Transition from Spherical to Deformed Shapes of Nuclei in the Monte Carlo Shell Model

Abstract

The transition from spherical to deformed shapes is studied in terms of large-scale shell-model calculations for Ba isotopes as a function of valence nucleon number with fixed single-particle space and Hamiltonian. A new version of the Monte Carlo shell model is introduced so as to incorporate pairing correlations efficiently, by utilizing condensed pair bases. The energy levels and electromagnetic matrix elements are described in agreement with experiments throughout the transitional region. The orbital M1 sum rule is calculated as a measure of the deformation evolution, and the Q-phonon picture is shown to be reasonable from spherical to deformed nuclei.

Level lifetimes and quadrupole moments from Coulomb excitation in the Ba chain and the N = 80 isotones

“…figure 3 (a) and (c)). The preliminary quadrupole moments (middle panel (b) of figure 3) agree with recent Monte-Carlo shell-model calculations [28,29]. Different model spaces are used for this calculations when the neutron number N is above or below the shell closure of N = 82.…”

“…Still, low-lying energy levels with positive parity and a e-mail: bauer@ikp.tu-darmstadt.de electrical quadrupole transition probabilities of neutronrich Ba isotopes have been successfully described throughout the transitional region in the framework of the Monte Carlo shell model based on a quadrupole-plus-pairing approach [5,6].…”

New effective interaction forpf-shell nuclei and its implications for the stability of theN=Z=28closed core

“…The pf shell is the current frontier of conventional methods, while the MCSM is applicable and useful in much larger model spaces, as demonstrated in Refs. [11,12,13,14]. This paper is organized as follows.…”

Monte Carlo Hamiltonian from stochastic basis

“…We have considered the matrix M ij ± δM ij and diagonalized it and computed correspondingly H ef f via Eqs. (4,5). This gives upper bounds on the error of energy eigenvalues and on the error in the wave functions.…”

“…In recent years, Monte Carlo methods have been widely used to solve problems in quantum physics. For example, with quantum Monte Carlo there has been improvement in nuclear shell model calculations [5]. A proposal to solve the sign problem in Monte Carlo Greens function method, useful for spin models has been made by Sorello [6].…”