The quadrupole collective model from a Cartan-Weyl perspective

TL;DR

This paper develops an algebraic approach to calculating matrix elements of quadrupole variables and momenta in nuclear collective models using a Cartan-Weyl perspective, simplifying computations through an intermediate state method.

Contribution

It introduces a novel algebraic framework based on SU(1,1)×O(5) for calculating matrix elements in nuclear collective models, enhancing computational efficiency.

Findings

Matrix elements are computed algebraically using a Cartan-Weyl approach.

The method simplifies calculations of quadrupole phonon operators.

The approach is demonstrated within a harmonic oscillator implementation.

Abstract

The matrix elements of the quadrupole variables and canonic conjugate momenta, emerging from collective nuclear models are calculated within a $SU(1,1)\times O(5)$ basis. Using a harmonic oscillator implementation of the SU(1,1) degree of freedom, it can be shown that the matrix elements of the quadrupole phonon creation and annihilation operators can be calculated in a pure algebraic way, making use of an intermediate state method.