Correlated Gaussian Hyperspherical Method for Few-Body Systems

TL;DR

This paper introduces a new numerical method combining correlated Gaussian basis functions with hyperspherical representation to efficiently analyze few-body quantum systems, demonstrating robustness and applicability to complex interactions.

Contribution

The paper presents a novel correlated Gaussian hyperspherical method for few-body systems, improving computational efficiency and accuracy over existing techniques.

Findings

Successfully applied to three- and four-body systems

Extracted key coefficients at unitarity for four-fermion systems

Proven to be robust and efficient

Abstract

We develop an innovative numerical technique to describe few-body systems. Correlated Gaussian basis functions are used to expand the channel functions in the hyperspherical representation. The method is proven to be robust and efficient compared to other numerical techniques. The method is applied to few-body systems with short range interactions, including several examples for three- and four-body systems. Specifically, for the two-component, four-fermion system, we extract the coefficients that characterize its behavior at unitarity.