# Determination of the scattering length for Rb-Cs X$^{1}\Sigma ^{+}$ ground electronic state using a variational method

## TL;DR

This paper calculates the scattering length for Rb-Cs atomic collisions using a variational R-matrix method with finite element expansion, providing accurate results and computational efficiency improvements.

## Contribution

It introduces a variational R-matrix approach with FEM for calculating scattering lengths, enhancing computational efficiency and accuracy for Rb-Cs interactions.

## Key findings

- Calculated scattering length for Rb-Cs ground state.
- Validated results against previous literature.
- Demonstrated efficiency of FEM-based R-matrix method.

## Abstract

We performed the calculation of the scattering length for the elastic collision between the rubidium and cesium atoms. For this we applied a variational procedure based on the R-matrix theory for unbound states employing the finite element method (FEM) for expansion of the wave-function in terms of a finite set of local basis functions. The FEM presents as advantages the possibility of the development of a efficient matrix inversion algorithm which significantly reduces the computation time to calculate the R matrix. We also tested a potential energy curve with spectroscopic accuracy obtained before from a direct adjustment procedure of experimental data of the $X^{1}\Sigma^{+}$ state based on genetic algorithm. The quality of our result was evaluated by comparing them with several ones previously published at literature.