Inversion doublets of 3N+N cluster structure in excited states of $^4$He

TL;DR

This study uses four-body calculations with correlated Gaussian bases to analyze excited states of helium-4, revealing cluster structures and the role of tensor forces, and identifying inversion doublet partners among negative-parity states.

Contribution

It provides a detailed analysis of helium-4 excited states, highlighting the cluster configurations and the significance of tensor forces in level spacing, especially for the $0^+_2$ state.

Findings

The $0^+_2$ state becomes a resonance.

Negative-parity states are inversion doublet partners of $0^+_2$.

Cluster configurations are identified as $^3$H+$p$ and $^3$He+$n$.

Abstract

Excited states of $^4$He are studied in four-body calculations with explicitly correlated Gaussian bases. All the levels below $E_{\rm x}$=26 MeV are reproduced reasonably well using realistic potentials. An analysis is made to show how the $0^+_2$ state becomes a resonance but those having almost the same structure as this state in different spin-isospin channels are not observed as resonances. The role of tensor force is stressed with a particular attention to the level spacing between the two $0^-$ states. The calculation of spectroscopic amplitudes, nucleon decay widths, and spin-dipole transition strengths demonstrates that the $0^+_2$ state and the three lowest-lying negative-parity states with $0^-$ and $2^-$ have $^3$H+$p$ and $^3$He+$n$ cluster configurations, leading to the interpretation that these negative-parity states are the inversion doublet partners of the $0^+_2$ state.