Quantum Monte Carlo Calculations of neutron-$\alpha$ Scattering via an Integral Relation

TL;DR

This paper extends Quantum Monte Carlo methods to accurately compute unbound nuclear states, specifically neutron-alpha scattering, by inferring long-range wave function amplitudes from short-range integrals, thus unifying bound and unbound state descriptions.

Contribution

The authors develop a new QMC-based integral relation method to calculate unbound states, enabling systematic studies of complex nuclear reactions within an ab initio framework.

Findings

Successfully reproduces neutron-alpha scattering results

Demonstrates the method's potential for complex nuclear systems

Provides a pathway for unified bound and unbound state calculations

Abstract

Nuclear physics seeks to describe both bound and unbound states within a unified predictive framework. While coordinate-space Quantum Monte Carlo (QMC) methods have successfully computed bound states for systems with $A \leq 12$, their application to unbound states remains limited. In this work, we extend the QMC approach to enable a broader range of unbound-state calculations. Our method infers long-range amplitudes in the wave function from integrals over the short-range interaction region. By evaluating these integrals using Green's Function Monte Carlo wave functions with the Argonne $v_{18}$ potential, we accurately reproduce existing results for neutron-alpha scattering. This approach provides a systematic pathway for studying more complex nuclear systems, including coupled-channel scattering and the effects of three-nucleon forces. It serves as a powerful tool for advancing $\textit{ab initio}$ calculations in nuclear reactions, paving the way for a unified framework that consistently describes both bound and scattering states within a single theoretical approach.