Redshift of the Lyman-αemission line of H-like ions in a plasma environment

Abstract

We present a critical assessment of the applicability of the Debye-Hückel (DH) approximation to the redshift of the Lyman-α emission line of the H-like ions under a dense plasma environment. By carefully considering the 2p → 1s transition spatially and temporally, our investigation suggests that the DH approximation may be applied to a limited number of H-like ions, such as the ones with Z between 5 and 18 or with Z greater than 50. Our numerical calculation, in fact, leads to quantitative agreement with the observed redshift of the well-isolated Lyman-α line at plasma density of the order of 1 × 10 22 cm −3 or higher with an electron temperature of several hundred eV of H-like Al 12+. Our study also yields simulated data consistent with those from more elaborate quantum mechanical approaches.

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

“…As a result, it is interesting to note that both the commonly accepted equation-of-state models adopted in the standard solar models, i.e., MHD (Mihalas-Hummer-Dappen) and OPAL (Optical Project at Livermore), include a Debye-H€ uckel term as the leading Coulomb correction to the free energy. 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.…”

“…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.…”

“…These two general features could easily be applied to extrapolate from a a) Electronic mail: 051420@mail.fju.edu.tw given single calculated dataset for a H-like or He-like ion to the corresponding data for other ions. The redshifts for the emission lines involved the inner shell electrons (e.g., the a lines) could be attributed qualitatively to the upward shifts of their energy levels due to an effective screened potential at a distance r from the nuclear charge Z, subject to a charge-neutral outside electron-ion plasma, given by 6,11,12…”

“…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.…”