Shell Model Symmetries-Honoring Franco Iachello

TL;DR

This paper explores symmetries and schematic interactions in the shell model, comparing calculations with collective models to understand transition strengths and nuclear properties.

Contribution

It introduces analysis of shell model symmetries and schematic interactions, providing comparisons with collective models for better understanding.

Findings

Transition strengths decrease exponentially with certain interactions

Shell model calculations align with collective model results for B(E2) and quadrupole moments

Symmetries of pairing interactions are characterized

Abstract

We discuss L=0 vs L=2 couplings, symmetries of the pairing interaction for neutrons and protons, and the J_{max} interaction. We show that certain schematic interactions yield exponentially decreasing transition strengths.We compare shell model calculations of B(E2)'s and quadrupole moments in the p-f shell with collective model results.