Study of various few-body systems using Gaussian expansion method (GEM)

TL;DR

This paper reviews the Gaussian expansion method (GEM), highlighting its high accuracy, wide applicability across various few-body systems, and successful predictions in nuclear physics, atomic physics, and exotic hadrons.

Contribution

It provides a comprehensive overview of GEM's methodology, demonstrating its effectiveness and versatility in solving few-body Schrödinger equations across multiple fields.

Findings

GEM achieves high accuracy in few-body calculations.

GEM successfully predicts properties before experimental confirmation.

GEM is applicable to a wide range of physical systems.

Abstract

We review our calculation method, Gaussian expansion method (GEM), and its applications to various few-body (3- to 5-body) systems such as 1) few-nucleon systems, 2) few-body structure of hypernuclei, 3) clustering structure of light nuclei and unstable nuclei, 4) exotic atoms/molecules, 5) cold atoms, 6) nuclear astrophysics and 7) structure of exotic hadrons. Showing examples in our published papers, we explain i) high accuracy of GEM calculations and its reason, ii) wide applicability of GEM and iii) successful predictions by GEM calculations before measurements. GEM was proposed 30 years ago and has been applied to a variety of subjects. To solve few-body Schroedinger equations accurately, use is made of the Rayleigh-Ritz variational method for bound states, the complex-scaling method for resonant states and the Kohn-type variational principle to S-matrix for scattering states. The total wave function is expanded in terms of few-body Gaussian basis functions spanned over all the sets of rearrangement Jacobi coordinates. Gaussians with ranges in geometric progression work very well both for short-range and long-range behavior of the few-body wave functions. Use of Gaussians with complex ranges gives much more accurate solution when the wave function has many oscillations.