By carefully following the spatial and temporal criteria of the Debye-Hückel (DH) approximation, we present a detailed theoretical study on the redshifts of the spectroscopically isolated ${\mathrm{He}}_{\alpha }$ lines corresponding to the $1s2p{}^{1}P\to 1s^2{}^{1}S$ emission from two-electron ions embedded in external dense plasma. We first focus our study on the ratio $R=\mathrm{\Delta }{\omega }_{\alpha }/{\omega }_o$ between the redshift $\mathrm{\Delta }{\omega }_{\alpha }$ due to the external plasma environment and the energy ${\omega }_o$ of the ${\mathrm{He}}_{\alpha }$ 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 ${\lambda }_D\left(Z\right)=(Z-1)D$. 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 ${\mathrm{He}}_{\alpha }$ line of the two-electron ions. In addition, our study has led to a nearly constant redshift $\mathrm{\Delta }{\omega }_{\alpha }$ 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.

• Received 4 September 2017

DOI:https://doi.org/10.1103/PhysRevA.96.052502