direct avenue for proton polarizabilities. The deuteron and ⁴He, as isoscalar targets, are sensitive to the average of proton and neutron polarizabilities, ${\alpha }_{E1}^{(\mathrm{p})}+{\alpha }_{E1}^{(\mathrm{n})}$ etc. In ³He, the sensitivity is to $2{\alpha }_{E1}^{(\mathrm{p})}+{\alpha }_{E1}^{(\mathrm{n})}$ etc. Experiments on different light nuclei provide important checks of theory systematics, and in particular of the unified χEFT description of meson-exchange currents in these nuclei. These binding effects must be subtracted in a model-independent theory approach.

The spin polarizabilities can be extracted at energies around or above 120 MeV by combining precise data and theory with a carefully selected set of double-polarized observables whose sensitivities are dominated by only one or two proton and neutron spin polarizabilities measured over a range of energies; see e.g. references [182, 183]. Again, proton polarizabilities are directly accessible with proton targets, but the isoscalar values from deuteron targets provide valuable cross checks. Since polarized ³He is an effective polarized-neutron target, neutron values can also be determined without knowing their proton counterparts [185].

Inelastic Compton scattering on the quasi-elastic ridge is dominated by the impulse approximation. Measurements of the neutron–photon interaction in QF kinematics therefore provide another avenue to extract neutron polarizabilities. High-quality theory is needed to control the corrections to the QF approximation (for first steps see reference [186]).

Lastly, we point out that a series of measurements over a wide kinematic range is not only necessary for high-accuracy determinations of scalar and spin polarizabilities. It also allows reconstruction of the functions α_E1(ω), β_M1(ω) and γ_i(ω), yielding the energy dependence of the dynamical polarizabilities, see recent progress in references [191, 192]. This provides stringent tests of our understanding of different low-energy QCD mechanisms and of the way they are manifest in Compton scattering.

4.1.5.1. Proton spin polarizabilities.

A monochromatic, high flux photon source with 10⁹ γ/s, with linear and circular polarizations of approximately 100%, can provide the definitive measurement of the proton spin polarizabilities. Figure 24 shows representative asymmetry data points for the Σ_2x asymmetry using a transversely polarized target and circularly polarized photons with 200 h of running at both 150 MeV and 290 MeV. This assumes a frozen-spin target similar to the Mainz design and a 4π γ-ray detector similar to the Mainz crystal ball. The beam conditions are shown in table 6. Figure 25 shows representative asymmetry data points for the Σ₃ asymmetry assuming an unpolarized target and linearly polarized photons. A conservative estimate is that statistical uncertainties in the polarizabilities can be reduced by a factor of ten or more relative to those in the Mainz results.

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Table 6. Suggested beam parameters for proton spin polarizability.

Parameter	Value
Energy range	150 to 300 MeV
Flux on target	109 γ/s
Relative energy resolution	2% FWHM
Polarization	Linear and circular, >95%
Beam diameter	5 mm on target
Time structure	Highest frequency available, pulse width < 1 ns

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Comprehensive discussions of theory predictions for the dependence of all double-polarized observables on the spin polarizabilities are provided in references [181–183]. To test the theory dependence of the analysis it will also be important to take data at lower energies, around 150 MeV. At incident energies below approximately 250 MeV, the recoil proton is undetectable because it does not escape the frozen-spin target cryostat. Without that, it is problematic to separate the Compton signal from backgrounds caused by coherent and QF Compton scattering on nuclear species in the polarized target and from the target cell wall. One way around this problem is to utilize a polarizable polystyrene scintillator as the target, where the scintillation light produced in the target is used to tag a Compton scattering event on the proton. A polarizable active target has been developed at Mainz and shown to function well.

4.1.5.2. Neutron scalar polarizabilities from elastic Compton scattering on deuterium.

HIγS has recently acquired Compton-scattering data on deuterium at 65 and 85 MeV. Extending the current HIγSγd data set to energies above 100 MeV and using a significantly higher beam intensity will greatly improve the extracted polarizabilities, since the sensitivity increases at higher energies.

A preliminary plot of the angular distribution of the cross section for ²H(γ, γ)²H is shown in figure 26. The inelastic contribution that is observed at backward angles, unresolved in the HIγS data, is the largest systematic uncertainty in the present experiment. Part of this resolution limitation is due to the NaI detectors themselves, but part stems from poor incident beam resolution: resolution was sacrificed in order to gain flux. The higher intensity at the NGLCGS would permit much tighter collimation, thus enabling a vast improvement in beam energy resolution without an unacceptable reduction in beam intensity.

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Nevertheless, the statistical error bars from HIγS shown in figure 26 are much lower than any previous experiment. By operating at a beam energy of 120 MeV or higher, while staying below the pion production threshold, and using several very large, high-resolution NaI detectors with FWHM values of less than 2% (as in the MAX-Lab experiment of references [194, 195]) the new measurements would not only be more sensitive to neutron scalar polarizabilities, but would also provide much better control of the uncertainties associated with the inelastic channel (tables 7 and 8).

Table 7. Suggested beam parameters for neutron scalar polarizabilities from deuteron.

Energy	120 MeV
Flux	5 × 108 at 1.5% FWHM
Polarization	Circular
Diameter	<20 mm on target
Time structure	TBD

Table 8. Suggested beam parameters for neutron spin polarizabilities from polarized ³He.

Parameter	Value
Energy range	100 to 140 MeV
Flux on target	5 × 108 γ/s
Relative energy resolution	2% FWHM
Polarization	Circular, polarization >95%
Beam diameter	5 mm on target
Time structure	20 MHz, pulse width < 1 ns

4.1.5.3. Neutron spin polarizabilities from elastic Compton scattering on polarized ³He.

Polarized ³He approximates a polarized neutron target. This statement can be quantified using ab initio wave functions calculated with χEFT potentials, see reference [185]. Such calculations also incorporate the meson-exchange currents that are needed for consistency with the potential. As ³He is doubly charged and contains more nucleon pairs, interference of polarizability effects with proton Thomson terms and meson-exchange currents is larger than for the deuteron or proton, leading to some enhanced polarizability signals for this target.

The calculations depicted in figure 27 suggest that the photon beam asymmetry with a transversely polarized target, Σ_2x , is the cleanest observable to determine a neutron spin polarizability. It is affected by ${\gamma }_{M1M1}^{(\mathrm{n})}$ much more strongly than it is by the scalar polarizabilities, and it is unaffected by any proton spin polarizabilities. Other neutron spin polarizabilities affect this observable, but with a different angular dependence. Measuring this observable over a range of angles and energies will be crucial for checking the χEFT theory of Compton scattering from ³He and ensuring that 'contamination' of the polarization observable from scalar polarizabilities is understood and under control.

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At 120 MeV, a similar sensitivity to neutron polarizabilities is predicted in the distribution of Σ_2z , as measured with a longitudinally polarized target. In this case, a linear combination of four spin polarizabilities could be determined from the measurements.

A high-density polarized ³He target has been built and tested at HIγS [199–201]. Given the demonstrated areal density of ³He, an experiment using the current HINDA detector array would collect on average ten elastic events per hour at each angle, assuming a beam intensity of 5 × 10⁸ γ/s. With a target polarization of 50%, statistical uncertainties of order 0.02 on Σ_2x and Σ_2z could be achieved in moderate running times. Operation at such a high beam intensity would require continued development of an effective shielding configuration against backgrounds from the target windows. Additional development work is needed to improve the capability of the HINDA array to discriminate cosmic-ray events, which contribute at the γ-ray energies of interest in this experiment.

4.1.5.4. Neutron scalar polarizabilities from elastic Compton scattering on ⁴He.

⁴He has a larger coherent Compton cross sections than any other nucleus discussed here, see figure 19 for the recent HIγS data on this reaction [202]. From a theoretical perspective, an accurate description of cross sections for ⁴He, which is more tightly bound than ²H or ³He, as a function of energy and angle, will challenge the χEFT description of Compton scattering on light nuclei. Thus, although measurements just below pion threshold hold the most promise for extractions of the neutron polarizabilities, ancillary measurements at lower energies are needed to check that the theory used for polarizability extractions is sufficiently accurate.

The higher flux and higher energy of the new facility mean that γ⁴He elastic scattering could yield neutron scalar polarizabilities of unprecedented precision. The prospects are illustrated in figure 28, where the angular distributions are plotted for 60, 90 and 120 MeV. We project that at 120 MeV the beam parameters of table 9, together with existing ⁴He target technology (see section 4.1.6 below), and the present HINDA detector array, can produce a cross-section measurement with 1% statistical error in just 150 h. This precision, combined with the estimated point-to-point systematic uncertainty (2% in solid angle) is depicted by the shaded bands in figure 28. With the statistical uncertainties at such a reduced level, we expect that systematics (including an estimated 1% for target density and 2% for flux) and χEFT truncation uncertainty will ultimately limit the accuracy attained for ${\alpha }_{E1}^{(\mathrm{n})}$ and ${\beta }_{M1}^{(\mathrm{n})}$. Even so, this represents a significant advance in our knowledge of ${\alpha }_{E1}^{(\mathrm{n})}$ and ${\beta }_{M1}^{(\mathrm{n})}$.

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Table 9. Suggested beam parameters for neutron scalar polarizabilities from ⁴He.

Parameter	Value
Energy range	60 to 120 MeV
Flux on target	108 to 109 γ/s
Relative energy resolution	3% FWHM
Polarization	None
Beam diameter	5 mm on target
Time structure	Highest frequency available, pulse width < 1 ns

In addition to the cross-section advantage provided by a ⁴He target (and also the obvious fact that the target is non-combustible), the energy resolution of the beam and detector become significantly less critical in this case, compared to deuterium. Since the first excited state of ⁴He is near 20 MeV, it is possible to obtain very clean, purely elastic γ-ray spectra with a ⁴He target. It is no longer necessary to impose tight beam collimation to achieve improved beam energy resolution, and greater photon fluxes on target are possible.

A measurement of coherent Compton scattering from ³He at similar angles and energies will provide complementary information, since it is sensitive to a different combination of neutron and proton polarizabilities. While ³He has a lower breakup threshold than ⁴He and does not offer quite the same cross-section advantage, extractions of ${\alpha }_{E1}^{(\mathrm{n})}-{\beta }_{M1}^{(\mathrm{n})}$ from γ³He scattering will, nevertheless, be a valuable cross-check that the theory used for polarizability extractions has nuclear effects under control. An experiment to measure the γ-³He elastic differential cross section is approved at HIγS and will run in 2019 at energies of 100 MeV and (later) 120 MeV [204]. The higher flux and extended energy range of the NGLCGS facility could provide enhanced sensitivity of this kind of ³He measurement to neutron polarizabilities.

4.1.5.5. Quasi-free neutron Compton scattering on light nuclei.

Much of the experimental information we have on QF Compton scattering on light systems comes from the Mainz experiment of Kossert et al with an unpolarized photon beam and a deuterium target [205]. The experiment used tagged bremsstrahlung at energies of E_γ = 200 to 400 MeV and the large NaI(Tl) spectrometer 'CATS' to detect the backscattered photon at 136°. In addition, the 'SENECA' array of liquid scintillators was used to detect the recoiling neutron (or proton). The cross section peaks at around 180 nb/sr at the Δ resonance. It rises from about 40 nb/sr to around 150 nb/sr as E_γ increases from 250 to 300 MeV, so there is definite benefit if one could run at around 300 MeV. A QF neutron Compton experiment at these energies with a polarized beam and a polarized ³He target would provide information on neutron dynamical spin polarizabilities in this energy regime. This would provide important constraints on these dynamical neutron spin-structure functions in this regime where the Δ(1232) and pion-cloud mechanisms both affect pion-production multipoles—constraints which would facilitate enhanced precision for the static values of the polarizabilities.

We note that Σ_2x for Compton scattering from a neutron is mainly sensitive to ${\gamma }_{E1E1}^{(\mathrm{n})}$, especially at forward angles, as seen in figure 29 [182, 183]. The sensitivity to ${\alpha }_{E1}^{(\mathrm{n})}-{\beta }_{M1}^{(\mathrm{n})}$ here is quite small. The kinematics of QF Compton scattering from deuterium at an incident energy of 300 MeV is displayed in figure 30.

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With a 10 cm LD target, a 1 sr detector for γ' and a photon beam intensity of 10⁹ γ/s, the Compton event rate would be about 70 Hz. Such a high rate of incident γ-rays also makes the use of a polarized ³He gas target feasible. A 30 cm, 10 bar target with a similar detector acceptance would produce an event rate of about 1.2 Hz. Given that the neutron angle is fairly tightly correlated to the γ' angle it should be possible to design the neutron arm of the detection system to match the acceptance of the γ'-arm.

Neutron spin polarizabilities could be accessed using two different implementations of double-polarization: either polarized beam, polarized target and TOF neutron detector or polarized beam, unpolarized target, and a TOF polarimeter to measure the polarization transfer to the recoiling neutron.

Typically, in a polarized experiment one measures an asymmetry in the counting rate when the beam helicity, target spin orientation, etc are reversed. The precision in measuring a polarized observable is given by: $\delta X=\sqrt{\frac{2}{{N}_{\mathrm{i}\mathrm{n}\mathrm{c}}.{F}^{2}}}$, where N_inc is the number of incident neutrons and F² is the experiment FOM. If the efficiency of the γ' arm is close to 100%, F² ∼ ɛ_n P², where ɛ_n is the efficiency of the neutron arm and P is either the target polarization or the analyzing power of the neutron polarimeter. In the polarized-beam-and-target approach, ɛ_n ∼ 0.2 and P ∼ 0.9 × 0.6 are readily obtainable, so that F² ∼ 5.8 × 10⁻². To obtain a precision of δX ∼ 0.01, N_inc should be about 3 × 10⁵, which could be collected in 80 h.

We prefer this option to the one where the polarization of the recoiling neutron is detected. The precision of a recoil-polarization detection experiment for a given N_inc could be similar, even though the FOM is lower, since a liquid target could be employed. But other complications regarding the detection of final-state neutron polarization—imprecise knowledge of the neutron analyzing power, complications in building a polarimeter that matches the solid angle of the γ' arm—favor a polarized-target experiment. But recoil-polarization detection should continue to be considered as an option for NGLCGS experiments.

History shows that polarizability measurements proceed at exactly the pace of the enabling technologies. It is telling that the first spin polarizability measurements followed the construction of a low-mass, high acceptance, frozen-spin target at Mainz, and that to drive this research further, a further extension of this device, an active polarized target, has been developed. In addition, without the construction of a modern, high-rate, highly segmented photon detector, covering a large fraction of the 4π solid angle, it will not be possible to suppress pion photoproduction backgrounds.

4.1.6.1. Unpolarized active gas targets.

4.1.6.2. Unpolarized liquid targets.

Liquid ³He and ⁴He targets are relatively standard technology. The liquid has a density about a factor of fifty greater than a 20 bar gas target. A cryogenic target system capable of liquefying ⁴He at 4 K, H₂ at 20 K, and D₂ at 23 K has already been developed at HIγS [206]; see figure 31. The apparatus was utilized in a series of Compton scattering experiments on deuterium and ⁴He at beam energies from 60 to 85 MeV. Cooling is provided by a 4 K Gifford–McMahon cryocooler. Liquid temperatures and condenser pressures are recorded throughout each run to ensure that the target's areal density is known to about 1%. Modifications are planned that will add the ability to liquefy ³He by lowering the system's base temperature to 1.5 K.

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Elastic Compton scattering measurements on liquid ⁴He and deuterium targets at the NGLCGS will require a high-resolution photon detector array to identify elastic scattering unambiguously. In the case of ⁴He, the requirement is not especially stringent, since the inelastic channel is about 20 MeV below the elastic peak. The situation is considerably more challenging for deuterium targets, where the breakup channel is only 2.2 MeV below the elastic peak. A program is underway at HIγS using the LD target with high-resolution beams and detectors to characterize the inelastic contribution at 65 and 85 MeV.

Both liquid ³He and ⁴He could also be used for QF Compton scattering, but the recoiling nucleon, and perhaps other fragments, would need to be detected in coincidence with the scattered photon. Time of flight to an external array could be used to measure the momentum of the recoil neutron. This would be very useful in reconstructing the QF event. If the energy is sufficiently high, similar techniques could be preformed for a recoiling proton. At lower energies a separate, active target could detect protons stopping in the target. The technique of using TOF for both neutrons and protons simultaneously could provide a tremendous advantage in the particular case of QF scattering from a deuterium target, where the proton QF measurement could provide a consistency check for the desired neutron QF result, since the two QF channels are completely symmetric.

4.1.6.3. Frozen-spin polarized target.

4.1.6.4. Active frozen-spin target.

As discussed in the physics justification section, there is great interest in making measurements of the proton spin polarizabilities at incident photon energies near pion threshold. However, at incident photon energies below approximately 250 MeV, recoil protons cannot escape from a frozen-spin target cryostat, and the identification of Compton scattering events from the sea of π⁰ → γγ events becomes problematic. At Mainz, for example, the direction of the recoil proton is used to differentiate Compton scattering events from π⁰ decay events. To enable Compton scattering measurements at lower energies, where the recoil proton is presently unobserved, an active frozen-spin target has been developed. The target material is a polarizable scintillator, employing Si photomultipliers to read out the scintillation. A similar active polarized target will be essential for this program.

An active frozen-spin target utilizes the same ³He/⁴He DR as a traditional frozen-spin target, with some modifications in and around the area that holds the target material. Discs of polystyrene doped with TEMPO are stacked inside the DR mixing chamber and held at 30 mK. Scintillation light from the discs is captured, redirected, and wavelength-shifted in a containing cylinder of wavelength-shifting material [208]. This cylinder is, in turn, affixed to a cylinder of plexiglass, which transports the light to silicon photomultipliers operating at 4 K [209] (see figure 32). In a recent test at Mainz, the active target achieved 50% polarization with a 70 h relaxation time. A target head which enables particle tracking is also under development. This could involve the use of printable scintillators in order to make a highly segmented, position-sensitive target head.

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4.1.6.5. Polarized ³He gas targets.

An essential part of the experimental apparatus shared by many of the Compton scattering polarizability experiments is a nearly 4π crystal detector for detection of the Compton-scattered photon. Near-4π acceptance is desirable for two reasons: (i) to enable data taking at multiple scattering angles simultaneously, and (ii) to suppress π⁰ → γγ events that would show up as double neutral hits in the detector. Surrounding the target with a charged-particle tracker—e.g., a cylindrical GEM or silicon tracker—would provide neutral/charged particle identification. For example, the tracking detector could be used to identify recoil protons, deuterons or helium nuclei from the Compton scattering reaction.

For the case of measuring the neutron polarizabilities, detectors suitable for photons or neutrons of energy around 100 MeV will be necessary. Good detection efficiency of neutral particles requires bulk material, and scintillators are generally used.

4.1.7.1. Inorganic scintillators for photon detection.

For photons one would use high-Z materials which have short radiation lengths. Since energy resolution will be important, scintillators are preferable to Cherenkov counters. Traditionally materials such as NaI(Tl) or CsI(Tl) have been used, like in HINDA at HIγS; see figure 33. However, (with thallium activation to increase light output) the scintillation is relatively slow and timing precision for TOF measurements is sub-optimal. Alternatively one can use materials such as:

• (a)  
  BaF₂: this has fast and slow scintillation components, with good timing properties and pulse shape discrimination (PSD) of relativistic and non-relativistic particles. The UV scintillation requires a quartz window photo-multiplier tube (PMT).
• (b)  
  PbWO₄: this material has quite a fast scintillation, good timing, short radiation length, and good radiation hardness. If we have a very high intensity facility, radiation hardness may become an issue in the long term.
• (c)  
  New developments in scintillator materials technology, such as the use of quantum dots. These aim to improve the light output and speed of the scintillation, and significant advances can be expected in the next few years.

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These materials are sensitive to γ-rays and neutrons above about 25 MeV as well as other generated background. For operation in intense radiation fields, the detectors should be highly segmented to keep singles rates at a manageable level. Uniformity of scintillation light collection is important if optimum energy resolution is to be obtained.

If the scintillation is in the visible region one can use silicon PMTs in place of the traditional vacuum tubes. These are relatively cheap, have very good timing properties, reasonable noise performance, and continue to improve.

4.1.7.2. Organic scintillators.

4.1.7.3. Time-of-flight techniques.

Compton scattering between an electron and a photon is shown in figure 34. We can list the four momenta of the electron and photon before and after collision as the following,

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Using conservation of four-momentum, we can express the energy of the outgoing photon as:

$$\begin{equation}{E}_{\gamma }\equiv \hslash {\omega }^{\prime }=\frac{\hslash \omega (1-\beta \,\mathrm{cos}\,{\theta }_{\mathrm{i}})}{1-\beta \,\mathrm{cos}\,{\theta }_{\mathrm{f}}+\frac{\hslash \omega }{{\mathcal{E}}_{\mathrm{e}}}(1-\mathrm{cos}\,{\theta }_{\mathrm{p}\mathrm{h}})},\end{equation} \tag{ 5.1 }$$

where ℏ is the reduced Planck constant, ℏω is the energy of the incoming photon, E_γ (or ℏω') is the energy of the outgoing photon, θ_i and θ_f are the angles between the momentum of the incoming and outgoing photons and that of the incident electron, ($\mathrm{cos}\,{\theta }_{\mathrm{i}}=\hat{p}\cdot \hat{k}$ and $\mathrm{cos}\,{\theta }_{\mathrm{f}}=\hat{p}\cdot \hat{{k}^{\prime }}$), and θ_ph is the angle between the two photons ($\mathrm{cos}\,{\theta }_{\mathrm{p}\mathrm{h}}=\hat{k}\cdot \hat{{k}^{\prime }}$).

For a collision between relativistic electrons and low energy photons, the energy of the scattered photons is peaked along the direction of the incident electrons. The back-scattered photon has the maximum energy in a head-on collision with θ_i = π and θ_f = 0,

$$\begin{equation}\hslash {\omega }^{\prime }=\frac{{\gamma }^{2}{(1+\beta )}^{2}}{1+{R}_{0}}\,\hslash \omega ,\end{equation} \tag{ 5.2 }$$

where ${R}_{0}=2{\gamma }^{2}(1+\beta )\hslash \omega /{\mathcal{E}}_{\mathrm{e}}$ is the recoil factor. When the recoil is small (R₀ ≪ 1), the maximum scattered photon energy is approximately, E_γ,max ≈ γ²(1 + β)² ℏω ≈ 4γ² ℏω, where the second approximation holds for ultra-relativistic electrons. The energy boost factor, 4γ², is responsible for the relativistic Doppler effect (or relativistic blue-shift) to transform an ordinary infrared or visible light photon into a high energy x-ray or γ-ray photon.

At the zero-recoil limit, the total cross section is rather small $\sigma \approx \frac{8\pi {r}_{\mathrm{e}}^{2}}{3}=6.652\times 1{0}^{-29}$ m² (i.e., the Thomson cross section). For the collision of a relativistic electron beam and a low-energy photon beam, scattered photons with the highest energy are concentrated around the direction of the incident electron beam. This kinematic feature enables the formation of a nearly monochromatic Compton photon beam by using a simple collimation technique.

Technological advancements relevant to the Compton CGSs have been reviewed and summarized in the 2010 US DOE Basic Energy Sciences sponsored workshop on Compact Light Sources [279]. This workshop examined the readiness of state of the art technology for compact light sources (including so-called 'inverse Compton scattering sources') including assessing cost-effectiveness, user access, availability, and reliability. The report also compared the performance of compact light sources to the third-generation storage rings and FELs. While the details can be found in the report, we will briefly describe and give updates to the two areas of technological development that can impact the development of Compton CGSs in the future.

5.2.1.1. Compton x-ray sources.

5.2.1.2. Laser-plasma accelerator based Compton sources.

5.2.1.3. New developments.

5.2.2.1. Electron storage rings.

5.2.2.2. Superconducting linacs.

Various optical systems have been used to increase the available laser beam intensity in Compton scattering experiments. Firstly, 'recirculator' systems [350] have demonstrated effective laser beam energy gains with an enhancement factor between 8 [284] and 20 [351] (an enhancement factor of about 30 is foreseen in reference [352]). Secondly, a FP cavity (optical resonator), a well-known optical device [353–355], can provide gain in excess of 10³. We shall concentrate here on 'external cavities' which are filled by external laser beams (i.e., not FELs). These devices can also act as circular [356] or linear polarization filters [357, 358] by geometrical or coating designs. Optical path length inside optical resonators ranges between micrometers up to 30 m [359]. This latter number sets a reasonable minimum laser pulse repetition rate at about 10 MHz, making FP cavity especially useful for CW electron beams (i.e., in a storage ring or superconducting linac). Nevertheless, it has recently been demonstrated at KEK [360] that FP cavity operated in a 'burst mode' [360] can also be used advantageously with a warm linac. In these devices, laser oscillators must be tightly locked to the resonator round-trip length. Highly efficient feedback methods are indeed well known [361] and have been extended to mode lock regime [362–365].

FP cavities using either two mirrors or four mirrors are of particular interest to achieve high gains. Two-mirror high-finesse (F ∼ 30 000) cavities operating with CW Nd:YAG oscillators have been used successfully for Compton polarimeters [366, 367] and Compton laser wire [368]. Moderate average power (few kW) has been routinely obtained with these cavities. However, two mirror cavities cannot provide stability and very strong focusing simultaneously. In addition, the cavity length tuning required for timing synchronization with the electron beam is not independent of the beam focus tuning. A good alternative is four-mirror cavities. They provide at the same time stability, strong focusing and an independent tuning of the cavity length and beam focusing. A main drawback with a four-mirror cavity is that the cavity modes are elliptical.

In the pulsed regime, the following state-of-the-art FP cavity performance has been obtained with table-top systems:

• High average power: about 700 kW (10 ps laser pulses) with a Yb-doped oscillator and a laser amplifier delivering more than 400 W [369].
• High finesse: a finesse of approximately 30 000 (power enhancement factor of 10 000) using a low power Ti:sapphire (3 ps laser pulses) oscillator [370].

Combining high average power and high finesse is presently under investigation in the context of compact Compton x-ray sources. Various optical cavities have already been implemented with an electron storage ring, a linac and ERL at KEK. For instance:

• Non-planar four-mirror cavity (178.5 MHz) filled by a 10–20 W Yb-doped, picosecond oscillator/fiber–amplifier system [371]. Up to 50 kW stored power was obtained routinely [372].
• Planar four-mirror cavities (357 MHz and 162.5 MHz) filled by a Nd-doped, picosecond oscillator/burst-amplifier systems [373, 374].

A four-mirror cavity with 70 kW stored power (with Nd-doped 65 MHz oscillator) is also routinely operated in a commercial Compact x-ray source [289].

From the above results, up to ∼100 kW average power in picosecond regime can be obtained by careful choice of the mirror substrates/coatings [369] and careful mechanical design. Low noise oscillators recently available enable the use of a high-finesse cavity in order to reduce the cost of high average power laser amplifiers. Eventually, to avoid mirror damage and to optimize the laser beam shape at the Compton IP, various cavity geometry and boundary shapes have been proposed [375–379].

Compared to a compact, high-power FP cavity driven by a multiple MHz external laser, a larger-scale and more complex FEL oscillator remains an attractive option as the photon beam drive for a high energy CGS because of its demonstrated extraordinary versatility in many areas. The oscillator FEL is well-known for its wavelength flexibility (e.g., the Duke storage ring FEL can be operated from 2.1 μm to 188 nm). More recently, the storage ring FEL has been developed to demonstrate several new capabilities which can have an important impact for a CGS, including simultaneous two-color lasing [380, 381] and the use of an 'optics-free' method to rapidly control and manipulate the laser beam (and γ-ray beam) polarization with an unprecedented level of precision [269, 382].

The required γ-ray beam performance at higher energies (table 11) can be realized with a storage ring based Compton CGS by colliding a GeV electron beam with a high-repetition laser beam (tens of MHz) inside a FP cavity with modest intracavity power. One possible design of such storage rings is shown in figure 35 with related machine parameters listed. This 200 m-long racetrack storage ring is comprised of two multi-bend achromatic arcs with a small emittance and a reasonably large dynamic aperture for the electron beam injection using conventional kickers. The performance projection of such a Compton CGS is provided below for a cross-angle collision configuration (θ = 6°).

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The storage ring should be developed to operate in a wide range of energies using specialized equipment with a large dynamic range of stability and reliability, including power supplies, magnets, kickers, beam diagnostics, etc [264, 383]. The flux performance of this medium energy CGS will be limited by the electron loss rate. To produce a medium energy γ-ray beam, a significant amount of energy is transferred from an electron to the photon, causing the electron to be lost outside the energy acceptance of the storage ring. In this electron-loss mode, the γ-ray flux will be limited by the electron injection rate into the storage ring. Instead of pushing the emittance limit, this storage ring should be optimized to store substantial beam currents and to allow flexible injection.

Energy range: γ rays in a wide energy range can be produced from 25 MeV to about 400 MeV (see the table in figure 36). This can be done by operating the storage ring at energies between 1.2 and 3.5 GeV, and by using one or more FP cavities at a few selected wavelengths between 1550 nm and 517 nm.

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Flux performance: the flux requirements in table 11 can be realized readily. A γ-ray beam with a total flux of about 3.4 × 10¹¹ γ/s (in the 4π solid angle) can be produced in a wide energy range. For example, a 350 MeV γ-ray beam of this intensity with a 95.4 MHz repetition rate can be produced using a 500 mA electron beam (3.27 GeV) and a modest 20 kW laser power inside a 517 nm FP cavity (see the detailed beam parameters in the table in figure 36). The corresponding collimated flux for a beam with an FWHM energy resolution of 2% is about 9 × 10⁹ γ/s. For those experiments requiring a lower repetition rate, 6 out of 64 rf buckets can be filled with the same bunch charge to produce a roughly 9.5 MHz beam with a collimated flux of about 8 × 10⁸ γ/s, and higher flux is possible by increasing the bunch charge. Furthermore, by increasing the intracavity laser power to 100 kW to match the capability of a high charge, high repetition rate booster injector (32 nC/cycle, 10 Hz), the total γ-ray flux can be increased to about 2 × 10¹² γ/s. Ultimately, the γ-ray flux for this medium energy CGS will be limited by the electron injection rate, not by the laser power in the FP cavity or the stored beam current in the storage ring.

Electron beam: to achieve a high average current, the electron beam will be stored in multiple bunches. The bunch pattern should be selectable as demanded for specific user experiments for either high flux operation at a high repetition rate, or a modest flux operation at a lower rate.

Laser beam: the FP cavity will be powered by a commercial laser (fiber or solid state) operated at tens to hundreds of MHz repetition rate with a picosecond pulse duration. The commonly available wavelengths are around 1064 and 1550 nm; their 2nd and/or 3rd harmonics can also be used with a lower power.

FP cavity and collision scheme: for this medium energy CGS, the required intracavity laser power is rather modest, reducing the need to push the FP cavity power limit. Both head-on collision and small cross-angle collision can be arranged using either a two-mirror or four-mirror cavity. The entire γ-ray energy range can be covered using one FP cavity specially designed to build up the laser power at both the fundamental wavelength at 1550 nm and its third harmonic at 517 nm (see the table in figure 36). To cover a wide intermediate energy range (from 30 to 200 MeV), a 1064 nm FP cavity is well suited and highly practical because the FP cavity technology at 1064 nm is well established and more mature than that for 1550 nm.

Energy resolution: the required γ-ray beam energy resolution (1.5%–2%, FWHM) can be met by using a narrow-band laser beam, and an electron beam with a small energy spread and reasonably small transverse emittance [384, 385]. The electron beam performance is readily achievable using the state-of-the-art storage ring magnetic optics design, taking advantage of recent advances in developing low-emittance storage ring based synchrotron radiation sources [386, 387].

Beam polarization: a well-collimated Compton γ-ray beam driven by a polarized laser beam can have a very high degree of polarization, either linear or circular. The relatively slow polarization manipulation (up to 10 Hz), switching between two polarization states (the horizontal and vertical, or left and right circular), can be realized using conventional polarizing optics (including Pockels cells) outside the FP cavity where the laser power is much lower.

Production modes: the medium energy CGS is likely to be operated as a single- or few-user facility. Several Compton sources can be installed in one or more straight sections as shown in figure 37. When operated simultaneously, the sum of γ-ray flux from all sources will be limited by the electron injection rate. For each CGS, a dedicated user target room with proper shielding and a beam dump should be constructed. Multiple target rooms are desirable as complex medium energy experiments will need a dedicated staging area to develop, test, and integrate experimental equipment while the other target room(s) is/are being used for production data-taking.

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Several challenges and important issues for this medium energy source are summarized here:

• Electron injection rate : the cost-effective choice for the injection is a full-energy, top-off booster injector. The booster injector needs to be designed to achieve high reliability, a fast injection cycle (up to 10 Hz), and a large average injection rate (few 10¹¹ to few 10¹² e⁻/s).
• Dual wavelength FP cavity : a dual wavelength FP cavity system will need to be developed to operate at both 1550 nm and 517 nm (the 3rd harmonic). The cavity mirrors should have very high reflectivity at both wavelengths. A new type of optical bench with additional third-harmonic generation optics, two sets of laser optics, feedbacks, and diagnostics for both wavelengths should be developed and then integrated with a shared FP cavity.
• Low beam background : to reduce the high energy radiation background, a short interaction region can be arranged to fully separate the γ-ray beam from the residual gas bremsstrahlung radiation, with two possible schemes illustrated in figure 35. This, together with ultra-high vacuum realized in advanced storage rings [388], will reduce the radiation background by at least two orders of magnitude compared to the already very low background achieved at the HIGS facility.

The following is a prioritized list of important R&D topics for such a medium-energy CGS:

• High priority
  • To develop a dual-wavelength high-finesse FP-cavity for 1550 nm and 517 nm;
  • To design a reliable injector for single- and multi-bunch injection with high charge;
• Medium priority
  • To design an energy-varying storage ring with small emittance and large dynamic aperture;
  • To design a specialized interaction region with ultra-high vacuum either in an arc section or in a chicane to minimize radiation background;
  • To develop laser beam optics for polarization switch (circular and linear), and for dual-wavelength operation;
  • To design radiation shielding to handle high local electron loss.

The required γ-ray beam performance at lower energies (table 12) can be realized with a storage ring based Compton CGS using a low energy electron beam (100s of MeV) and multiple high power FP cavities. One possible design of such storage rings is shown in figure 37 with related machine design parameters listed. This 60 m-long storage ring is comprised of four five-bend achromatic arcs with a small emittance and a reasonably large dynamic aperture.

For this low energy storage ring design, the intrabeam scattering (IBS) effect needs to be properly controlled/mitigated. IBS is a process in which lossless collisions between electrons in the same bunch lead to an increase of the electron beam distribution in all three dimensions, which will result in the transverse beam size growth, especially for low energy and small-emittance storage rings. Because of a strong IBS effect, there is no need to push the low emittance limit. One such an example storage ring design is shown in figure 37. At 500 MeV, this ring has a horizontal natural emittance about 3.4 nm rad and the IBS effect increases the beam emittance to about 7.5 nm rad with 1000 mA beam current in 24 bunches, and with the help of a third harmonic rf cavity. The third-order harmonic cavity is used to lengthen the electron bunch by a factor of three in order to increase the beam lifetime which is mainly limited by large angle electron–electron collisions (the so-called Touschek effect). A more complete design of a low energy storage ring based CGS with a modest intracavity power (20 kW) can be found in [389].

Energy range: this storage ring based Compton source is a versatile gamma-ray factory. It can produce γ rays in a wide range of energies from 1.5 to about 30 MeV (see the table in figure 38). This is done by changing the electron beam energy from 350 to 750 MeV, and by using FP cavities driven by commercial lasers at multiple wavelengths.

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Flux performance: at the low energy end, the γ-ray flux is determined by the electron beam current stored in the storage ring, intracavity laser power, and collision configuration. Below 5 to 8 MeV, very high flux performance is available using a high power FP cavity driven by lasers operating at their fundamental wavelengths (e.g. 1064 or 1550 nm). For example, for production of 4.4 MeV γ rays in a small cross-angle collision configuration (θ = 6°) using a 1000 mA, 500 MeV electron beam and a 100 kW laser beam inside a 1064 nm FP cavity, the total γ-ray flux is estimated to be 2.2 × 10¹² γ/s, and the corresponding flux on target with 2% energy resolution (FWHM) is about 6.5 × 10¹⁰ γ/s (see a list of consistent operational parameters in the table in figure 38). Using the same electron and laser beam parameters, the total flux can be increased to 2–3 × 10¹³ γ/s, assuming head-on collision can be realized. Between 15 and 30 MeV using an FP cavity driven by either a 2nd or 3rd harmonic laser beam, the CGS will be operated in the electron-loss mode, producing a lower total flux, on the order of few 10¹¹ γ/s as limited by the electron injection rate. Between 5 and 15 MeV, the total γ-ray flux will range from few 10¹¹ to few 10¹² γ/s (or higher), determined by specific choices of operational parameters.

Electron beam: to achieve a high average current, the electron beam will be stored in multiple bunches, typically with a vacuum clearing gap. This gap in the γ-ray beam can be used as the start of the time trigger for many experiments. In the example storage ring (figure 37), when fully filled, the electron bunch rate is 122 MHz.

Laser beam: the FP cavities will be powered by commercial MHz lasers (fiber or solid state) with commonly available wavelengths around 1064 and 1550 nm. The 2nd and/or 3rd harmonic laser beam can also be used. The lasers with high average power and excellent beam quality will be essential for achieving high flux.

FP cavity and collision scheme: both head-on collision and small cross-angle collision can be arranged. For the head-on collision, a simple and compact two-mirror cavity can be used; it may be possible to install such a cavity in an arc section between two adjacent dipole magnets as shown in figure 37. For the cross-angle collision, a four-mirror cavity can be implemented in a dedicated straight section.

Energy resolution: a beam energy resolution of about 2% (FWHM) can be readily realized by properly collimating the γ-ray beam. To achieve higher resolution (⩽1%), a narrow-band drive laser will be required and the resolution impact due to the electron beam energy spread and angular spread should be minimized.

Beam polarization: highly polarized, well-collimated Compton γ-ray beams can be produced using a polarized drive laser beam. For certain experiments requiring helicity switch (as fast as 50 Hz), polarizing optics (including Pockels cells) can be utilized outside the FP cavity.

Production modes: like a storage ring based synchrotron radiation user facility, this low energy gamma-ray factory can be operated as a multiple user facility with several γ-ray beamlines. As shown in figure 37, several Compton sources can be installed in straight sections and arc sections. For each source, a dedicated user target room with proper shielding and a beam dump will be constructed. The gamma-ray facility can be operated in the single- or multi-user mode. In the single-user mode, the experiment on the floor can take full control of the γ-ray beam production, including having the ability to change both electron beam current and energy. In the multi-user mode, all CGSs share the electron beam, therefore, individual beamlines do not have the control of the electron beam current and energy. Beamlines can be developed with the independent energy tuning capability—this can be realized by constructing a special FP cavity which allows variation of the collision angle. It is worth pointing out that the flux will be reduced as the collision angle is increased. This gamma-ray factory provides a full energy coverage (1.5–30 MeV) by operating multiple beamlines using lasers of several different wavelengths and by running the storage ring at a few pre-determined energies.

Several challenges and important issues for this low energy source are summarized here:

• High power FP cavity design : the main challenge for this low energy source is to develop a very high power FP cavity (⩾100 kW) operating at 50 to 200 MHz with a very small beam size at the collision point (radius ∼ 40 μm or smaller). The smallest beam size practically realizable will be limited by the high intracavity power.
• Dual wavelength FP cavity : any CGS on this storage ring can greatly expand its energy coverage by using a dual-wavelength FP cavity (e.g. at both 1550 nm and 517 nm).
• Electron injection rate : there are two viable choices for the injector: (1) a low-cost, full-energy, top-off booster injector; and (2) a full-energy room-temperature linac injector at a higher cost. At low energies, the γ-ray flux is not limited by the injection rate. At higher energies in the electron-loss mode, the γ-ray flux will be limited by the electron injection rate.

The following is a prioritized list of important R&D topics for such a low energy CGS:

• High priority
  • To develop a very high power FP cavity (⩾100 kW) with a small beam size (⩽40 μm);
  • To develop a dual-wavelength high-finesse FP-cavity (e.g. 1550/517 nm);
• Medium priority
  • To design an energy-varying storage ring with small emittance and large dynamic aperture;
  • To design a specialized interaction region with ultra-high vacuum either in an arc section or in a chicane to minimize radiation background;
  • To develop laser beam optics for fast polarization switch (circular and linear), and for dual-wavelength operation;
  • To design radiation shielding to handle large local electron loss.

The required γ-ray beam performance at lower energies (table 12) can also be realized with a Compton CGS based on an ERL and one or more FP laser cavities. One possible design of such gamma source is shown in figure 39 with related machine parameters listed. This ERL is comprised of a double-sided linac with two-pass recirculation loop and an additional loop for γ-ray beam generation.

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The key components of ERL are similar to the compact ERL [288], in which generation of a narrow-band Compton scattered beam was recently demonstrated. The main linac and the injector linac are both L-band (1.3 GHz) superconducting structures. The electron gun is a high-voltage (500 kV) DC gun with a multi-alkali photocathode, which can generate a small-emittance beam, ɛ_n ⩽ 1 mm mrad, at a bunch charge of 200–300 pC [390].

Flux performance: the performance of an ERL with an electron beam energy of 500 MeV and a laser wavelength of 1064 nm is shown in a table (see figure 40).

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Energy range: a wide γ-ray energy range can be achieved by changing the electron energy and laser wavelength (1064 nm and 532 nm). In this design, the electron beam energy is varied from 100 to 750 MeV to cover γ-ray energies from 0.18 to 20 MeV. An electron beam below 370 MeV can be delivered by bending the beam out after a single turn or single linac to simplify operation.

Laser beam: because the energy range of the ERL is large, the laser system does not need to adjust to wavelengths longer than 1064 nm. To get to higher γ-ray energies it will be necessary to frequency-double the laser light to 532 nm using an LBO crystal.

FP cavity and collision scheme: two types of FP cavities can be used for the γ-ray generation with a head-on or small cross-angle configuration as shown in figure 39. In order to stack laser pulses synchronizing with the electron bunch, the cavity frequency should be equal to the bunch repetition rate (81.25 MHz) or its sub-harmonic. Parameters of laser beam and expected γ-ray flux are summarized in a table (part of figure 40). The flux requirement, 10¹³ γ/s, can be obtained with head-on collision, and an intra-cavity laser power of 70 kW with a tight laser focus at IP (beam size ∼ 15 μm). Separate cavities are needed for 1064 nm and 532 nm operation due to the need for very high reflectivity in the cavity.

Energy resolution: the ERL provides excellent beam quality so that the energy resolution is determined by the angular acceptance of the γ-ray beam collimation aperture. The high brightness of the electron beam allows a very small electron beam size even for a small beta function of 5–10 cm while still providing a small angular spread. The rms energy spread is typically much less than 10⁻³. The laser must be as narrow band as possible. A γ-ray beam energy spread of 1%–2% (FWHM) should be easily attainable.

Beam polarization: the γ-ray beam polarization is determined by the laser system. As with the storage ring design, polarization changes at a 50 Hz rate are attainable.

Production modes: an operation of low repetition rate, 10 MHz or less, is possible by simply reducing electron bunch repetition or reducing the collision rate with a kicker magnet at the expense of total flux. Multiple collision points can be placed in the recirculation loop. Since the collision rate is small enough (10⁻⁴ for this design), electron beam degradation due to multiple collisions is negligible. As in the case of storage ring sources, simultaneous experiments will be possible at some fixed γ-ray energies unless a tunable laser or variable angle system is developed.

The proposed CGS can be realized with existing technologies in principle. Technical risks remaining to be resolved are summarized as follows:

Electron source performance: a photocathode used for the generation of small-emittance electron beams has a limited life time. The Cornell injector demonstrated extraction of a 40 mA beam for 4 h without significant reduction of quantum efficiency [391] and, using the same gun design, the LEReC project [345] at Brookhaven National Laboratory demonstrated multi-day operation at 30 mA. The required emittance from the injector has been demonstrated [390]. Operation of an 8 mA, 115 MeV ERL was demonstrated at JLab [392] and a proof-of-principle experiment of ERL-based Compton source was conducted at the compact ERL [288].

High current linac operation: the accelerator modules for this design will see up to 80 mA in total with accelerating and decelerating beams. This much current will produce copious higher order modes (HOMs) that must be heavily damped. L-band cryomodules for high-current beams have been designed and fabricated at Cornell and KEK [393, 394].

FP cavity performance: a FP cavity was developed at Lyncean Technologies to store laser power of 70 kW with a beam waist of 40 μm [289] and a cavity at the cERL was 10 kW with 24 μm (horizontal) and 32 μm (vertical) spot sizes [288]. In addition, a cavity was developed for non-accelerator environment at Max-Planck Institute to store laser power of 670 kW with a reported rms beam size of 13 μm × 17 μm at focus [369]. A FP cavity to store intra-cavity laser power of 70 kW with a beam waist of 15 μm must be proven. Such a cavity requires state-of-the-art low-loss mirror coatings and thermally stable mirror substrates.

Preservation of injector beam quality: though the Cornell injector has demonstrated excellent performance, it is necessary to preserve this beam quality through a large number of long beam transport arcs. Each of these is subject to wakefields, longitudinal space charge (LSC) forces, and coherent synchrotron radiation (CSR) induced emittance growth. Designs have been developed to minimize any increase in the transverse emittance in an isochronous arc. The emittance growth can be kept to very small levels. A more serious problem is the longitudinal phase space distortion leading to a growth in the projected energy spread. Some of this may be compensated by rf cavities. A harmonic rf cavity might be required to take out higher-order curvature.

Operational issues: some of the scattered electrons may be lost when operating at very high photon energy. These losses must be controlled and understood. The levels of loss look tolerable and many electrons will still be energy-recovered but it is important to control where the electrons are lost. Continuous energy tuning in ERLs has not been demonstrated, yet. Sophisticated algorithms must be developed to tune up the beam transport at a new energy as the energy is changed.

We recommend to conduct the following R&D items:

• High priority
  • Laser stacker at 1064 nm and 532 nm to verify the power, beam size, and intensity at the IP;
  • Endurance runs with CsKSb cathodes at 20 mA;
  • Lattice designs for ERL with CGS with CSR and LSC compensation.
• Medium priority
  • Beam breakup and HOM loading simulations for ERL with CGS (e.g. Cornell and KEK modules);
  • Diagnostic development for high current beams and backscattering setup.