Cluster and toroidal aspects of isoscalar dipole excitations in $^{12}$C

TL;DR

This paper explores low-energy isoscalar dipole excitations in carbon-12, revealing a developed 3-alpha cluster state and a toroidal dipole mode, with implications for understanding nuclear vorticity and excitation mechanisms.

Contribution

It introduces a combined theoretical approach to distinguish cluster and toroidal modes in $^{12}$C, highlighting the nature of low-energy dipole states beyond traditional models.

Findings

Identification of two low-energy dipole modes: a cluster state and a toroidal mode.

The cluster state involves large amplitude cluster motion beyond 1p-1h space.

The toroidal dipole mode is mainly described by 1p-1h excitations and excitable by the toroidal dipole operator.

Abstract

We investigated cluster and toroidal aspects of isoscalar dipole excitations in $^{12}$C based on the shifted basis antisymmetrized molecular dynamics combined with the generator coordinate method, which can describes 1p-1h excitations and $3\alpha$ dynamics. In the $E=10-15$ MeV region, we found two low-energy dipole modes separating from the giant dipole resonance. One is the developed $3\alpha$-cluster state and the other is the toroidal dipole mode. The cluster state is characterized by the large amplitude cluster motion beyond the 1p-1h model space, whereas the toroidal dipole mode is predominantly described by 1p-1h excitations on the ground state. The low-energy dipole states are remarkably excited by the toroidal dipole operator, which can measure the nuclear vorticity. For compressive dipole transition strengths, a major part is distributed in the $30-50$ MeV region for the giant dipole resonance, and 5\% of the total energy weighted sum exist in the $E<20$ MeV region.