The last decade has witnessed both quantitative and qualitative progresses in Shell Model studies, which have resulted in remarkable gains in our understanding of the structure of the nucleus. Indeed, it is now possible to diagonalize matrices in determinantal spaces of dimensionality up to 10^9 using the Lanczos tridiagonal construction, whose formal and numerical aspects we will analyze. Besides, many new approximation methods have been developed in order to overcome the dimensionality limitations. Furthermore, new effective nucleon-nucleon interactions have been constructed that contain both two and three-body contributions. The former are derived from realistic potentials (i.e., consistent with two nucleon data). The latter incorporate the pure monopole terms necessary to correct the bad saturation and shell-formation properties of the realistic two-body forces. This combination appears to solve a number of hitherto puzzling problems. In the present review we will concentrate on those results which illustrate the global features of the approach: the universality of the effective interaction and the capacity of the Shell Model to describe simultaneously all the manifestations of the nuclear dynamics either of single particle or collective nature. We will also treat in some detail the problems associated with rotational motion, the origin of quenching of the Gamow Teller transitions, the double beta-decays, the effect of isospin non conserving nuclear forces, and the specificities of the very neutron rich nuclei. Many other calculations--that appear to have ``merely'' spectroscopic interest--are touched upon briefly, although we are fully aware that much of the credibility of the Shell Model rests on them.

The shell model as a unified view of nuclear structure

Energy levels of Z = 11−21 nuclei (IV)

https://www.cns.s.u-tokyo.ac.jp/~shimoura/research/nuc_data/pdf/13.pdf

Energy levels of light nuclei A = 13-15

A new approach is proposed for a unified description of strongly coupled deep inelastic (DI) scattering, fusion, fission and quasi-fission (QF) processes of heavy-ion collisions. The standard (most important) degrees of freedom of the nuclear system, unified driving potential, and a unified set of dynamic equations of motion are used in this approach. This makes it possible to perform a full (continuous) time analysis of the evolution of heavy nuclear systems, starting from the approaching stage, moving up to the formation of the compound nucleus and eventually emerging into two final fission fragments. The calculated mass, charge, energy and angular distributions of the reaction products agree well with the corresponding experimental data. It gives us hope to obtain rather accurate predictions for the probabilities of superheavy element formation in near-barrier fusion reactions.

https://iopscience.iop.org/article/10.1088/0954-3899/31/7/024/pdf

Unified consideration of deep inelastic, quasi-fission and fusion fission phenomena

A quantal transport theory for nuclear collective motion: The merits of a locally harmonic approximation

Collective potential energy surfaces have been systematically calculated for the symmet­ ric fission of the five isotopes of the elements Th, Pu, Cm, Cf, Fm and No and the eight isotopes of the element U. The calculation is performed on the basis of Strutinsky's pre­ scription in which the liquid drop model of v. Groote and Hilf and the modified two-center harmonic oscillator shell model are used for macroscopic and microscopic parts, respectively. Effects of mass asymmetry at the second saddle point are investigated. The properties of the ground state, the second minim urn and the first and second saddle points along the static fission path are discussed in comparison with the results of Moller and Nix. The structure of the potential energy surface is found to come mainly from the shell structure which is strongly related to the distance between the mass centers of the nascent fragments. Special attentions are given to the fragment mass distributions and the constancy of the heavy fragment masses is partially explained on the basis of the properties of the second barrier. § I. Introduction Since the late 1960's, a renewed interest has been aroused 111 the structure of the potential energy surface for the fission process. It was motivated mainly by the discoveries of the fission isomer!) and the related resonant structure of the fission cross section. 2J The calculation based on the liquid drop model was proved not to be able to reproduce these featuers and in 1967 a new method for the calculation of the potential energy-- the macroscopic-microscopic model'J __ was proposed. Since then, calculations based on this model have been widely made and the fission isomer has been theoretically explained as a shape isomer. It is caused by the shell structure of a largely deformed nucleus and the fact that the shell structure appears at such a large deformation has made a drastic change m our knowledge of the nuclear structure. 4J The structure of the potential energy surfaces of the heavy nuclei is at present fairly well known. 5 J~sJ For the actinide nuclei, a typical feature is that there exists a second minimum and as a result the fission barrier is split into two, the inner barrier and the outer barrier. The calculated heights of these barriers and the second minimum were compared with the experimental data and overall agreement

/pdf/potential-energy-surfaces-for-the-fission-of-the-actinide-4l7isgkgxg.pdf

Potential Energy Surfaces for the Fission of the Actinide Nuclei

Variation of transport coefficients for average fission dynamics with temperature and shape

On the nature of nuclear dissipation, as a hallmark for collective dynamics at finite excitation☆

Finite Range Distorted Wave Calculations on Reactions C13(p, n)N13, B11(p, n)C11 and Al27(n, p)Mg27

An approach is proposed for studying the spreading properties of the Gamow-Teller resonance (GTR) in heavy nuclei including the coupling to 2p2h configurations and the ground-state correlations beyond RPA. The GTR is generated by a proton p-neutron h (Trp-~h) phonon within the renormalized RPA. The second-order configuration mixing beyond RPA is realized by constructing two-phonon configurations, in which one of two intermediate phonon states is a ~rp-eh phonon. The numerical calculations are performed in the parent nuclei 9°Zr and 2°sPb making use of M3Y nucleon-nucleon interaction and the single-particle wave functions obtained in the standard harmonic oscillator potential. The single-particle energies around the Fermi surface are substituted with the empirical values or those given by a Woods-Saxon potential. The results obtained provide a reasonable account for recent experimental findings on the GTR in these nuclei. The extension of the present approach to highly excited (hot) nuclei is also provided. The GTR is found to be stable against temperatures up to T = 6 MeV. @ 1997 Elsevier Science B.V.

Shuhei Yamaji

Papers

Potential Energy Surfaces for the Fission of the Actinide Nuclei

Variation of transport coefficients for average fission dynamics with temperature and shape

On the nature of nuclear dissipation, as a hallmark for collective dynamics at finite excitation☆

Finite Range Distorted Wave Calculations on Reactions C13(p, n)N13, B11(p, n)C11 and Al27(n, p)Mg27

Study of the Gamow-Teller resonance in 9°Nb and 208Bi