Resonances and collisional properties of neutron-rich helium isotopes in the adiabatic hyperspherical representation

TL;DR

This paper employs the adiabatic hyperspherical representation to study resonances and collisional properties of neutron-rich helium isotopes, providing insights into their bound states, resonances, and scattering processes using a simplified interaction model.

Contribution

It introduces a novel application of the adiabatic hyperspherical method to three- and four-body helium systems with a simplified interaction model, reproducing key nuclear properties.

Findings

Reproduces $^{6}$He bound and resonance states.

Analyzes $^{6}$He electric quadrupole transition.

Studies $^{7}$He scattering and recombination processes.

Abstract

This work treats few-body systems consisting of neutrons interacting with a $^{4}{\mathrm{He}}$ nucleus. The adiabatic hyperspherical representation is utilized to solve the $N$-body Schr$\ddot{\mathrm{o}}$dinger equation for the three- and four-body systems, treating both $^{6}{\mathrm{He}}$ and $^{7}{\mathrm{He}}$ nuclei. A simplified central potential model for the $^{4}{\mathrm{He}}-n$ interaction is used in conjunction with a spin-dependent three-body interaction to reproduce $^{6}{\mathrm{He}}$ bound-state and resonance properties as well as properties for the $^{8}{\mathrm{He}}$ nucleus in its ground-state. With this Hamiltonian, the adiabatic hyperspherical representation is used to compute bound and scattering states for both $^{6}{\mathrm{He}}$ and $^{7}{\mathrm{He}}$ nuclei. For the $^{6}{\mathrm{He}}$ system, the electric quadrupole transition between the $0^{+}$ and $2^{+}$ state is investigated. For the $^{7}{\mathrm{He}}$ system, $^{6}{\mathrm{He}}+n$ elastic scattering is investigated along with the four-body recombination process $^{4}{\mathrm{He}}+n+n+n\rightarrow$$^{6}{\mathrm{He}}+n$ and breakup process $^{6}{\mathrm{He}}+n\rightarrow$$^{4}{\mathrm{He}}+n+n+n$.