Quadrupole collective states within the Bohr collective Hamiltonian

Abstract

The article reviews the general version of the Bohr collective model for the description of quadrupole collective states, including a detailed discussion of the model's kinematics. The quadrupole coordinates, momenta and angular momenta are defined and the structure of the isotropic tensor fields as functions of the tensor variables is investigated. After a comprehensive discussion of the quadrupole kinematics, the general form of the classical and quantum Bohr Hamiltonian is presented. The electric and magnetic multipole moment operators acting in the collective space are constructed and the collective sum rules are given. A discussion of the tensor structure of the collective wavefunctions and a review of various methods of solving the Bohr Hamiltonian eigenvalue equation are also presented. Next, the methods of derivation of the classical and quantum Bohr Hamiltonian from the microscopic many-body theory are recalled. Finally, the microscopic approach to the Bohr Hamiltonian is applied to interpret collective properties of 12 heavy even-even nuclei in the Hf-Hg region. Calculated energy levels and E2 transition probabilities are compared with experimental data.

Shell-model-based deformation analysis of light cadmium isotopes

“…An extensive study has been carried out by Srebrny et al [94] describing deformed nuclei by a Nilsson ellipsoidal deformed potential [106][107][108], equating the experimental (or theoretical, as derived from our present LSSM calculations) P …”

“…In Figure 2 we present a comparison of the theoretical β values corresponding to the 0 termediate steps, an increasing concentration into just a few states shows up in approaching 108 Cd. One observes a transition from a highly fragmented trend for the 0 + 2 , and even more so for the 0 + 3 state moving through the nuclei with, to a situation in 108 Cd, with the 0 + 2 state exhibiting a similar character as the ground state.…”

Shape Coexistence in the Neutron-Deficient Even-EvenHg182−188Isotopes Studied via Coulomb Excitation

“…These results can be analyzed in terms of the quadrupole deformation parameters, Q and δ, which are universal variables of quadrupole collective models within the General Bohr Hamiltonian (GBH) [27]. Using the quadrupole sum rules approach [28][29][30][31] the quadrupole invariants, hQ 2 i and hQ 3 cosð3δÞi, can then be obtained.…”

Skyrme energy-density functional approach to collective modes of excitation in exotic nuclei

“…The similar attempts of the EDF-based collective Hamiltonian starting from the Gogny interaction [12,13], the relativistic Lagrangian [14,15] and the Skyrme interaction [16] have been made for description of the large-amplitude collective motion. The cranking approximation, however, has been applied to calculate the inertial functions [12,13,14,15,16], and the timeodd components of the mean field remain largely unexplored except for a few attempts in the adiabatic time-dependent Hartree-Fock-Bogoliubov theories [17,18,19].…”

“…The cranking approximation, however, has been applied to calculate the inertial functions [12,13,14,15,16], and the timeodd components of the mean field remain largely unexplored except for a few attempts in the adiabatic time-dependent Hartree-Fock-Bogoliubov theories [17,18,19]. Our method includes the time-odd mean fields in the inertial functions.…”