Explicitly correlated Gaussians with tensor pre-factors: analytic matrix elements

TL;DR

This paper derives analytic matrix elements for a specialized form of explicitly correlated Gaussians with tensor pre-factors, facilitating variational calculations in few-body nuclear and particle physics systems.

Contribution

It introduces new analytic formulas for matrix elements involving tensor pre-factor Gaussians, enabling more efficient calculations in complex quantum systems.

Findings

Derived explicit formulas for overlap, kinetic, and Coulomb matrix elements.

Validated formulas with hydrogen atom p- and d-wave calculations.

Enhanced computational tools for few-body quantum systems.

Abstract

We consider a specific form of explicitly correlated Gaussians -- with tensor pre-factors -- which appear naturally when dealing with certain few-body systems in nuclear and particle physics. We derive analytic matrix elements with these Gaussians -- overlap, kinetic energy, and Coulomb potential -- to be used in variational calculations of those systems. We also perform a quick test of the derived formulae by applying them to p- and d-waves of the hydrogen atom.