Complex-scaled no-core shell model calculations of bound and unbound nuclear states in light nuclei

TL;DR

This paper introduces a method to incorporate complex scaling into the no-core shell model, enabling the calculation of both bound and unbound nuclear states in light nuclei using realistic interactions.

Contribution

It presents a new procedure for applying complex scaling within the no-core shell model framework to study nuclear resonance states.

Findings

Successfully calculated bound states of light nuclei.

Determined resonance states of $^5$He and $^5$Li.

Demonstrated the method's applicability with realistic interactions.

Abstract

The complex scaling method is commonly used to describe decaying states, but its applications are limited because the Hamiltonian operator must contain only relative coordinates. This has hindered the use of complex scaling in models defined with laboratory single-particle coordinates, and in particular one of the most important model in low-energy nuclear physics, the no-core shell model. We will then present a straightforward procedure for introducing complex scaling in the no-core shell model in order to calculate nuclear resonance states. For that matter, the complex-scaled two-body matrix elements must firstly be determined, and the resulting many-body Hamiltonian complex symmetric matrix must be diagonalized afterwards. Applications pertain to the bound ground states of the lightest nuclei $^2{\rm H}$, $^3{\rm H}$, $^3{\rm He}$, and $^4{\rm He}$, as well as the resonance ground states of $^5$He and $^5$Li, whereby the realistic interaction Daejeon16 is utilized.