Symplectic structure and monopole strength in 12C

TL;DR

This paper explores the connection between monopole transition strength and cluster structures in excited states of carbon-12 using an algebraic model based on symplectic algebra, revealing classification of states via a quantum number.

Contribution

It introduces an $Sp(2,R)_z$ algebraic framework to efficiently describe $^{12}$C cluster states and their monopole transitions, linking algebraic structure to physical observables.

Findings

States with strong monopole transitions are classified by an $Sp(2,R)_z$ quantum number.

The algebraic model reduces basis states needed for describing $^{12}$C cluster structures.

The $Sp(2,R)_z$ algebra effectively captures the relation between monopole strength and cluster configurations.

Abstract

The relation between the monopole transition strength and existence of cluster structure in the excited states is discussed based on an algebraic cluster model. The structure of $^{12}$C is studied with a 3$\alpha$ model, and the wave function for the relative motions between $\alpha$ clusters are described by the symplectic algebra $Sp(2,R)_z$, which corresponds to the linear combinations of $SU(3)$ states with different multiplicities. Introducing $Sp(2,R)_z$ algebra works well for reducing the number of the basis states, and it is also shown that states connected by the strong monopole transition are classified by a quantum number $\Lambda$ of the $Sp(2,R)_z$ algebra.