Table of contents

The symmetry energy describes how the energy of nuclear matter rises as one goes away from equal numbers of neutrons and protons. This is very important to describe neutron rich matter in astrophysics. This article reviews our knowledge of the symmetry energy from theoretical calculations, nuclear structure measurements, heavy-ion collisions, and astronomical observations. We then present a roadmap to make progress in areas of relevance to the symmetry energy that promotes collaboration between the astrophysics and the nuclear physics communities.

This paper addresses the critical importance of an unambiguous separation of the different components of the total fusion cross-section, which is a great theoretical and experimental challenge, in order to make further progress in the field of low-energy fusion of weakly bound nuclei. Recent theoretical developments in this area are reviewed. Calculations based on a classical dynamical reaction model indicate that the contribution of sequential fusion to the complete fusion cross-section is very substantial. A toy quantum model is presented, which introduces position projection operators. These can be useful for a quantitative understanding of complete and incomplete fusion of weakly bound nuclei within a more realistic quantum model.

The open issues in the development of models for the breakup of exotic nuclei and the link with the extraction of structure information from experimental data are reviewed. The question of the improvement of the description of exotic nuclei within reaction models is approached in the perspective of previous analyses of the sensitivity of these models to that description. Future developments of reaction models are suggested, such as the inclusion of various channels within one model. The search for new reaction observables that can emphasize more details of exotic nuclear structure is also proposed.

Compound-nuclear processes play an important role for nuclear physics applications and are crucial for our understanding of the nuclear many-body problem. Despite intensive interest in this area, some of the available theoretical developments have not yet been fully tested and implemented. We revisit the general theory of compound-nuclear reactions, discuss descriptions of pre-equilibrium reactions, and consider extensions that are needed in order to get cross section information from indirect measurements.

The application of momentum-space three- and four-body scattering equations to the description of nuclear reactions involving systems of three and four nucleons is reviewed, and major achievements and challenges are identified. The calculations include realistic state-of-the-art interactions between nucleon pairs, together with the Coulomb interaction between protons. The effect of including three- and four-nucleon forces is discussed. Further calculations are shown involving the study of nuclear reactions where three-body degrees of freedom play a significant role. These studies involve not just an attempt to describe data in terms of a full three-body model that is solved numerically in a converged way, but also to use this exact framework to validade and test the accuracy of approximate reaction methods such as continuum discretized coupled channel (CDCC), distorted wave impulse approximation (DWIA), plane-wave impulse approximation (PWIA) and the Glauber multiple scattering approach. These comparisons are able to teach researchers under which conditions approximate methods can be used to extract important structural information about exotic nuclei. Prospects and challenges are discussed.

We outline how three-body models of the reaction A(d, p)B can be related to the underlying many-body problem and discuss the problems involved in making a precise connection. Various approximate methods for taking into account coupling to deuteron break-up channels are discussed and a practical way of correcting the adiabatic approximation is outlined. We emphasize issues that relate to the use of the A(d, p)B reaction as a tool for nuclear structure studies.

A relativistic formulation of reaction theory for nuclei with a dynamics given by a unitary representation of the Poincaré group is developed. Relativistic dynamics is introduced by starting from a relativistic theory of free particles to which rotationally invariant interactions are added to the invariant mass operator. Poincaré invariance is realized by requiring that simultaneous eigenstates of the mass and spin transform as irreducible representations of the Poincaré group. A relativistic formulation of scattering theory is presented and approximations emphasizing dominant degrees of freedom that preserve unitarity, exact Poincaré invariance and exchange symmetry are discussed. A Poincaré invariant formulation of a (d,p) reaction as a three-body problem is given as an explicit example.

Important efforts have been dedicated in the past few years to describe near-barrier heavy-ion collisions with microscopic quantum theories like the time-dependent Hartree–Fock approach and some of its extensions. However, this field is still facing important challenges such as the description of cluster dynamics, the prediction of fragment characteristics in damped collisions, and sub-barrier fusion by quantum tunnelling. These challenges are discussed and possible approaches to solve them are presented.

The overlap functions between the nuclear wave functions in initial and final states are important structural quantities that enter the amplitudes of nuclear reactions such as transfer, knockout and radiative capture. They carry information about the single-particle structure and about the nucleon–nucleon interactions and correlations in atomic nuclei. The current status of knowledge of overlap functions is reviewed with an emphasis on their theoretical calculation. The open problems associated with their prediction are highlighted and challenges are discussed.

Detailed theories of nuclear reactions now lead to and require extensive computations. Only then can their results be used to make verifiable predictions and to contribute to the development of nuclear physics. I focus on low-energy reactions of nucleons and light clusters on heavier nuclei, and discuss the computational challenges in the evaluation of coupled-channel theories of those reactions.

Problems in applying random-matrix theory (RMT) to nuclear reactions arise in two domains. To justify the approach, statistical properties of isolated resonances observed experimentally must agree with RMT predictions. That agreement is less striking than would be desirable. In the implementation of the approach, the range of theoretically predicted observables is too narrow.

We discuss the application of the chiral N³LO forces to three-nucleon reactions and point to the challenges which will have to be addressed. Present approaches to solve three-nucleon Faddeev equations are based on a partial-wave decomposition. A rapid increase of the number of terms contributing to the chiral three-nucleon force when increasing the order of the chiral expansion from N²LO to N³LO forced us to develop a fast and effective method of automatized partial-wave decomposition. At low energies of the incoming nucleon below ≈20 MeV, where only a limited number of partial waves is required, this method allowed us to perform calculations of reactions in the three-nucleon continuum using N³LO two- and three-nucleon forces. It turns out that inclusion of consistent chiral interactions, with relativistic 1/m corrections and short-range 2π-contact term omitted in the N³LO three-nucleon force, does not explain the long standing low energy A_y-puzzle. We discuss problems arising when chiral forces are applied at higher energies, where large three-nucleon force effects are expected. It seems plausible that at higher energies, due to a rapid increase of a number of partial waves required to reach convergent results, a three-dimensional formulation of the Faddeev equations which avoids partial-wave decomposition is desirable.

A new non relativistic quark model to calculate the spectrum of heavy quark mesons is developed. The model is based on an interquark potential interaction that implicitly incorporates screening effects from meson-meson configurations. An analysis of the bottomonium spectrum shows the appearance of extra states as compared to conventional non screened potential models.

We update our estimate of the cross section for Higgs production in gluon fusion at next-to-next-to-next-to-leading order in ${{\alpha }_{s}}$ in view of the recent full computation of the result in the soft limit for infinite top mass, which determines a previously unknown constant. We briefly discuss the phenomenological implications. Results are available through the updated version of the ggHiggs code.

We substantially refine our previously developed model for the suppression of Υ mesons in the quark–gluon plasma formed in 2.76 TeV PbPb collisions at the LHC. It accounts for gluodissociation of the six bottomium states Υ(ns), ${{\chi }_{b}}(nP)$ with $n=1,2,3$, collisional damping of these states as described in a complex potential, screening of the real part of the potential, and the subsequent decay cascade. In the hydrodynamical calculation of the expanding fireball, we take into account the effect of transverse expansion on the suppression factors, and finite transverse momenta of the heavy mesons in the medium. The running of the coupling is considered, resulting in larger gluodissociation decay widths. The initial central temperature is found to be 550 MeV at 0.1 fm/c. Our results are in good agreement with recent centrality-dependent CMS and ALICE data. The calculated suppression of the excited states relative to the ground state Υ(1S) is not strong enough in peripheral collisions. Additional mechanisms are discussed. Predictions for 5.52 TeV are made.

A joint effort of cryogenic microcalorimetry (CM) and high-precision Penning-trap mass spectrometry (PT-MS) in investigating atomic orbital electron capture (EC) can shed light on the possible existence of heavy sterile neutrinos with masses from 0.5 to 100 keV. Sterile neutrinos are expected to perturb the shape of the atomic de-excitation spectrum measured by CM after a capture of the atomic orbital electrons by a nucleus. This effect should be observable in the ratios of the capture probabilities from different orbits. The sensitivity of the ratio values to the contribution of sterile neutrinos strongly depends on how accurately the mass difference between the parent and the daughter nuclides of EC transitions can be measured by, for example, PT-MS. A comparison of such probability ratios in different isotopes of a certain chemical element allows one to exclude many systematic uncertainties, and thus could make feasible a determination of the contribution of sterile neutrinos on a level below 1%. Several electron capture transitions suitable for such measurements are discussed.

We extract the u- and d-quark contributions to the nucleon electromagnetic form factors in a relativistic light-front quark model using unified description of nucleon and Roper electromagnetic properties.

Using transition form factors calculated via light cone QCD sum rules in full theory, we comparatively analyze the rare radiative ${{\Sigma }_{b}}\to \Sigma \gamma$ decay in the standard model (SM) and models with one or two universal extra dimensions, such as beyond the SM scenarios. We estimate the total decay width and branching ratio associated with this decay channel in the SM and compare the obtained results with those of scenarios with one or two universal extra dimensions. We discuss how the results of universal extra dimensional models approach the SM predictions when the compactification factor of extra dimension is increased.

The dependence of the fourth order QCD calculation of the ${{R}_{{{e}^{+}}{{e}^{-}}}}$ ratio on the renormalization scheme is studied with the aim of assessing the physical relevance of the PMS optimized result at low energies.

The reformulated dynamical cluster-decay model (DCM) is applied to study the role of the neck-length parameter for the decay of even-A and α-structured $^{56}{\rm N}{{{\rm i}}^{*}}$ formed in the ${}_{{}}^{32}{\rm S}_{{}}^{{}}+{}_{{}}^{24}{\rm Mg}_{{}}^{{}}$ reaction at ${{E}_{c.m.}}=60.5\;{\rm MeV}$. Experimentally, light particles (LPs, $A\leqslant 4$) emission cross-section and individual fragments (from A = 12 to 28) emission cross-section are measured for this reaction at ${{E}_{{\rm c}.{\rm m}.}}=60.5\;{\rm MeV}$. In the present work, we have reproduced the measured data of LPs emission cross-section and mass spectra of A = 12–28 fragments by varying the neck-length parameter $\vartriangle R$ and the factor ${{\alpha }_{c}}$, which is present in the hydrodynamical mass calculation. From the fitted $\vartriangle R$ values, polynomial relations are obtained for 4n-structured (even and α-fragments, A = 12, 16, 20, 24 and 28), 4n+1-structured odd mass fragments (A = 13, 17, 21, and 25), 4n+2-structured (even and non-α fragments, A = 14, 18, 22, and 26) and 4n+3-structured odd mass fragments (A = 15, 19, 23 and 27). Experimentally, there is no data for fragments A = 5–11 emission cross-section. In order to account for the cross-section information about these fragments, we have extrapolated the $\vartriangle R$ values for these fragments with the use of fitted polynomial relations. To fit the calculated LPs emission cross section with the measured data, we kept $\vartriangle R$ values of fragments A = 5–28 and tuned the $\vartriangle R$ value of LPs alone. The fitted $\vartriangle R$ value of LPs is as 1.3146 fm. With the use of fitted $\vartriangle R$ values of fragments A = 1–4 and A = 12–28 and extrapolated $\vartriangle R$ values of fragments A = 5–11, our calculated overall cross-section values of the LPs emission and individual fragments (A = 12–28) emission cross-section are found to be in better agreement with the experimental data.

In the real-time thermal field theory, the pion self-energy at finite temperature and density is evaluated where the different mesonic and baryonic loops are considered. The interactions of pion with the other mesons and baryons in the medium are governed by the effective hadronic Lagrangian densities whose effective strength of coupling constants have been determined from the experimental decay widths of the mesons and baryons. The detail branch cut structures of these different mesonic and baryonic loops are analyzed. The Landau cut contributions of different baryon and meson loops become only relevant around the pion pole and it is completely appeared in presence of medium. The in-medium spectral function of pion has been plotted for different values of temperature, baryon chemical potential as well as three momentum of the pion. A noticeable low mass probability in pion spectral function promise to contribute in the low mass dilepton enhancement via indirect modification of ρ self-energy for $\pi \pi$ loop.

We use a diagrammatic method to derive the Faddeev equations of the coupled NΛΛ–ΞNN system and apply them to the bound-state problem of the $(I,{{J}^{P}})=(\frac{1}{2},{{\frac{1}{2}}^{+}})$ channel. We use as input the nucleon–nucleon, nucleon–hyperon and hyperon–hyperon interactions obtained from a chiral constituent quark model. We explore different parametrizations of the quark–quark interacting potential. While the $N\Lambda \Lambda$ system alone is unbound, the full coupled channel problem NΛΛ–ΞNN may present a three-baryon bound state just below threshold. Different from double-$\Lambda$ hypernuclei with four nucleons or more, where the Pauli principle acts strongly because there is no room for more that four nucleons in S wave, in $_{\Lambda \Lambda }^{3}$H the full $N\Xi$ interaction can act in S wave.

The theoretical procedure of supersymmetric quantum mechanics (SQM) is adopted for the first time to study quasi-bound states of a weakly bound nuclear system using microscopic potential. The density dependent M3Y (DDM3Y) effective interaction was found earlier to give a satisfactory description of radioactivity, nuclear matter and scattering. In the present work, we have microscopically generated a two-body potential in a single folding model using the DDM3Y effective interaction. From this potential, SQM generated a family of isospectral potentials for ¹¹Be (¹⁰Be + n). We investigated the 5/2⁺, 3/2⁻ and 3/2⁺ resonance states of ¹¹Be. The experimental data and the present calculations of excitation energies of the above resonance states are found to be in good agreement.