Proton and neutron correlations in $^{10}$B

TL;DR

This study uses antisymmetrized molecular dynamics to analyze proton-neutron correlations and the effects of spin-orbit interactions on energy spectra in $^{10}$B, revealing the importance of genuine NNN forces for level ordering.

Contribution

It introduces a detailed analysis of $^{10}$B states focusing on $pn$ correlations and the role of spin-orbit interactions, highlighting the significance of genuine NNN forces.

Findings

The $3^+_10$ state gains significant spin-orbit energy, lowering its energy.

The $1^+_10$ state shows minimal energy gain from spin-orbit interaction.

Spin-orbit interaction influences $pn$ pair configurations differently depending on the state.

Abstract

We investigate positive-parity states of $^{10}$B with the calculation of antisymmetrized molecular dynamics focusing on $pn$ pair correlations. We discuss effects of the spin-orbit interaction on energy spectra and $pn$ correlations of the $J^\pi T=1^+_10$, $=3^+_10$, and $0^+_11$ states. The $1^+_10$ state has almost no energy gain of the spin-orbit interaction, whereas the $3^+_10$ state gains the spin-orbit interaction energy largely to come down to the ground state. We interpret a part of the two-body spin-orbit interaction in the adopted effective interactions as a contribution of the genuine $NNN$ force, and find it to be essential for the level ordering of the $3^+_10$ and $1^+_10$ states in $^{10}$B. We also apply a $2\alpha+pn$ model to discuss effects of the spin-orbit interaction on $T=0$ and $T=1$ $pn$ pairs around the 2$\alpha$ core. In the spin-aligned $J^\pi T=3^+0$ state, the spin-orbit interaction affects the $(ST)=(10)$ pair attractively and keeps the pair close to the core, whereas, in the $1^+0$ state, it gives a minor effect to the $(ST)=(10)$ pair. In the $0^+1$ state, the $(ST)=(01)$ pair is somewhat dissociated by the spin-orbit interaction.