# Individual dipole toroidal states: main features and search in (e,e') reaction

## TL;DR

This study investigates low-energy toroidal and compressional states in $^{24}$Mg using QRPA with Skyrme forces, analyzing their properties and proposing a method to identify them in electron scattering experiments.

## Contribution

The paper provides a detailed analysis of toroidal and compressional states, including their responses and transition probabilities, and introduces a two-step scheme for their identification in inelastic electron scattering.

## Key findings

- Identification of specific toroidal and compressional states in $^{24}$Mg.
- Analysis of the interplay between convective and magnetization nuclear currents.
- Proposal of a two-step scheme for distinguishing these states in experiments.

## Abstract

Individual low-energy E1 toroidal and compressional states (TS and CS) produced by the convective nuclear current ${\bf j}_{\rm c}$ were recently predicted for $^{24}$Mg in the framework of quasiparticle random-phase-approximation (QRPA) with Skyrme forces. In the present QRPA study with Skyrme parametrization SLy6, we explore in more detail properties of these states (toroidal and compressional responses, current distributions, and transitions probabilities $B(E1K, 0^+0 \to 1^-K),\; B(E3K, 0^+0 \to 3^-K)$, $B(M2K, 0^+0 \to 2^-K)$ with $K=$0 and 1) and analyze the possibility to discriminate and identify TS in inelastic electron scattering to back angles. The interplay of the convective ${\bf j}_{\rm c}$ and magnetization ${\bf j}_{\rm m}$ nuclear currents is thoroughly scrutinized. A two-step scheme for identification of TS in $(e,e')$ reaction is proposed. The key element of the scheme is the strong interference of the orbital and spin contributions, resulting in specific features of E1 and M2 transversal form factors.