The Fifth Conference “ Nuclear Science and Its Application”, 14-17 October 2008
BOSON MAPPING OF THE FERMION DYNAMICAL MODEL OF
NUCLEI
K. BAKTYBAYEV1. N. KOILYK1, K. RAMANKULOV2.
1. Kazakhstan, Almaty al-Farabi University 2. Kazakhstan, Abaipedagogical University
In the interacting boson model (IBM) boson degrees of freedom are introduced which are believed and, at least in some cases, have been shown, to be related to collective shell-model fermion pairs. The IBM with s-and d-boson has proven to be very efficient and useful in phenomenologically descrybing and correlating extensive pieces of experimental data. The formulation of fermion dynamical symmetry model (FDSM) on a description of collective states and relies on algebraic
Section II. Basic Problems O f Nuclear Physics
The Fifth Conference “ Nuclear Science and Its Application”, 14-17 October 2008
symmetry concepts is directly related to the shell structure. The building blocks of FDSM are correlated fermion pairs S, S’ and D chosen as the pair creation and annihilation operators together with a set multipole operators close an Sp(6) or SO(8) and an SU(2) algebra.
In the present work we investigate boson mappings [1,2] relevant to the fermionic FDSM. We discuss several boson mapping procedures which transcribe an FDSM Hamiltonian into a boson one and compare the results. Hereby IBM-type Hamiltonians are constructed with an aim to test the applicability of different boson mapping procedures.
Fermion theory was rpepresented into boson’s space by Daison, Belyaev-Zelevinski and Senority methods. The solutions o f represented boson equation were used to same platinum isotopes and it gave a good results. It was shown that FDSM and its boson representation gave a good explanation of experimental data. So it was shown that from the Hamiltonian of FDSM could be constructed boson type IBM-Hamiltonian by representation. So fermion theory gives microscopically base of phenomenological approaches.
The results of the various mapping procedures are compare in different regions o f the Z=50- 82, N=82-126 shell.
It should be notes that the correspondence between the IBM and FDSM has also been studied from a group theoretical point of view.
Section II. Basic Problems O f Nuclear Physics
