Redshift of the Heα emission line of He-like ions under a plasma environment

Abstract

By carefully following the spatial and temporal criteria of the Debye-H\uckel (DH) approximation, we present a detailed theoretical study on the redshifts of the spectroscopically isolated ${\mathrm{He}}_{\ensuremath{\alpha}}$ lines corresponding to the $1s2p{\phantom{\rule{0.16em}{0ex}}}^{1}P\ensuremath{\rightarrow}1{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S$ emission from two-electron ions embedded in external dense plasma. We first focus our study on the ratio $R=\mathrm{\ensuremath{\Delta}}{\ensuremath{\omega}}_{\ensuremath{\alpha}}/{\ensuremath{\omega}}_{o}$ between the redshift $\mathrm{\ensuremath{\Delta}}{\ensuremath{\omega}}_{\ensuremath{\alpha}}$ due to the external plasma environment and the energy ${\ensuremath{\omega}}_{o}$ of the ${\mathrm{He}}_{\ensuremath{\alpha}}$ line in the absence of the plasma. Interestingly, the result of our calculation shows that this ratio $R$ turns out to vary as a nearly universal function of a reduced Debye length ${\ensuremath{\lambda}}_{D}(Z)=(Z\ensuremath{-}1)D$. Since the ratio $R$ dictates the necessary energy resolution for a quantitative measurement of the redshifts and, at the same time, the Debye length $D$ is linked directly to the plasma density and temperature, the dependence of $R$ on $D$ should help to facilitate the potential experimental efforts for a quantitative measurement of the redshifts for the ${\mathrm{He}}_{\ensuremath{\alpha}}$ line of the two-electron ions. In addition, our study has led to a nearly constant redshift $\mathrm{\ensuremath{\Delta}}{\ensuremath{\omega}}_{\ensuremath{\alpha}}$ at a given $D$ for all He-like ions with $Z$ between 5 and 18 based on our recent critical assessment of the applicability of the DH approximation to atomic transitions. These two general features, if confirmed by observation, would offer a viable and easy alternative in the diagnostic efforts of the dense plasma.