# Double charge-exchange phonon states

## TL;DR

This paper investigates double charge-exchange phonon states in neutron-rich nuclei, deriving approximate laws for their energies using commutator relations, and analyzing the effects of Coulomb and strong nuclear interactions.

## Contribution

It introduces a novel analytical approach employing quartic and double commutator relations to estimate energies of double charge-exchange states in nuclei.

## Key findings

- Approximate laws for energy differences: $E_{DIAS} - 2E_{IAS} \\sim 1.5 A^{-1/3}$ MeV.
- Energy difference $E_{DGTR} - E_{DIAS} - 2(E_{GTR} - E_{IAS}) \\sim 16 A^{-1}$ MeV.
- Coulomb effects dominate $E_{DIAS} - 2E_{IAS}$, while strong interaction differences influence $E_{DGTR} - E_{DIAS}$.

## Abstract

We study double charge-exchange phonon states in neutron-rich nuclei, in particular the double isobaric analog states and the double Gamow-Teller excitations, induced by the double isospin operator $\sum_{i,j=1}^At_-(i) t_-(j)$ and spin-isospin operator $\sum_{i,j=1}^A{\sigma}(i) t_-(i){\sigma}(j) t_-(j)$, respectively. We employ quartic commutator relations to evaluate the average energies $E_{\rm DIAS} - 2E_{\rm IAS}$ and $E_{\rm DGTR}-E_{\rm DIAS} - 2(E_{\rm GTR}-E_{\rm IAS})$, and conventional double commutator relations to evaluate the average energies of $E_{\rm GTR}-E_{\rm IAS}$ and $E_{\rm IAS}$. We have found that the corrections due to quartic commutators follow the approximate laws: $E_{\rm DIAS} - 2E_{\rm IAS}\approx \frac{3}{2} A^{-1/3}$ MeV and $E_{\rm DGTR}-E_{\rm DIAS} - 2(E_{\rm GTR}-E_{\rm IAS})\approx 16 A^{-1}$ MeV. While the former is dominated by direct Coulomb effects, since Coulomb exchange cancels out to some extent with isospin symmetry breaking contributions originated form the nuclear strong force, the latter is sensitive to the difference in strength between the spin and spin-isospin chanels of the strong interaction.