Shell model method for Gamow-Teller transitions in heavy, deformed nuclei

Abstract

A method for calculation of Gamow-Teller transition rates is developed by using the concept of the Projected Shell Model (PSM). The shell model basis is constructed by superimposing angularmomentum-projected multi-quasiparticle configurations, and nuclear wave functions are obtained by digonalizing the two-body interactions in these projected states. Calculation of transition matrix elements in the PSM framework is discussed in detail, and the effects caused by the Gamow-Teller residual forces and by configuration-mixing are studied. With this method, it may become possible to perform a state-by-state calculation for β-decay and electron-capture rates in heavy, deformed nuclei at finite temperatures. Our first example indicates that, while experimentally known Gamow-Teller transition rates from the ground state of the parent nucleus are reproduced, stronger transitions from some low-lying excited states are predicted to occur, which may considerably enhance the total decay rates once these nuclei are exposed to hot stellar environments.

Projected shell model for Gamow-Teller transitions in heavy, deformed nuclei

“…together with the Ikeda sum-rule can then be used for testing the codes and checking numerical correctness [32].…”

“…An initial attempt for the PSM to calculate GT transitions was reported in Ref. [32]. The work has recently been extended to odd-mass systems, which will be reported elsewhere [33].…”

A shell model method for weak interaction rates in heavy, deformed nuclei

“…Here, we present a preliminary example published in [8]. In the left panel of The other transition probabilities associated with the excited states are our prediction.…”

“…Within the framework of the PSM, a computer code for GT rates has recently been developed and tested [8]. Here, we present a preliminary example published in [8].…”

The Ground State Nilsson Quantum Numbers of the Odd-Odd138,140Pr Nuclei

“…where t 1/2 is the half-life and f is a dimensionless quantity depending on the charge of the nucleus and the energy and multipolarity of the transition [7]. |M if | 2 is nuclear matrix element and it is defined as:…”