Precise energy eigenvalues of hydrogen-like ion moving in quantum plasmas

TL;DR

This paper derives the electrostatic potential for a moving charge in quantum plasma and uses variational methods to calculate the energy levels of hydrogen-like ions, revealing shifts and crossings influenced by plasma density and ion velocity.

Contribution

It provides an analytic form of the potential in quantum plasma and applies variational calculations to determine precise energy eigenvalues under these conditions.

Findings

Energy levels shift towards the continuum with increasing plasma density.

Level crossing phenomena occur as ion velocity varies.

Potential includes Debye-Huckel and wake components.

Abstract

The analytic form of the electrostatic potential felt by a slowly moving test charge in quantum plasma is being derived. It has been shown that the potential composed of two parts: Debye-Huckel screening term and near-field wake potential which depends on the velocity of the test charge and the number density of the plasma electrons. Rayleigh-Ritz variational calculation has been done to estimate precise energy eigenvalues of hydrogen-like ion under such plasma environment. A detailed analysis shows that the energy levels are gradually moves to the continuum with increasing plasma electron density while level crossing phenomenon have been observed with the variation of ion velocity.