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The Tenth International Spring Seminar on Nuclear Physics was held in Vietri sul Mare from May 21 to May 25, 2010. This Seminar was the tenth in a series of topical meetings held every two or three years in the Naples area. The series began with the Sorrento meeting in 1986 and continued with the Capri meeting in 1988, the Ischia meeting in 1990, the Amalfi meeting in 1992, the Ravello meeting in 1995, the S. Agata meeting in 1998, the Maiori meeting in 2001, the Paestum meeting in 2004, and the Vico Equense meeting in 2007.

For this tenth meeting we returned to Salerno Bay and met in the small town of Vietri. While the location of the Conference has never been the same, what remained invariant is the aim of these meetings, which is to discuss recent advances and new perspectives in nuclear structure experiments and theory in a pleasant and friendly atmosphere.

It is by now well established that we have entered a new era in Nuclear Physics research with the advent of radioactive ion beam facilities. While nuclear structure studies are currently being performed in several laboratories where RIBs are available, the development of new facilities, which will provide high-intensity beams, is in progress or under discussion in Europe, Asia and North America. At this meeting we had a comprehensive overview of this fascinating field and of future scenarios thanks to the participation of leaders of the most important projects.

The results that are becoming available for nuclei far from stability are highlighting new themes of research, such as the evolution of the shell structure when moving towards the particle drip lines, and stimulating a proficuous interplay between experiment and theory. On the other hand, new ideas and the development of more powerful computational tools promise a deeper understanding of the structure of nuclei in terms of the basic interactions between their constituents.

As usual, the program of the meeting consisted of general talks and of more specialized seminars, the latter including most of the contributions submitted by participants. The speakers covered five main topics: i) Nuclear Structure far from Stability: New Advances and Perspectives; ii) From Nuclear Forces to Nuclear Structure; iii) Exploring Nuclear Shell Structure: Experiment and Theory; iv) New Aspects of Collective Nuclear Motion; and v) Special Topics.

We received 63 manuscripts out of the 77 invited papers and contributions presented at the Seminar. All of these have been peer reviewed and are collected in this volume. We would like to thank all the anonymous colleagues who have acted as referees to assess the suitability of the various articles for publication in the Journal of Physics: Conference Series. We are confident that the high quality of both invited and contributed papers contained in these Proceedings will be appreciated by the nuclear physics community.

As was the case for most of the previous Seminars, the Vietri Seminar also ended with a Round Table Discussion on the theme 'Trends and Perspectives in Nuclear Structure'. N Benczer-Koller, B A Brown, A Faessler, B Fornal, O Sorlin, and I Talmi kindly agreed to be on the panel and their remarks were essential in bringing about the active involvement of the audience.

The Conference had about 100 participants from some 20 countries (please see PDF for list of participants). This is well in line with the tradition of these meetings, as is the fact that about 50% of the present participants attended one or more of the previous Seminars.

We gratefully acknowledge the financial support of the Istituto Nazionale di Fisica Nucleare and the University of Naples Federico II who helped make the Seminar possible. We also acknowledge the support provided in various ways by the Dipartimento di Scienze Fisiche which acted as host to the Seminar.

Aldo Covello Angela Gargano Editors

LOCAL ORGANIZING COMMITTEE

A Covello (Chair) A Gargano (Co-Chair) L Coraggio (Scientific Secretary) F Andreozzi N Itaco G La Rana N Lo Iudice A. Porrino

INTERNATIONAL ADVISORY COMMITTEE

SPONSORS OF THE SEMINAR

Dipartimento di Scienze Fisiche, Università di Napoli "Federico II" Istituto Nazionale di Fisica Nucleare Università di Napoli Federico II

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

The surprising variation of the cross sections for the production of the most neutron-rich nuclei by the fragmentation of ⁴⁸Ca and ⁷⁶Ge beams at Michigan State University (MSU) continues to show the importance of determining the properties of exotic nuclei. Future detailed studies of such exotic nuclei are being assured through the establishment of the Facility for Rare Isotope Beams (FRIB), a cutting-edge research facility to advance understanding of rare nuclear isotopes and the evolution of the cosmos, by the US Department of Energy at MSU. The new facility is expected to take something less than a decade to design and build and will provide a broad range of research opportunities for an international community. The facility is based on a superconducting-RF driver linear accelerator that will provide a maximum beam power of 400 kW for all beams ranging from uranium accelerated to 200 MeV/u, to lighter ions with increasing energy, down to protons at 600 MeV/nucleon. Rare isotope beam production at a beam power of 400 kW has never been done and presents a number of large challenges. The heart of the FRIB facility will be a next-generation three-stage projectile fragment separator specifically designed to handle the very intense primary and secondary beams.

The Argonne Tandem Linear Accelerator System (ATLAS) at Argonne National Laboratory (ANL) provides a wide range of stable ion beams and radioactive beams which have contributed to our understanding of nuclear structure and reactions. Until now, most radioactive ion beams at ATLAS were produced in flight using light-ion reactions such as (p, n), (d, n), (d, p), (d,³He), and (³He,n). Within the next few months, the radioactive ion beam program at ATLAS will acquire much extended, new capabilities with the commissioning of a new facility: the CAlifornium Rare Isotope Breeder Upgrade (CARIBU). CARIBU will supply ion beams of ²⁵²Cf fission fragments, which are thermalized in a gas catcher. The singly- and doubly-charged ions extracted from the gas catcher will be mass-separated and either delivered to a low-energy experimental area, or charge bred with a modified ECR source and subsequently reaccelerated by the ATLAS facility. Properties of hundreds of these neutron-rich nuclides will be investigated using ion traps, decay stations, the newly commissioned HELical Orbit Spectrometer (HELIOS), and other available experimental equipment such as Gammasphere and the FMA. HELIOS was constructed to take advantage of rare ion beams, such as those provided by CARIBU, through light-ion transfer reactions in inverse kinematics, and represents a new approach to the study of direct reactions in inverse kinematics which avoids kinematic broadening. Experiments are currently being conducted with HELIOS, and first results with the d(²⁸Si,p) and d(¹²B,p) reactions have shown excellent energy resolution.

The aim of the SPES (Selective Production of Exotic Species) project is to provide high intensity and high-quality beams of neutron-rich nuclei to perform forefront research in nuclear structure, reaction dynamics and interdisciplinary fields like medical, biological and material sciences. SPES is a second generation ISOL radioactive ion beam facility, part of the INFN Road Map for the Nuclear Physics and supported by the italian national laboratories LNL (Legnaro) and LNS (Catania). It represents an intermediate step toward the future generation European ISOL facility EURISOL. It is based on the ISOL method with an UCx Direct Target able to sustain a power of 10 kW. The primary proton beam will be delivered by a Cyclotron accelerator with an energy of more then 40 MeV and a beam current of 200 μA. Neutron-rich radioactive ions will be produced by Uranium fission at an expected fission rate in the target of the order of 10¹³ fissions per second. The exotic isotopes will be re-accelerated by the ALPI superconducting LINAC up to energies of 10-13 AMeV, for masses in the region of A=130 amu, with an expected rate on the secondary target of 10⁸ pps.

Light- and heavy ion beams from the K=130 cyclotron are used to produce nuclei far from stability at the Accelerator Laboratory of the Department of Physics of the University of Jyväskylä(JYFL), Finland. Novel instruments at the target and focal-plane areas of a gas-filled recoil separator for in-beam tagging measurements are available for probing structures of very neutron deficient and very heavy nuclei. Bunched and cooled radioactive beams from the IGISOL system are available for studies of nuclear ground-state properties by employing Penning traps and laser systems. Recent results from measurements at these two facilities are presented. Future plans will also be introduced.

The systematic change of shell structure in both weakly bound and resonant neutron one-particle levels in nuclei towards the neutron drip line is exhibited, solving the coupled equations derived from the Schrödinger equation in coordinate space with the correct asymptotic behaviour of wave functions for r → ∞. The change comes from the behaviour unique in the one-particle motion with low orbital angular momenta compared with that with high orbital angular momenta. The observed deformation of very neutron-rich nuclei with N ⪆ 20 in the island of inversion is a natural result of this changed shell structure, while a possible deformation of neutron-drip-line nuclei with N ≈ 51, which are not yet observed, is suggested.

We study the excitation of low-lying dipole states in very-neutron rich nuclei (so called Pygmy Dipole Resonances). The states are described within the Hartree-Fock plus RPA formalism, using different parametrizations of the Skyrme interaction. We show how the combined information from reaction processes involving the Coulomb and different mixtures of isoscalar and isovector nuclear interactions can provide a clue to reveal the characteristic features of these states.

Radioactive ion beams are produced at INFN- Laboratori Nazionali del Sud (LNS) by means of the two operating accelerators, the Tandem and the Superconducting Cyclotron (CS), originally designed to accelerate stable beams. Both the ISOL (Isotope Separation On Line) and the IFF (In-Flight Fragmentation) methods are exploited to produce RIBs in two different ways at different energies: in the first case, the Cyclotron is the primary accelerator and the Tandem accelerates the secondary beams, while in the second case radioactive fragments are produced by the Cyclotron beam in a thin target with energies comparable to the primary beam energy. The ISOL facility is named EXCYT (Exotics at the Cyclotron and Tandem) and was commissioned in 2006, when the first radioactive beam (⁸Li) has been produced. The IFF installation is named FRIBs (in Flight Radioactive Ion Beams), and it has started to produce radioactive beams in 2001, placing a thin target in the extraction beam line of the Cyclotron. The development of both facilities to produce and accelerate radioactive ion beams at LNS, is briefly described, with some details on the future prospects that are presently under consideration or realization.

The present operation status of the RIKEN Radioactive Ion Beam Factory (RIBF) and recent research highlights are reported. One of the major devices of the RIBF, an electron scattering facility for short-lived nuclei, is described in detail. This facility will open a completely new research field of structure studies of short-lived nuclei.

GANIL presently offers unique opportunities in nuclear physics and in many other fields that arise from not only the provision of low-energy stable beams, fragmentation beams and re-accelerated radioactive species, but also from the availability of a wide range of state-of-the-art spectrometers and instrumentation. A few examples of recent highlights are presented. With the construction of SPIRAL2 over the next few years, GANIL is in a good position to retain its world-leading capability. As selected by the ESFRI committee, the next generation of ISOL facility in Europe is represented by the SPIRAL2 project to be built at GANIL (Caen, France). SPIRAL 2 is based on a high power, CW, superconducting LINAC, delivering 5 mA of deuteron beams at 40MeV (200KW) directed on a C converter+ Uranium target and producing therefore more 10¹³ fissions/s. The expected radioactive beams intensities in the mass range from A=60 to A=140, will surpass by two order of magnitude any existing facilities in the world. These unstable atoms will be available at energies between few KeV/n to 15 MeV/n. The same driver will accelerate high intensity (10μA to 1 mA), heavier ions (Ar up to Xe) at maximum energy of 14 MeV/n. Under the 7FP program of European Union called *Preparatory phase*, the SPIRAL2 project has been granted a budget of about 4M to build up an international consortium around this new venture. The scientific pillars of the future facility, the status of the construction of SPIRAL2 accelerator and associated physics instruments in collaboration with EU and International partners will be presented.

Different Liquid Drop Model mass formulae have been studied. They include a Coulomb diffuseness correction Z²/A term and pairing and shell energies of the Thomas-Fermi model. The influence of the selected charge radius, the curvature energy and different forms of the Wigner term has been investigated. Their coefficients have been determined by a least square fitting procedure to 2027 experimental atomic masses. The different fits lead to a surface energy coefficient of 17-18 MeV. A large equivalent rms radius (r₀ = 1.22 − 1.24 fm) or a shorter central radius may be used. A rms deviation of 0.54 MeV can be reached between the experimental and theoretical masses. The remaining differences come from the determination of the shell and pairing energies. Mass predictions are given for exotic nuclei.

The ⁸Li elastic scattering on ⁴He in inverse kinematics has been studied in order to search for ⁸Li-α cluster configurations in excited states of ¹²B. The experimental technique, the inverse kinematic thick target method (TTIK), involved a ⁸Li beam provided by the EXCYT facility at an initial energy of E_b=30.6 MeV which is continuously degraded down to zero in the passage through a helium extended thick target. After the interaction, the recoil alpha particles were detected by using four ΔE-E silicon detector telescopes. The explored ⁸Li-α centre-of-mass energy ranges from E_CM=2.7 MeV up to E_CM=9.6 MeV. A micro-channel plate, placed before the gas chamber, is used to measure the time interval between the entrance of the ⁸Li into the chamber and the arrival of the recoil alpha particle on the detectors. This "time interval" measurement improves the TTIK technique allowing the discrimination of elastic from inelastic events. In this paper, the experimental technique will be described and the preliminary results for the elastic cross section will be shown.

Elastic scattering and direct reactions have been studied for the collisions induced by the three Beryllium isotopes ^9,10,11Be, on a medium mass ⁶⁴Zn target at energies around the Coulomb barrier. The elastic scattering angular distributions, measured for the three systems at the same center of mass energy, were analyzed within the Optical Model and reaction cross-sections were deduced from optical model calculations. For the ¹¹Be induced reaction the transfer/break-up angular distribution was also extracted.

We present the first steps towards the realization of a novel experimental scheme to measure β-ν correlations in the β decay of ⁶He, for the purpose of Fundamental Interaction studies. Our method is based on a novel use of an ion trapping device, the Electrostatic Ion Beam Trap (EIBT) coupled to a d+t neutron generator. The EIBT which has not been previously considered for Fundamental Interaction studies, exhibits potentially very significant advantages over other state of the art experimental schemes aimed at precision measurements of the β–ν angular correlation coefficient.

In recent years, there has been substantial progress in the derivation of nuclear forces from chiral effective field theory (EFT). Accurate two-nucleon forces have been constructed at next-to-next-to-next-to-leading order (N³LO) and applied (in some cases together with three-nucleon forces at NNLO) to nuclear few and many-body systems—with a fair deal of success. This may suggest that the 80-year old nuclear force problem has finally been cracked. Not so! Some pretty basic issues are still unresolved, like, the proper renormalization of the two-nucleon potential and subleading many-body forces. In this contribution, I will focus on the latter issue.

We have carried out calculations for nuclear matter, neutron stars and finite nuclei using NN potentials with and without the medium-dependent modifications based on the Brown-Rho (BR) scalings. Using the V_low−k low-momentum interactions derived from such potentials, the equations of state (EOS) for symmetric and asymmetric nuclear matter, for densities up to ~ 5ρ₀, are calculated using a RPA method where the particle-particle hole-hole ring diagrams are summed to all orders. The medium effects from both a linear BR scaling (BR₁) and a non-linear one (BR₂) are considered, and they both are essential for our EOSs to reproduce the nuclear matter saturation properties. For densities ρ below ρ₀, results from BR₁ and BR₂ are close to each other. For higher densities, the EOS given by BR₂ is more desirable and is well reproduced by that given by the interaction (V_low−k+TBF) where V_low−k is the unsealed low-momentum interaction and TBF is an empirical Skyrme three-body force. The moment of inertia of neutron stars is ~ 60 and ~ 25M_⊙km² respectively with and without the inclusion of the above BR₂ medium effects. Effects from the BR scaling are important for the long half-life, ~ 5000yrs, of the ¹⁴C − ¹⁴N β-decay.

The No Core Shell Model (NCSM) has been successful in describing the properties of light nuclei, A ≤ 16, starting from the fundamental interactions among the A nucleons, but it is currently difficult to extend the NCSM to heavier nuclei, because of the extremely large model spaces involved in the calculations. We present a new procedure, based on performing two unitary transformations on the Hamiltonian, so as to obtain the core, one-body, two-body and perhaps three-body input necessary for performing Standard Shell Model (SSM) calculations for nuclei. Such SSM calculations can be easily performed for sd- and pf-shell nuclei. We demonstrate the accuracy of our approach by applying to it nuclei within the 0p-shell.

A new method is given for the model-space effective interaction. Introducing a new operator in place of the Q-box in the Krenciglowa-Kuo (KK) method, we derive a new equation for the effective interaction. This equation can be viewed as an extension of the KK method. We show that this equation can be solved both in iterative and non-iterative ways. We observe that the iteration procedure brings about fast acceleration of convergence compared to the KK approach. We also find that the non-iterative calculation reproduces successfully any set of the true eigenvalues of the original Hamiltonian. This non-iterative calculation can be made regardless of the magnitudes of the overlaps with the model space and the energy differences between the unperturbed energy and the eigenvalues to be solved.

I will review several issues related to the nuclear matter equation of state, with particular emphasis on isospin-asymmetric matter. I will stress the importance of pursuing a microscopic approach towards a better understanding of dense and exotic matter.

We report on a shell-model study of Sn isotopes beyond N = 82 employing a realistic effective interaction derived from the CD-Bonn nucleon-nucleon potential renormalized through use of the V_low-k approach. At present, the most exotic Sn isotope for which some experimental information exists is ¹³⁴Sn with an N/Z ratio of 1.68. It is the aim of our study to compare the results of our calculations with the available experimental data and to make predictions for the neighboring heavier isotopes which may be within reach of the next generation of radioactive ion beam facilities. The very good agreement between theory and experiment obtained for ¹³⁴Sn gives confidence in the predictive power of our realistic shell-model calculations.

The tensor force in effective interactions is discussed. We show that the tensor force in low-momentum effective interactions V_lowk and effective interactions for shell model studies are almost identical to that of the bare nucleon-nucleon interaction. We use realistic nuclear forces and microscopic theories of effective interactions. We calculate V_lowk by the technique of similarity transformation. The effective interaction for the nuclear shell model is calculated by folded diagram theory. The monopole contribution from the tensor force is analyzed by a spin-tensor decomposition.

We study the neutron-rich calcium isotopes performing shell-model calculations with a realistic effective interaction. This is derived from the CD-Bonn nucleon-nucleon potential renormalized by way of the V_low–k approach, considering ⁴⁸Ca as an inert core and including the neutron 0_g9/2 orbital. We compare our results with experiment and with the results of a previous study where ⁴⁰Ca was assumed as a closed core and the standard 1p0f model space was employed. The calculated spectroscopic properties are in both cases in very good agreement with the available experimental data and enable a discussion on the role of the g_9/2 single-particle state in the heavy-mass Ca isotopes.

We study the effects of the tensor term of the effective nucleon-nucleon interaction on nuclear excited states. Our investigation has been conducted by using a self-consistent Random Phase Approximation approach. We investigate various nuclei in different regions of the isotopes chart. Results for a set of calcium isotopes are shown.

Over the last few years there has been considerable progress in both experimental facilities and theoretical calculations of magnetic moments of low-lying, short-lived nuclear states. In particular, the competition between collective and single particle excitations in the region around 70 ≤ A ≤ 100 has been examined. Recent data on Pd isotopes are presented. Newly developed techniques are applicable to work with radioactive beams. However, experimental limitations have emerged and will be discussed especially in their relations to the determination of absolute magnetic moments as opposed to relative measurements of moments in chains of isotopes.

The multipole mixing ratios of ΔI = 1 transitions between levels in rotational bands built on single-particle states in odd neutron nuclei are dependent on the configurations of the states. In particular, the mixing ratio can be used to distinguish between several possible single-particle configurations if interpreted with the particle plus axial-rotor model (PRM). This work features the first determination of the ground-state configurations of ^109,111Ru. The single-particle structures of the ground states of ¹⁰¹Zr and ^103,105,107Mo as well as excited states in ^103,107Mo are also investigated, with a new result found in ¹⁰⁷Mo.

A finite rank separable approximation for the quasiparticle random phase approximation with Skyrme interactions is applied to study properties of the Gamow-Teller resonances and the spin-dipole resonances in some spherical nuclei. It is shown that characteristics calculated within the suggested approach are in a good agreement with available experimental data.

A matrix diagonalization algorithm we developed in the past years has been revised and implemented for large scale shell model calculations using a spin uncoupled basis so as to obtain a sparse Hamiltonian matrix. The dimensions of such a matrix are reduced drastically by a procedure that combines an effective projection of the good angular momentum with an importance sampling specific of the method. Its numerical implementation on ¹¹⁶Sn illustrates the simplicity of the method and the fast convergence of the iterative procedure.

For over four decades, the Skyrme functional within various parametrizations has been used to calculate nuclear properties. In the last few years there was a number of attempts to improve its performance and introduce generalized forms. In particular, the most general phenomenological quasi-local energy density functional, which contains all combinations of density, spin-density, and their derivatives up to the sixth order (N³LO), was proposed in [1]. Since in the phenomenological-functional approaches, the particle-particle (pp) channel is treated independently of the particle-hole (ph) channel, there remains a question of what pairing interaction is suitable to use within the N³LO energy functional. In the present study, we use the separable, finite-range, translationally invariant interaction given in [2] and we present the first test-case application of this pairing interaction within the code HOSPHE that is able to treat the N³LO energy density functional.

A new method for constructing a Hamiltonian for configuration interaction calculations with constraints to energies of spherical configurations obtained with energy-density-functional (EDF) methods is presented. This results in a unified model that reproduces the EDF binding-energy results in the limit of single Slater determinants, but can also be used for obtaining energy spectra and correlation energies with renormalized nucleon-nucleon interactions. The three-body and/or density-dependent terms that are necessary for good nuclear saturation properties are contained in the monopole corrections obtained from the EDF. Applications to binding energies and spectra in the region of ¹³²Sn are given.

It is shown that the three-body forces in the 1f_7/2 shell, for which recently evidence was claimed on the basis of spectroscopic properties of the Ca isotopes and N = 28 isotones, can be most naturally explained as an effective interaction due to excluded higher-lying shells, in particular the 2p_3/2 orbit.

A new sequence of gamma rays with energies of 572, 499, 585, and 674 keV has been identified in ⁶⁷Cu populating the 7/2⁻ level at 2362 keV. Owing to the strong population of the 2362-keV level via an ℓ = 3 proton pickup reaction, that level is assigned to be an f_7/2⁻¹ 2-particle-1-hole "intruder" proton configuration, and the new levels are found to form a sequence consistent with intruder sequences in the adjacent odd-mass Cu isotopes and in the odd-mass Sb isotopes. The changing position of the intruder sequence in the odd-mass Cu isotopes is discussed and related to the onset of collectivity associated with the presence of g_9/2 neutrons beyond N = 40. The increase in collectivity is also discussed for a number of isotonic and isotopic chains as more protons or neutrons, respectively, are added beyond an oscillator shell boundary. For most of these systems, the ℓ −1/2 levels show a systematic "hockey-stick-like" behaviour with a sharp decrease in energy with the addition of the first protons or neutrons, owing to both the added collectivity and the tensor interaction, and then a lower slope when collectivity changes are diminished and only the tensor interaction is influencing the changes in level positions.

The decay of a T_1/2 = 19(3) μs isomeric state from ¹²⁵Cd has been observed using γ-ray spectroscopy at the Lohengrin mass spectrometer of the Institut Laue-Langevin, Grenoble. Two coincident γ rays were observed to be emitted from the decay of this isomeric state, contradicting recently published data on this nucleus. Realistic shell-model calculations have been performed to interpret the decay scheme, allowing a spin and parity of 19/2⁺ to be assigned to the isomeric state. All configurations contributing to this isomeric state have amplitudes less than 7 %. Experimental data have recently been published on the decays of μs isomeric states in ^127,128,130Cd. Realistic shell-model calculations for these nuclei are presented which reproduce the known experimental decay schemes reasonably well.

Pairing plays a crucial role in nuclear spectra and attempts to describe it has a long history in nuclear physics. The limiting case in which all single particle states are degenerate, but with different s-wave pairing strengths was only recently solved. In this strong coupling limit the nuclear pairing Hamiltonian also exhibits a supersymmetry. Another solution away from those limits, namely two non-degenerate single particle states with different pairing strengths, was also given. In this contribution these developments are summarized and difficulties with possible generalizations to more single particle states and d-wave pairing are discussed.

The auxiliary-field Monte Carlo (AFMC) method, also known as the shell model Monte Carlo (SMMC), enables us to calculate microscopically statistical and collective properties of nuclei in the presence of strong correlations. These calculations can be carried out in shell model spaces that are many orders of magnitude larger than spaces that can be treated with conventional diagonalization methods. A recent major development has been the extension of the AFMC approach to heavy nuclei. Such applications to heavy nuclei have been a major challenge. On the conceptual level, a crucial question is whether a truncated spherical shell model Hamiltonian can describe the proper collectivity observed in heavy nuclei and, in particular, the rotational character of strongly deformed nuclei. On the technical level, the low excitation energies make it necessary to perform calculations down to much lower temperatures. At such low temperatures the propagator becomes ill-conditioned and requires the introduction of stabilization methods.

The Recoil Distance Method is known as a very powerful tool for measuring the lifetimes of excited nuclear levels in the picosecond region. Usually, for each level, coincidences with the shifted part of a feeding transition are used to avoid the bias from the accumulated delay in the higher lying cascade, by means of the Differential Decay Curve Method. Here, an integral version of the Decay Curve Method is proposed and discussed. This technique has several noticeable advantages, particularly when the overall statistics of the results is limited owing to the weak beam current, as expected with radioactive ion beams.

Gamma rays in the π⁻²ν² nucleus ²⁰⁸Hg and π⁻¹ν² nucleus ²⁰⁹Tl have been studied at Gammasphere using deep-inelastic reactions induced by a 1360 MeV²⁰⁸ Pb beam on a thick ²³⁸U target. Previously unknown yrast γ-ray cascades above the 8⁺ and 17/2⁺ nanosecond isomers in ²⁰⁸Hg and ²⁰⁹Tl, respectively, were identified in coincidence with known γ rays deexciting the isomers. Yrast levels up to spin 13⁻ in ²⁰⁸Hg have been located, and they are interpreted in light of the structure of the ²¹⁰Pb isotone and with the help of shell model calculations. Shell model calculations by using the V_low–k realistic interaction have been performed for ²¹⁰Pb and ²⁰⁸Hg, and compared with experiment. The V_low–k effective Hamiltonian seems to account well for the properties of these neutron-rich shell model nuclei.

Recent experimental results obtained for neutron-rich nuclei of mass A~60-70 at LNL are presented together with the shell model interpretation. The development of a new region of deformation approaching the neutron number N = 40 in Cr, Fe and Co isotopes is discussed. A new effective interaction (LNPS) that considers the full fp shell model space for protons and the p_3/2, p_1/2, f_5/2, g_9/2, d_5/2 orbitals for the neutrons allows to reproduce, for the first time, the different structure properties of these nuclei. The configurations of the calculated states suggest the development of a new island of inversion at N ~ 40.

The Dirac Hamiltonian with relativistic scalar and vector harmonic oscillator potentials has been solved analytically in two limits. One is the spin limit for which spin is an invariant symmetry of the Dirac Hamiltonian and the other is the pseudo-spin limit for which pseudo-spin is an invariant symmetry of the the Dirac Hamiltonian. The spin limit occurs when the scalar potential is equal to the vector potential plus a constant, and the pseudospin limit occurs when the scalar potential is equal in magnitude but opposite in sign to the vector potential plus a constant. Like the non-relativistic harmonic oscillator, each of these limits has a higher symmetry. For example, for the spherically symmetric oscillator, these limits have a U(3) and pseudo-U(3) symmetry respectively. We shall discuss the eigenfunctions and eigenvalues of these two limits and derive the relativistic generators for the U(3) and pseudo-U(3) symmetry. We also argue, that, if an anti-nucleon can be bound in a nucleus, the spectrum will have approximate spin and U(3) symmetry.

By using the Q3D magnetic spectrograph of the Maier-Leibnitz-Laboratorium at München, particle-hole states in ²⁰⁸Pb are investigated. The reaction ²⁰⁸Pb(p, p') via seven known isobaric analog resonances in ²⁰⁹Bi and the reaction ²⁰⁷Pb(d,p) were studied. An instrumental resolution of about 3keV for protons without energy loss in the target is achieved; depending on the effective target thickness the peak shape becomes asymmetric with a tail of 3-8 keV width. A dozen doublets of states at less than 2 keV or even vanishing distance are resolved by the selective excitation in different analog resonances. For excitation energies 3.9 < E^x⪅6.1 MeV in ²⁰⁸Pb, 80 states with negative parity and 30 states with positive parity are predicted by the shell model. Most states are identified and work is going on to determine their structure.

Tensor effects in shell evolution are studied within the mean-field approach. Particular attention is paid to the analysis of the proton magic gap Z = 8. Hartree-Fock calculations with Skyrme and Gogny interactions are performed where the tensor term has a zero and finite range, respectively. Results obtained with and without the tensor component are compared between them and with the experimental data. To complete this analysis, the tensor effect is also investigated within the relativistic Hartree-Fock model.

It turns out that the tensor effect can be easily identified in the evolution of the proton magic gap Z = 8. We suggest to explicitly include the data associated to this gap evolution as new constraints in the fitting procedures when the tensor contribution is taken into account at the mean-field level.

The excitation energies of the first 2⁺ states (E(2⁺₁)) of even-even ^134–140Sn have been calculated using shell model with empirical SMPN and realistic CWG interactions in the π(gdsh) × ν(hfpi) valence space above ¹³²Sn core. The CWG predicts nearly constant E(2⁺₁) for ^134–138Sn isotopes, normally expected for singly-magic nuclei, and a weak shell closure at ¹⁴⁰Sn. The prediction of SMPN differs dramatically, decreasing E(2⁺₁) with increasing valence neutron number for ^134–138Sn and a strong shell closure at ¹⁴⁰Sn. This variation predicted by SMPN has striking similarity with the variation of experimental E(2⁺₁) of even – even ^18–22O and ^42–48Ca, clearly showing that the N =84-88 spectra exhibit the effect of gradually filling up the ν(2f_7/2) orbital which finally culminates in a new shell closure at ¹⁴⁰Sn (N = 90). Spin-tensor decomposition of SMPN and CWG and the variation of their components with valence neutron number reveals that the origin of the decreasing E(2⁺) and shell closure at ¹⁴⁰Sn might lie in the three-body effects. Calculations with CWG3M interaction, which is obtained by including a simple 3-body monopole term in the CWG predict decreasing E(2⁺₁) for ^134–138Sn and a shell closure at ¹⁴⁰Sn.

The single-particle spectrum of deformed shell-model states in nuclei, is shown to exhibit a supersymmetric pattern. The latter involves deformed pseudospin doublets and intruder levels. The underlying supersymmetry is associated with the relativistic pseudospin symmetry of the nuclear mean-field Dirac Hamiltonian with scalar and vector potentials.

The relativistic Hartree-Fock (RHF) and Random Phase Approximation (RPA) methods are self-consistently applied to two issues of current interest. The first application is related to the isospin mixing corrections in the problem of super-allowed 0⁺ → 0⁺β-transitions and the unitarity of the CKM matrix. The second application concerns the prediction of inclusive neutrino-nucleus cross-sections, where the results of the present model are compared with other approaches.

Covariant Density functional theory is used as a basis for a microscopic description of spectroscopic properties of quantum phase transitions in nuclei. Since it is well known that the mean field approximation breaks down in transitional nuclei, where configuration mixing and fluctuations connected with broken symmetries play an important role, a theory is developed which uses the Relativistic Generator Coordinate Method to perform configuration mixing calculations of angular momentum and particle number projected wave functions. As applications with show 3D-calculations of the spectrum of low-lying collective states in the nucleus ²⁴Mg. This method can also be used to study the behavior of characteristic physical quantities as a function of the physical control parameter, the number of nucleons, in the region of quantum phase transitions.

A goal of nuclear physics is to determine the validity of the nuclear shell model and to express the various models of nuclear phenomena as sub-models of this model. It is also profitable to start from a phenomenological model interpretation of nuclear data and use the results to design an effective shell-model description of the data. This paper suggests a method for deriving effective shell-model spaces for rotational nuclei and indicates that new methods are needed for deriving effective interactions for rotational nuclei.

The structure of some low-lying states in the N=80 and N=84 isotones is investigated within the quasiparticle-phonon model. The calculations reproduce the experimental levels, the electromagnetic transition strengths, and the selection rules. They account also for the M1 splittings observed in ¹³⁸Ce, ¹⁴⁴Nd and ¹⁴²Ce and relate them to correlations specific of each nucleus.

The rate of stellar formation of carbon at high temperatures (T > 3 GK) may increase beyond that which is expected from the Hoyle state at 7.654 MeV due to contributions from higher lying states in ¹²C. The long sought for second 2⁺ state predicted at 9 – 10 MeV excitation energy in ¹²C was predicted to significantly increase the production of ¹²C. An Optical Readout Time Projection Chamber (O-TPC) operating with the gas mixture of CO₂ (80%) + N₂(20%) at 100 torr with gamma beams from the HIγS facility of TUNL at Duke was used to study the formation of carbon (and oxygen) during helium burning. Preliminary measurements were carried out at beam energies: E = 9.51, 9.61, 9.72, 10.00, 10.54, 10.84 and 11.14 MeV. Extra attention was paid for separating the carbon dissociation events, ¹²C(γ,3α), from the oxygen dissociation events, ¹⁶O(γ, α)¹²C. Complete angular distributions were measured giving credence to a newly identified 2⁺ state just below 10.0 MeV.

Collective excitations are one of the most common and interesting features of many-body systems. Of particular interest are those collective modes which can be interpreted in terms of vibrations. Nuclei show a large variety of such modes, both low-lying and high-lying. In particular the giant dipole resonance is due to the coherent motion of protons against neutrons. Its analogue in metal clusters is the dipole plasmon excitation, due to the oscillation of electrons against the positive ions. The Random Phase Approximation (RPA) is extensively used as a microscopic theory to study the basic properties of these collective excitations. In the derivation of RPA use is made of the Quasi Boson Approximation (QBA). It consists in replacing the expectation values in the correlated ground state with those in the uncorrelated (Hartree-Fock) one. Strictly related to QBA is the feature of RPA of predicting a harmonic spectrum. On the other hand, the existence of anharmonicities in the multiphonon spectra of nuclei and their relevance in various physical processes are well established. Overcoming QBA has represented the starting point of many attempts aiming at improving RPA. A recently developed approach in this line will be presented and discussed. A very nice property of RPA is to satisfy Energy Weighted Sum Rules (EWSR). However, some violations are present in several extensions of RPA. We will show how to cure this shortcoming.

Using the ²⁰Ne + ¹²C fusion-evaporation reaction at E_20Ne = 33 MeV and the multidetector array GASP in conjuction with the EUCLIDES charged particle detector, angular correlations of coincident pairs of γ transitions and lifetimes in mirror nuclei ³¹S and ³¹P have been measured at the Piave-Alpi accelerator of the Laboratori Nazionali di Legnaro. A comparison of the determined B(E1) strengths of the analog mirror 7/2⁻ → 5/2⁺ transitions indicates the presence of a violation of isospin symmetry.

The self-consistent quasiparticle RPA (SCQRPA) is constructed to study the effects of fluctuations on pairing properties in nuclei at finite temperature and z-projection M of angular momentum. Particle-number projection (PNP) is taken into account within the Lipkin-Nogami method. Several issues such as the smoothing of superfluid-normal phase transition, thermally assisted pairing in hot rotating nuclei, extraction of the nuclear pairing gap using an improved odd-even mass difference are discussed. A novel approach of embedding the PNP SCQRPA eigenvalues in the canonical and microcanonical ensembles is proposed and applied to describe the recent empirical thermodynamic quantities for iron, molybdenum, dysprosium, and ytterbium isotopes.

A Hamiltonian of the Interacting Boson Model (IBM) is determined microscopically starting from the mean-field calculation. The potential energy surface (PES) by the Skyrme mean-field method is mapped onto the PES of the IBM to yield the interaction strengths of the IBM Hamiltonian, by which levels and wave functions of excited states are calculated with good angular momentum and the particle number. The response of the rotating nucleon system is mapped onto the corresponding boson system in order to determine the coefficient of the rotational kinetic-like term microscopically. By the present method, not only the three dynamical symmetries of IBM but also the recently proposed critical-point symmetries of shape-phase transitions are well reproduced. In particular, the experimental rotational band of the SU(3) nucleus in Sm isotopic chain is reproduced quite nicely. We also point out the quantum fluctuation effect on the binding energies, which is included by the diagonalization of the IBM Hamiltonian determined by the comparison to the Skyrme PES. Systematic results for spectra for Os isotopes are also presented.

An extended Vlasov equation, derived from the time-dependent Hartree–Fock–Bogoliubov equation of motion, is used to study the effects of pairing on the nuclear density-density linear response function in semiclassical approximation. Within the approximations adopted here, the fluctuations of the pairing field are purely imaginary and play a crucial role in eliminating a spurious mode that gives fluctuations of the number of particle and in reproducing the correct value of the energy-weighted sum rule. The semiclassical approach seems to have some difficulty in describing pairing vibrations. Further work on this problem is needed.

The Second Random Phase Approximation (RPA) is a natural extension of RPA obtained by introducing more general excitation operators where two particle-two hole configurations, in addition to the one particle-one hole ones, are considered. Some Second RPA results with Skyrme force in ¹⁶O are presented. Different levels of approximation are compared and in particular the quality of the diagonal approximation is tested. The issue of the rearrangement terms to be used in the matrix elements beyond the standard RPA ones, when density-dependent force are used, is briefly discussed. Two approximated, and generally used, schemes are used: the rearrangement terms are neglected in the matrix elements beyond RPA or evaluated with the RPA prescription. As a general feature of Second RPA results, a several-MeV shift of the strength distribution to lower energies is systematically found with respect to RPA distributions.

The isospin dependence of the level density, both through the level density parameter and the symmetry energy contribution has been evaluated. The effects on the most relevant observables in fusion evaporation reactions have been estimated by using the statistical model. We present here the results for the ¹³⁴Sn +⁴ He reaction, whose measurement will be possible with the second generation RIB facilities SPES and SPIRAL2. Sizeable effects are predicted on the light particle energy spectra and multiplicities and evaporation residue distribution. In particular, the measure of evaporation residue yields and light particle multiplicities are expected to unfold the two effects. In addition, the same calculations have been carried out for reactions induced by stable beams, in order to search for clues of isospin effects. In this case, the direct comparison of the experimental light charged particle energy spectra for the two reactions ⁷Li+^58,64Ni at the same excitation energy and angular momentum, is proposed as a good approach to observe isospin effects.

The branching between the E0 0⁺₂ → 0⁺₁ and the E2 0⁺₂ → 2⁺₂ transitions in ¹⁵⁶Dy and ¹⁶⁰Er were measured following the decay of ¹⁵⁶Ho and ¹⁶⁰Tm. A potential of the 4th order of the deformation parameter β, the "Lo Bianco potential", was chosen to describe the U(5) − SU(3) first order shape phase transition, covering the whole transitional path. The comparison of the excitation spectra and the measured ratios of reduced transition probabilities, X(E0/E2), with the calculations, indicates that ¹⁵⁶Dy is in the spherical region, while ¹⁶⁰Er is located in the deformed region, but quite close to the critical point.

Some representative cases of the description and analysis of giant resonances within the self-consistent separable random-phase-approximation model (SRPA) based on the Skyrme functional are discussed. It is shown that SRPA with SLy6 force well describes the dipole giant resonance in rare-earth and actinide regions. The sensitivity of the E1 strength near the particle thresholds to nuclear deformation is scrutinized. Finally, the open problems of description of spin-flip M1 resonance are discussed.

In recent experiments at the GSI, Darmstadt, time-modulated orbital Electron Capture (EC) decays of H-like ¹⁴⁰Pr⁵⁸+, ¹⁴²Pm⁶⁰⁺ and ¹²²I⁵²+ ions with one electron in the K-shell, coasting in the ESR storage ring with velocity β = 0.71, were observed. The EC-branches observed using time-resolved Schottky Mass Spectroscopy show exponential decay curves time-modulated with periods T = 7.06(8) s, T = 7.10(22) s, and T = 6.16(3) s and amplitudes a = 0.18(3), a = 0.23(4), and a = 0.16(2) for ¹⁴⁰Pr, ¹⁴²Pm, and ¹²²I decays, respectively. The β⁺ branch of ¹⁴²Pm shows no modulation with a < 0.03. As origin of the modulation, we propose quantum beats produced by massive neutrino mass-eigen states emitted in the two body weak decay. From the modulation frequency a value for the difference of the quadratic mass values m²₂ − m²₁ = 2.22(3) × 10⁻⁴ eV² is deduced, which is 2.9 times larger than the value derived by the KamLAND antineutrino oscillation experiment. The origin of the small modulation amplitudes is discussed as the result of partial restoration of the interference terms which are expected to cancel for the usual assumed unitarity of the neutrino flavour mixing matrix.

In the 1950s the possibility of forming a ''super-radiant'' (SR) state in a gas of atoms confined to a volume of a size smaller than the wave length of radiation was suggested by Dicke. The atoms, with two levels, are coupled through their common radiation field. This indirect coupling leads to a redistribution of lifetimes among unstable intrinsic states. A strongly decaying SR state is created at the expense of the rest of the states of the system. Recently the connection of this mechanism to the notion of doorway states in low-energy nuclear reactions, was pointed out. The conditions for appearance of such doorways in nuclear physics processes are discussed.

We explore the influence of the deformation on the nuclear matrix elements of the neutrinoless double beta decay (NME), concluding that the difference in deformation -or more generally in the amount of quadrupole correlations- between parent and grand daughter nuclei quenches strongly the decay. We correlate these differences with the seniority structure of the nuclear wave functions. In this context, we examine the present discrepancies between the NME's obtained in the framework of the Interacting Shell Model and the Quasiparticle RPA. In our view, part of the discrepancy can be due to the limitations of the spherical QRPA in treating nuclei which have strong quadrupole correlations. We surmise that the NME's in a basis of generalized seniority are approximately model independent, i. e. they are "universal".

The Quasi-particle Random Phase Approximation (QRPA), the Shell Model (SM), the angular momentum projected Hartee-Fock-Bogoliubov approach (HFB) and the Interacting Boson Model (IBM) are compared with each other for the determination the neurinoless double beta decay. The different approaches are compared specifically concerning the the angular momenta and parities of the neutron pairs, which are changed into two protons by the 0νββ-decay.

The cluster description of near coexistence phases (e.g. Fisher theory) requires an evaluation of cluster surface entropy. This surface degeneracy can be estimated with lattice models where clusters appear. The maximum probability lies near the maximum cluster surface. At low temperatures, clusters are forced to be nearly spherical by the surface energy and the associated Boltzmann factor. At higher temperatures and near criticality, the fractal dimension of clusters changes so that clusters become fractal. In the MIT bag model, where there is no surface energy, bags are always fractal.

A survey of chaotic dynamics in atomic nuclei is presented, using on the one hand standard statistics of quantum chaos studies, and on the other a new approach based on time series analysis methods. The study of shell-model spectra in the pf shell shows that nuclear chaos is strongly isopin dependent and increases with excitation energy. On the other hand, it is found that chaotic quantum systems exhibit 1/f noise and regular systems exhibit 1/f² behaviour. It is shown that the time series approach can be used to calculate quite accurately the fraction of missing levels and the existence of mixed symmetries in experimental level spectra.

In this and the follow-up article we briefly discuss what we believe represents one of the most serious problems in contemporary nuclear structure: the question of statistical significance of parametrizations of nuclear microscopic Hamiltonians and the implied predictive power of the underlying theories. In the present Part I, we introduce the main lines of reasoning of the so-called Inverse Problem Theory, an important sub-field in the contemporary Applied Mathematics, here illustrated on the example of the Nuclear Mean-Field Approach.

We present examples and illustrate associated tests of statistical significance of the parameter fitting procedures in the nuclear mean-field context using a phenomenological toy-model based on the spherical Woods-Saxon Hamiltonian. We calculate the variance-covariance matrix and compare the standard estimates of the confidence intervals (and more generally – the uncertainty distributions) based on the standard χ²-fitting as opposed to a more general Monte-Carlo simulations. We give arguments for the superiority of the latter approach.