Energy levels of neutral atoms via a new perturbation method

TL;DR

This paper introduces a new analytical perturbation method to accurately compute energy levels of neutral atoms with Yukawa potential, improving convergence speed and providing results for various screening parameters.

Contribution

The paper presents a novel perturbation approach for solving the Schrödinger equation with Yukawa potential, enhancing accuracy and computational efficiency.

Findings

Scaled screening parameter $oldsymbol{ extit{ extalpha}}^{'}$ ranges from 0 to 0.4.

Method improves convergence speed of energy eigenvalues.

Energy levels for various $oldsymbol{ extalpha}^{'}$ values are reported.

Abstract

The energy levels of neutral atoms supported by Yukawa potential, $V(r)=-Z exp(-\alpha r)/r$, are studied, using both dimensional and dimensionless quantities, via a new analytical methodical proposal (devised to solve for nonexactly solvable Schrodinger equation). Using dimensionless quantities, by scaling the radial Hamiltonian through $y=Zr$ and $\alpha^{'}=\alpha/Z$, we report that the scaled screening parameter $\alpha^{'}$ is restricted to have values ranging from zero to less than 0.4. On the other hand, working with the scaled Hamiltonian enhances the accuracy and extremely speeds up the convergence of the energy eigenvalues. The energy levels of several new eligible scaled screening parameter $\alpha^{'}$ values are also reported.