SO/sub 8/ model of collectivity in nuclei

Conference · Sat Jan 01 00:00:00 EST 1983

OSTI ID:5975231

Ginocchio, J N

The interacting boson model (IBM) has been very successful in giving a unified and simple description of the spectroscopic properties of a wide range of nuclei, from vibrational through rotational nuclei. The three basic assumptions of the model are that (1) the valence nucleons move about a doubly closed core, (2) the collective low-lying states are composed primarily of coherent pairs of neutrons and pairs of protons coupled to angular momentum zero and two and (3) these coherent pairs are approximated as bosons. Thus the IBM is an approximation to the nuclear shell model in which the number of degrees of freedom are reduced drastically. Once these assumptions are made, the effective Hamiltonian can then be written in terms of neutron monopole (angular momentum zero) and quadrupole (angular momentum two) bosons and proton monopole and quadrupole bosons. Since each nucleus will have a fixed number of nucleon pairs this boson Hamiltonian will conserve the number of bosons. Phemonologically, the Hamiltonian is assumed to be finite and to be a sum of a boson self-energy Hamiltonian plus pairwise interactions between bosons. However, the parameters of the boson Hamiltonian depend smoothly on the mass of the nucleus. The mass dependence of these parameters presumably arise because of two effects resulting from the approximations made. In this review we shall show how it is possible to have fermion Hamiltonians which have a class of collective eigenstates composed entirely of monopole and quadrupole pairs of fermions. Hence these models satisfy the assumptions (1) and (2) above but no boson approximation need be made. Thus the Pauli principle is kept in tact. Furthermore the fermion shell model states excluded in the IBM can be classified by the number of fermion pairs which are not coherent monopole of quadrupole pairs. Hence the mixing of these states into the low-lying spectrum can be calculated in a systematic and tractable manner.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 5975231
• Report Number(s): LA-UR-83-1310; CONF-830143-1; ON: DE83012683
• Resource Relation: Conference: Workshop on bosons in nuclei, Philadelphia, PA, USA, 28 Jan 1983
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
NUCLEAR MODELS
COLLECTIVE EXCITATIONS
HAMILTONIANS
EIGENSTATES
FERMIONS
INTERACTING BOSON MODEL
MATRIX ELEMENTS
MONOPOLES
NUCLEAR STRUCTURE
QUADRUPOLES
SAMARIUM ISOTOPES
SHELL MODELS
SO GROUPS
YRAST STATES
ENERGY LEVELS
ENERGY-LEVEL TRANSITIONS
EXCITATION
ISOTOPES
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MULTIPOLES
QUANTUM OPERATORS
RARE EARTH ISOTOPES
SYMMETRY GROUPS
653007* - Nuclear Theory- Nuclear Models- (-1987)