Spin dependent operators in correlated gaussian bases

TL;DR

This paper introduces new, simplified formulae for spin-dependent operator matrix elements within the correlated Gaussian basis, enhancing computational efficiency and universality in quantum few-body problem calculations.

Contribution

It provides novel, compact expressions for spin-dependent matrix elements using geometrical functions, improving upon the cumbersome formulas in prior methods.

Findings

New formulae for spin-dependent matrix elements derived

Expressions expressed in universal geometrical functions

Enhanced numerical applicability for quantum few-body problems

Abstract

In their textbook, Suzuki and Varga [Y. Suzuki and K. Varga, {\em Stochastic Variational Approach to Quantum-Mechanical Few-Body Problems} (Springer, Berlin, 1998)] present the stochastic variational method with the correlated Gaussian basis in a very exhaustive way. The matrix elements for central potentials are put under a pleasant form but the elements for spin dependent operators, when treated, are given as very cumbersome expressions. In this paper, we find a lot of new formulae for those elements. Their expressions are given in terms of the same geometrical functions that appear in the case of central potentials. These functions get therefore a universal status; this property is very useful for numerical applications.