Shape mixing as an approximation to shell model24Ne

Band mixing calculations have been done for²⁴Ne including the two degenerate prolate and oblate Hartree-Fock states and also some particle-hole excited states in the projection formalism using an interaction obtained by Preedom and Wildenthal. The energy spectrum agrees very well with the experimental results as well as the exact shell model calculations. Thus the band mixing calculations provide a good approximation to the lengthy exact shell-model calcuations. In addition they offer a physical insight into the collective nature of the nucleus as nuclear states are described in terms of only a few ‘intrinsic’ states.     

Shape coexistence and the N = 28 shell closure far from stability

The masses of 31 neutron-rich nuclei in the range A = 29-47 have been measured. The precision of 19 masses has been significantly improved and 12 masses were measured for the first time. The neutron-rich Cl, S, and P isotopes are seen to exhibit a change in shell structure around N = 28. Comparison with shell model and relativistic mean field calculations demonstrate that the observed effects arise from deformed prolate ground state configurations associated with shape coexistence. Evidence for shape coexistence is provided by the observation of an isomer in 43S.     

Shape coexistence in the neutron deficient Pb isotopes and the configuration-constrained shell correction approach

Calculations of shape-isomeric states in neutron deficient lead isotopes have been performed using the configuration-constrained shell correction method with a Woods-Saxon average potential and a monopole pairing interaction. This approach enables us to decompose the ground state potential energy surface in separate parts characterized uniquely by the number of occupied intruder orbitals. The calculations reproduce the positions of the excited 0⁺ intruder states. The isotope¹⁹⁶Pb is discussed in detail.     

Charge transfer in the shell model

the mechanism of charge transfer is incorporated into the shell model in an effort to better describe the lattice dynamics of crystals of the zincblende structure. The long-wavelength aspects of the resulting new model are treated in detail. A preliminary application is made to GaAs.     

Semiclassical quantization of the shell model

The classical limit of the nuclear shell model is shown to be a many-dimensional hamiltonian system in which the coordinates and momenta are the coherent-state parameters of the original quantum system. Several methods for semiclassical quantization of this system are discussed, including surfaces of section and the Birkhoff-Gustavson transformation to action-angle variables. Application to a schematic three-level shell model indicates some of the new problems involved in requantizing multi-dimensional systems which are not present in one-dimensional examples. These include difficulties in finding periodic orbits and the onset of stochasticity.     

Self-consistency in the projected shell model

The projected shell model is a shell-model theory built up over a deformed BCS mean field. Ground state and excited bands in even-even nuclei are obtained through diagonalization of a pairing plus quadrupole Hamiltonian in an angular momentum projected 0-, 2-, and 4-quasiparticle basis. The residual quadrupole-quadrupole interaction strength is fixed self-consistently with the deformed mean field and the pairing constants are the same used in constructing the quasiparticle basis. Taking ¹⁶⁰Dy as an example, we calculate low-lying states and compare them with experimental data. We exhibit the effect of changing the residual interaction strengths on the spectra. It is clearly seen that there are many J^π = 0⁺, 1⁺, 4⁺ bandheads whose energies can only be reproduced using the self-consistent strengths. It is thus concluded that the projected shell model is a model with essentially no free parameters. The predicted energy of the 2⁺ bandhead lies however in nearly twice the experimental value.     

Frontiers and challenges of the nuclear shell model

Two recent developments of the nuclear shell model are presented. One is a breakthrough in computational feasibility owing to the Monte Carlo Shell Model (MCSM). By the MCSM, the structure of low-lying states can be studied with realistic interactions for a wide, nearly unlimited basically, variety of nuclei. The magic numbers are the key concept of the shell model, and are shown to be different in exotic nuclei from those of stable nuclei. Its novel origin and robustness will be discussed. Received: 1 May 2001 / Accepted: 4 December 2001     

Multi-nucleon transfer spectroscopy in the shell model

Formulas for calculating multi-nucleon transfer spectroscopic amplitudes tailored for use with the Rochester-Oak Ridge shell-model computer programs are presented. Expressions are given for the evaluation of three- and four-particle coefficients of fractional parentage. Predictions of α-particle spectroscopic factors for ${}^{58}\text{Ni}\text{+ α →}{}^{62}\text{Zn}\text{,}{}^{60}\text{Ni}\text{+ α →}{}^{64}\text{Zn}\text{,}\text{and}{}^{40}\text{Ca}\text{+ α →}{}^{44}\text{Ti}$ are compared with experiment.     

Off shell states in the dual model

We present a class of Lorentz invariant, gauge invariant off-shell amplitudes for the ordinary Veneziano and Ramond-Neveu-Schwarz dual models. They correspond to interactions with the string which are local in space-time.     

Nucleon-pair approximation to the nuclear shell model

Atomic nuclei are complex systems of nucleons–protons and neutrons. Nucleons interact with each other via an attractive and short-range force. This feature of the interaction leads to a pattern of dominantly monopole and quadrupole correlations between like particles (i.e., proton–proton and neutron–neutron correlations) in low-lying states of atomic nuclei. As a consequence, among dozens or even hundreds of possible types of nucleon pairs, very few nucleon pairs such as proton and neutron pairs with spin zero, two (in some cases spin four), and occasionally isoscalar spin-aligned proton–neutron pairs, play important roles in low-energy nuclear structure. The nucleon-pair approximation therefore provides us with an efficient truncation scheme of the full shell model configurations which are otherwise too large to handle for medium and heavy nuclei in foreseeable future. Furthermore, the nucleon-pair approximation leads to simple pictures in physics, as the dimension of nucleon-pair subspace is always small. The present paper aims at a sound review of its history, formulation, validity, applications, as well as its link to previous approaches, with the focus on the new developments in the last two decades. The applicability of the nucleon-pair approximation and numerical calculations of low-lying states for realistic atomic nuclei are demonstrated with examples. Applications of pair approximations to other problems are also discussed.     

Quantum chaos in the two-center shell model

Within an axially symmetric two-center shell model single-particle levels with Ω=1/2 are analyzed with respect to their level-spacing distributions and avoided level crossings as functions of the shape parameters. Only for shapes sufficiently far from any additional symmetry, ideal Wigner distributions are found as signature for quantum chaos.     

Projector operators for the no-core shell model

Projection operators for the use within the ab initio no-core shell model are suggested. The text was submitted by the author in English.     

Padé approximants and the effective shell model interaction

A scheme for approximating the effective interaction in the presence of an intruder state is discussed. The method, which employs the Padé approximation for individual matrix elements in an appropriately transformed basis, is shown to be reliable for a 3 × 3 Hamiltonian matrix.     

迈耶夫人与核壳层模型

介绍了迈耶夫人的生平和她对物理学的主要贡献,回顾了她从幻数入手,继而建立原子核壳层模型的过程,以及由此带给我们的启示.     

Hole states in nuclei and the continuum shell model

The hole spectral function which determines the cross section of direct nucleon removal processes is studied in the framework of the continuum shell model with residual interactions. An expression for the spectral function is derived which covers both the bound and continuous parts of the hole spectrum and allows for an exact inclusion of all correlations (except for continuum-continuum coupling) in a restricted space of shell-model configurations. The shell-model approach is compared to the Green function formulation of the spectral function, and some formal relationships between both formulations are established. The results of previous calculations of the spectral function via a second-order mass operator are discussed in the light of the shell-model formalism.     

On the extended basis shell model and two-nucleon transfer

The enhancement of two-nucleon transfer reactions predicted by the extended basis shell-model (EBSM) calculations of Feng, Ibarra and Vallieres and other theorists, is shown to be a higher order manifestation of the pairing effects in nuclei. A simple schematic model is introduced which illustrates the constructive interference of the contributions from the highly excited shell-model states included in the EBSM. The model can be used to estimate the effect of ground-state correlations of the closed-shell core. The results indicate that the assumption of an inert core in EBSM calculations introduces negligible error in cases in which the addition of a nucleon pair to a closed shell is treated. However, in the case of two-nucleon removal from a closed shell, including the effects of correlations may significantly enhance the cross section. A suggestion is made for including these effects in EBSM calculations.     

The rotating two-center shell model

The rotating two-center shell model with five deformation parameters has been studied. Spectra showing the dependence of the shell structure on nuclear elongation, necking, mass asymmetry, and angular velocity are exhibited and inferences concerning the stability of rotating nuclei and the changes in deformation with spin are drawn. Finally we examine the limits for stability of a composite system in heavy-ion reactions.     

Shape coexistence and the N = 20 shell closure far from stability by inelastic scattering

Following mass measurements in the region N = 20 and N = 28, we have studied inelastic nuclear scattering for the nuclei ³⁴Si, ³³Al and ³²Mg. No evidence for a low-lying shape isomeric 0⁺ state was found in ³⁴Si, and an upper limit for the population cross-section could be established, rendering its existence very unlikely. A new transition was found in ³³Al, that is a good candidate for a 2p-2h state and therefore a determination of the 2p-2h gap at N = 20. Inelastic nuclear scattering strongly excites 3^- states, as seen in ³⁴Si. A strong transition was found in ³²Mg that should correspond to the first 3^- in this nucleus, lying very low as compared to theory and systematics in this region. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: mittig@ganil.fr