Transition probabilities in the U(6) limit of the Symplectic Interacting Vector Boson Model

TL;DR

This paper analyzes the transition probabilities within the U(6) limit of the Symplectic Interacting Vector Boson Model, providing analytical expressions and comparing theoretical results with experimental nuclear data.

Contribution

It derives analytical matrix elements for Sp(12,R) generators in the U(6) limit and applies them to calculate E2 transition probabilities in nuclei.

Findings

Analytical expressions for transition matrix elements are obtained.

Comparison with experimental data validates the model's predictions.

The symplectic extension enhances the description of nuclear collective states.

Abstract

The tensor properties of the algebra generators and the basis are determined in respect to the reduction chain $Sp(12,R) \supset U(6)% \supset U(3)\otimes U(2)\supset O(3)\otimes (U(1)\otimes U(1))$, which defines one of the dynamical symmetries of the Interacting Vector Boson Model. The action of the Sp(12,R) generators as transition operators between the basis states is presented. Analytical expressions for their matrix elements in the symmetry-adapted basis are obtained. As an example the matrix elements of the E2 transition operator between collective states of the ground band are determined and compared with the experimental data for the corresponding intraband transition probabilities of nuclei in the actinide and rare earth region. On the basis of this application the important role of the symplectic extension of the model is analyzed.