[en] The many-particle helicity transformation is found to satisfy general conditions imposed on transformation to pseudo space-spin degrees of freedom in heavy nuclei. Both mean-field and many-particle estimates are presented to show that the nucleons in the helicity-transformed representation are bound by a strongly nonlocal potential with an effectively reduced spin-orbit interaction strength. Since the helicity and chirality transformations are closely related and coincide in the ultrarelativistic limit, pseudospin symmetry in heavy nuclei seems to be connected to chiral symmetry of high energy hadrons

[en] The phenomenological symplectic model with a Davidson potential is used to construct rotational states for a rare-earth nucleus with microscopic wave functions. The energy levels and E2 transitions obtained are in remarkably close agreement (to within a few percent) with those of the rotor model with vibrational shape fluctations that are adiabatically decoupled from the rotational degrees of freedom. An analysis of the states in terms of their SU(3) content shows that SU(3) is a very poor dynamical symmetry but an excellent quasi-dynamical symmetry for the model. It is argued that such quasi-dynamical symmetry can be expected for any Hamiltonian that reproduces the observed low-energy properties of a well-deformed nucleus, whenever the latter are well-described by the nuclear rotor model

[en] The pseudo-SU(3) model is an algebraic shell-model theory that takes full advantage of pseudo-spin symmetry in a proton-neutron formalism where the spin degree of freedom is explicitly taken into account. The usual Hamiltonian is extended to include the pairing interaction which couples states of different irreducible SU(3) representations. The effect of the pairing is investigated in full-space(untruncated) schematic calculations and its influence on the moments of inertia, B(E2) values, and quadrupole moments is illustrated. Finally, the pseudo-SU(3) model is applied to a systematic study of a number of light rare-earth nuclei, comparing calculated results to experimental data and other theories

[en] The primary achievement of the symplectic model is to give a realistic microscopic shell-model expression of the nuclear collective model. However, in applications of the model, one has to contend with the fact that its Hilbert spaces, like those of the shell model, are infinite dimensional. This means that truncation of the model Hilbert space to a finite-dimensional subspace is inevitable. Nevertheless, it is in principle possible to get results to any desired accuracy if a sequence of increasingly large, but finite-dimensional subspaces of the full Hilbert space can be determined so that truncation to the subspaces of the sequence leads to rapidly convergent results. We show in this paper that generator coordinate (also called coherent state) bases can be constructed and optimized to give extraordinarily rapid convergence. This makes it possible to perform accurate symplectic model calculations with realistic microscopic Hamiltonians by a method that is essentially an angular-momentum projected, multi-determinant, Hartree-Fock calculation for which powerful but highly practical methods, that make a minimal use of group theory, have been developed. It is shown that the techniques developed give a natural representation of the intrinsic states of rotational bands as beta- and/or gamma-vibrational wave functions. The techniques are illustrated by computation of beta-vibrational wave functions for the ground-state and one-phonon excited rotational bands of ⁸Be for a microscopic Hamiltonian with a Brink-Boeker two-body interaction

[en] Complete rotation-vibrational spectra and electromagnetic transition rates are obtained for Hamiltonians of diatomic molecules and nuclei with Davidson interactions. Analytical results are derived by dynamical symmetry methods for diatomic molecules and a liquid-drop model of the nucleus. Numerical solutions are obtained for a many-particle nucleus with quadrupole Davidson interactions within the framework of the microscopic symplectic model. (author)

[en] The pairing-plus-quadrupole model, realized in the framework of the Elliott SU(3) scheme, is used to study the combined effects of the quadrupole-quadrupole, pairing, and spin-orbit interactions on ground state shapes of nuclear systems. Relevant measures for nuclear deformation are reviewed. Representation mixing induced by the symmetry-breaking pairing and spin-orbit forces is shown to soften the deformation. The angular momentum dependence of the results is discussed. (orig.)

[en] Shell-model calculations for 58Cu and 64Ge in the pf5/2g9/2 model space using a realistic interaction are reported and compared to those generated using an appropriately renormalized counterpart of the interaction in the truncated pf5/2 subspace. The results suggest that reliable computations can be performed in a space that does not explicitly include the intruder level so long as the interaction as well as the transition operators are renomalized appropriately

[en] Shell-model calculations for upper fp-shell nuclei using realistic interactions are reported. Valence nucleons beyond the N=28=Z core are considered to fill levels of the normal parity upper fp-shell and the unique parity configurations that consists either of the g9/2 level or the whole gds-shell. These two cases are handled within a standard M-scheme approach and an SU(3) picture, respectively. Results for low-lying energy spectra, single-particle occupancies and symmetry properties of the eigenstates are reported. Various truncations are considered that key on the number of nucleon pairs allowed to occupy the unique-parity space. The calculations demonstrate the importance of the unique-parity space to the structure of upper fp-shell nuclei

[en] Algebraic models developed over the past 2-3 decades have helped to bridge the gap between macroscopic (collective model) and microscopic (shell-model) theories of nuclear structure. Consequences of a correspondence between the triaxial rotor model and a generic SU(3) theory are the subject of this review. 13 refs., 1 fig

[en] The origin and consequences of pseudo-spin symmetry in nuclear physics, which is exact for an oscillator potential with one-body orbit-orbit (v_ll) and spin-orbit (v_ls) interaction strengths in the ratio μ = 2 v_ll / v_ls = 0.5, are considered. Specifically, the v_ls ≅ 4 v_ll condition is shown to be consistent with relativistic mean-field results and a pseudo-LS shell-model coupling scheme. The complementarity of good pseudo-spin symmetry and a residual quadrupole-quadrupole interaction is also explored; in this case, the pseudo-spin picture extends to the pseudo-SU(3) scheme, which applies to superdeformed phenomena. (Author). 15 refs, 1 fig, 2 tabs