The nucleon-pair shell description of the collective excitations of spherical nuclei

Abstract

Low-lying collective excitations of nuclei are described in the SD-pair shell approach. To facilitate the computational difficulties the Hilbert space cutoff is performed up to SD-pair, in which a microscopic justification of the model of interacting bosons is given. The diagonalization of the fermionic Hamiltonian in the cutoff space is applied to the study of the spectra structure and reduced probabilities of the electromagnetic transitions B (E2) in the spherical isotopes of Ruthenium with the atomic weight A = 100,102,104. These values are compared with their experimental data.

Fermion Theory of Collective States of Nuclei, Its Application to the Structure of Real Systems

“…As the core of this nuclei in protons and neutrons states is taken the low energy states of the strontium nucleus with Z = 38 and N = 50 [10].The proton shell of the strontium nucleus is completed by filling the 2 / level.…”

“…On the other hand, the observed changes in the parameters of the IBM model as a function of N and Z are in good agreement with the first approximation of the approach that takes into account the severity schemes in interacting fermion systems [5][6][7].Attempts were also made to substantiate the IBM by calculating model parameters from detailed microscopic approaches. The description of collective states in terms of fermion degrees of freedom is an interesting and important problem in the theory of nuclear structure.But because of the difficulty of carrying out numerical calculations in a huge shell-model space for nuclei with a sufficiently large number of particles, we have to use some types of truncating schemes for the fermion space.In many cases, the so-called SD -pair circumcision of the enormous fermion-shell space is used, however, difficulties remain regarding the application of "realistic" SD -nucleated pairs as building blocks in the model [8][9][10][11].To overcome such obstacles in the microscopic calculations, the parameters of the IBMare determined by the method of mapping the collective shell space into the bosonic one, and then systematic calculations are carried out in the bosonic space. The Ohtsuka-Arima-Yakello (OAY) map [12,13] based on the generalized seniority scheme was used most of all [14].…”