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-Hückel (DH) approximation, we present a detailed theoretical study on the redshifts of the spectroscopically isolated He α lines corresponding to the 1s2p 1 P → 1s 2 1 S emission from two-electron ions embedded in external dense plasma. We first focus our study on the ratio R = ω α /ω o between the redshift ω α due to the external plasma environment and the energy ω o of the He α 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 λ D (Z) = (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 He α line of the two-electron ions. In addition, our study has led to a nearly constant redshift ω α 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.

Variation of the oscillator strengths for the α emission lines of the one- and two-electrons ions in dense plasma

“…3,4 Following a detailed assessment of the spatial and temporal criteria of the DH approximation, 5,6 we have shown recently that the DH approximation could be applied to the atomic processes subject to outside dense plasma, involving transitions limited to those between lowlying atomic states, which are dictated by the short-ranged interaction between the innermost atomic orbitals. [5][6][7] With a much improved experimental energy resolution E DE (see, e.g., Refs. 8 and 9), together with the agreement we reported recently between the simulated redshift based on the DH model 6,7 and the earlier observed value for the H-like Al 12þ ion, 8 more extensive measurements for the redshifts subject to dense plasma with a density of 10 22 cm -3 or higher could offer an alternative approach to the typical plasma diagnostic efforts based on the change of the line profile due to complicated collisional processes.…”

“…[5][6][7] With a much improved experimental energy resolution E DE (see, e.g., Refs. 8 and 9), together with the agreement we reported recently between the simulated redshift based on the DH model 6,7 and the earlier observed value for the H-like Al 12þ ion, 8 more extensive measurements for the redshifts subject to dense plasma with a density of 10 22 cm -3 or higher could offer an alternative approach to the typical plasma diagnostic efforts based on the change of the line profile due to complicated collisional processes.…”

“…Our recent works have shown that the estimates of the atomic data based on the DH approximation depend very much on the choice of A. 6,7 With the exception of a very few limited studies involving the low-lying atomic states, many of the recent atomic structure calculations based on the DH approximation [13][14][15][16][17][18][19][20][21][22] and a few on the modified DH approximation 23,24 failed to meet the spatial criterion of the DH approximation, especially those with A ¼ 0 when the atomic orbits overlap substantially with the outside plasma electrons.…”

“…With the plasma-free energy separation between the 2p and 1s states of H-like ions given by x o ¼ 10:204Z 2 eV, one leads immediately to the ratio R given by Eq. (10), or effectively the required experimental energy resolution if the redshifts of the Lyman-a are to be measured as discussed in Ref 7…”

Variation of the transition energies and oscillator strengths for the 3C and 3D lines of the Ne-like ions under plasma environment

“…The influence of the plasma environment to the atomic processes is a challenging many-body problem and several sophisticated and complicated models were developed over the years to understand such processes [22][23][24][25]. On the other hand, the Debye-Hückel (DH) model, with its simplicity [26], could easily capture the important qualitative features over several orders of magnitude in plasma temperature and density, and, at the same time, offer the physical interpretation as a reliable reference for other theoretical models [21,[27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. Recently, we present a critical assessment of the DH approximation in terms of the spatial and temporal criteria for dense plasma which limits its applicability to atomic processes that are short-ranged in nature for the H-like and Helike ions with nucleus charge Z between 5 and 18 [21,28,29].…”