Description of He isotopes using the particle-particle random-phase approximation model

TL;DR

This paper uses the two-neutron RPA model to describe helium isotopes, revealing shell inversion in $^{9}$He and providing insights into their ground and excited states, including energies and wave functions.

Contribution

It introduces a unified RPA framework linking helium isotopes' properties, emphasizing the role of $^{9}$He in understanding other isotopes and shell inversion phenomena.

Findings

Shell inversion of $2s$-$1p_{1/2}$ in $^{9}$He

Ground states of $^{9}$He and $^{10}$He are slightly unbound

Accurate two-neutron separation energy in $^{8}$He

Abstract

The two-neutron RPA model has been used to describe helium isotopes with N (the neutron number) = 4, 6, 7, 8 in their ground and excited states. The properties of all these isotopes are given by a single system of equations so that their properties are interdependent. Since the ground states of $^{9}$He and $^{10}$He are still not well established, we have looked how the properties of $^{9}$He induce the properties of the other isotopes, energies and wave functions. Our results suggest an inversion of $2s$-$1p_{1/2}$ shells in $^{9}$He. The corresponding ground states of $^{9}$He and $^{10}$He are slightly unbound and respectively $1/2^+$ and $0^+$ states while the $1/2^-$ and $0^+$ seen in experiments appear to be excited states. With this assumption on $^{9}$He, we get not only a nice picture of $^{10}$He but also a very good two-neutron separation energy in $^{8}$He.