L. Próchniak

Quadrupole collective states within the Bohr collective Hamiltonian

The article reviews the general version of the Bohr collective model for the description of quadrupole collective states, including a detailed discussion of the models 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.

Collective quadrupole excitations in the 50 < Z, N < 82 nuclei with the general Bohr Hamiltonian

Abstract The general Bohr Hamiltonian is applied to a description of low-lying collective excitations in even-even isotopes of Te, Xe, Ba, Ce, Nd and Sm. The collective potential and inertial functions are determined by means of the Strutinsky method and the cranking model, respectively. A shell-dependent parametrization of the Nilsson potential is used. An approximate particle-number projection is performed in the treatment of pairing correlations. The effect of coupling with the pairing vibrations is taken into account approximately when determining the inertial functions. The calculation does not contain any free parameter.

The low-lying quadrupole collective excitations of Ru and Pd isotopes☆

Abstract Quadrupole excitations of even-even Ru and Pd isotopes are described within a microscopic approach based on the general collective Bohr model which includes the effect of coupling with the pairing vibrations. The excitation energies and E2 transition probabilities observed in 104–114 Ru and 106–110 Pd are reproduced in the frame of the calculation containing no free parameters. Particularly interesting are 104 Ru and 106–110 Pd where good agreement to very rich information based on Coulomb excitation experiments is achieved.

COLLECTIVE PROPERTIES OF STABLE EVEN–EVEN Cd ISOTOPES

We analyze collective properties of the 110-116Cd isotopes in the framework of the general Bohr Hamiltonian which is obtained from the ATDHFB theory with the Skyrme interaction. Calculated energies and B(E2) transition probabilities and experimental data are in good agreement.

Collective states of transitional nuclei

The “quadrupole plus pairing” collective model is constructed for the microscopic description of low-lying collective states of even-even transitional nuclei. Inclusion of the model to the core-quasiparticle coupling model in order to describe odd nuclei is realized. An approximation scheme suitable for investigation of the quadrupole excitations is demonstrated. Exemplary results of microscopic calculations for the Ru isotopes are shown.