Hydrogen-like ions in plasma environment

TL;DR

This paper investigates the behavior of hydrogen-like ions in various plasma environments, deriving new scaling relations, analyzing plasma effects on bound states, and calculating oscillator strengths and polarizabilities.

Contribution

It introduces generalized scaling ideas for plasma screening effects, derives new relations connecting plasma parameters, and provides analytical expressions for oscillator strengths and polarizabilities.

Findings

Increased plasma screening reduces bound states around ions.

Scaling relations connect critical screening constants with ion charge.

Analytical formulas for oscillator strengths and polarizabilities are established.

Abstract

The behavior of H-like ions embedded in astrophysical plasmas in the form of \emph{dense, strongly and weakly coupled} plasmas are investigated. In these, the increase and decrease in temperature is impacted with a change in confinement radius $(r_{c})$. Two independent and generalized scaling ideas have been applied to modulate the effect of plasma screening constant ($\lambda$) and charge of ion ($Z$) on such systems. Several new relations are derived to interconnect the original Hamiltonian and two scaled Hamiltonians. In exponential cosine screened Coulomb potential (ECSCP) (dense) and weakly coupled plasma (WCP) these scaling relations have provided a linear equation connecting the critical screening constant $(\lambda^{(c)})$ and $Z$. Their ratio offers a state-dependent constant, beyond which, a particular state vanishes. Shannon entropy has been employed to understand the plasma effect on the ion. With increase in $\lambda$, the accumulation of opposite charge surrounding the ion increases leading to a reduction in number of bound states. However, with rise in ionic charge $Z$, this effect can be delayed. The competing effect of plasma charge density ($n_e$) and temperature in WCP and ECSCP is investigated. A recently proposed simple virial-like theorem has been established for these systems. Multipole ($k=1-4$) oscillator strength (OS) and polarizabilities for these are studied considering $1s, 2s$ states. As a bonus, analytical closed-form expressions are derived for $f^{(k)}$ and $\alpha^{(k)} (k=1-4)$ involving $1s$ and $2s$ state, for \emph{free H-like ion}.