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

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 $J^{\pi }T=1_1^{+}0$, $=3_1^{+}0$, and $0_1^{+}1$ states. The $1_1^{+}0$ state has almost no energy gain of the spin-orbit interaction, whereas the $3_1^{+}0$ 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 $3_1^{+}0$ and $1_1^{+}0$ 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.

Comments: 12 pages 9 figures