Confined helium on Lagrange meshes

TL;DR

This paper applies the Lagrange-mesh method to study confined helium atoms, achieving high-precision energy calculations and properties under various confinement conditions with efficient computation.

Contribution

It introduces a novel application of the Lagrange-mesh method to confined helium atoms, providing highly accurate results for energies and pressures in different confinement scenarios.

Findings

Achieved 11-15 significant figure accuracy in energy calculations.

Successfully modeled both soft and hard confinement scenarios.

Improved upon existing literature results for larger confinement radii.

Abstract

The Lagrange-mesh method has the simplicity of a calculation on a mesh and can have the accuracy of a variational method. It is applied to the study of a confined helium atom. Two types of confinement are considered. Soft confinements by potentials are studied in perimetric coordinates. Hard confinement in impenetrable spherical cavities is studied in a system of rescaled perimetric coordinates varying in [0,1] intervals. Energies and mean values of the distances between electrons and between an electron and the helium nucleus are calculated. A high accuracy of 11 to 15 significant figures is obtained with small computing times. Pressures acting on the confined atom are also computed. For sphere radii smaller than 1, their relative accuracies are better than $10^{-10}$. For larger radii up to 10, they progressively decrease to $10^{-3}$, still improving the best literature results.