Abstract
We explore the dynamical symmetries of the shell model number conserving algebra, which define three types of pairing and quadrupole phases, with the aim to obtain the prevailing phase or phase transition for the real nuclear systems in a single shell. This is achieved by establishing a correspondence between each of the pairing bases with the Elliott’s SU(3) basis that describes collective rotation of nuclear systems. This allows for a complete classification of the basis states of different number of particles in all the limiting cases. The probability distribution of the SU(3) basis states within theirs corresponding pairing states is also obtained. The relative strengths of dynamically symmetric quadrupole-quadrupole interaction in respect to the isoscalar, isovector and total pairing interactions define a control parameter, which estimates the importance of each term of the Hamiltonian in the correct reproduction of the experimental data for the considered nuclei.
Highlights
The present-day microscopic approaches for the description of the complex nuclear spectra are based either on mean-field methods or on shell model [1]
We explore the dynamical symmetries of the shell model number conserving algebra, which define three types of pairing and quadrupole phases, with the aim to obtain the prevailing phase or phase transition for the real nuclear systems in a single shell
As stated in the Introduction, the dynamical symmetries unified in the reduction schemes presented in Figs. 1 and 2 can be considered as different phases, corresponding to the different types of residual interactions [21], that are included in the microscopic plus Quadrupole Model (PQM)
Summary
The present-day microscopic approaches for the description of the complex nuclear spectra are based either on mean-field methods or on shell model [1]. Both are employing complicated computer intensive algorithms and are rather cumbersome, time consuming and difficult for direct application to the interpretation of the experimental results. In this paper we outline such dynamical symmetries that can be identified in the number conserving shell model algebra They introduce the two most important residual interactions of the many-body nuclear system - the pairing and quadrupole-quadrupole interaction, which are the fundamental terms in the microscopic version of the Pairing plus Quadrupole Model (PQM) [2,3,4]. It is our further aim to establish possible relations between the subalgebras in the chains of the dynamical symmetries and to employ them in evaluating the importance of each interaction in the formation of the nuclear spectra
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