# Critical parameters and spherical confinement of H atom in screened Coulomb potential

## TL;DR

This paper reports precise critical parameters for three screened Coulomb potentials and investigates spherical confinement effects on a hydrogen atom in a dense plasma, using the generalized pseudospectral method for high accuracy.

## Contribution

It provides new accurate estimates of critical parameters for Hulthén, Yukawa, and exponential cosine screened potentials and studies spherical confinement effects with detailed eigenvalue calculations.

## Key findings

- Accurate critical parameters for all states with n ≤ 10.
- Enhanced eigenvalue accuracy for confined hydrogen atom.
- First-time presentation of some critical parameters.

## Abstract

Critical parameters in three screened potentials, namely, Hulth\'en, Yukawa and exponential cosine screened Coulomb potential are reported. Accurate estimates of these parameters are given for each of these potentials, for all states having $n \leq 10$. Comparison with literature results is made, wherever possible. Present values compare excellently with reference values; for higher $n,\ell$, our results are slightly better. Some of these are presented for first time. Further, we investigate the spherical confinement of H atom embedded in a dense plasma modeled by an exponential cosine screened potential. Accurate energies along with their variation with respect to box size and screening parameter are calculated and compared with reference results in literature. Sample dipole polarizabilities are also provided in this case. The generalized pseudospectral method is used for accurate determination of eigenvalues and eigenfunctions for all calculations.