Quantum-number–dependent energy level shifts of ions in dense plasmas: A generalized analytical approach

Abstract

-Dense plasma effects on bound energy levels have been studied with relativistic atomic structure simulations that include intermediate coupling and configuration interaction. A general analytical formula is proposed that predicts the energy of LSJ-split levels for wide conditions of density and finite temperature and any atomic element. The achieved precision of the analytical approach allowed even to describe energy level crossings and the breakdown of level degeneration induced by dense plasma effects. Finally, a further simplification of the proposed method is developed that requests only information on energy level energies and quantum numbers of isolated atoms that are readily available. Copyright c EPLA, 2012Introduction. -Energy level shifts of ions in dense plasmas have been found experimentally and theoretically for many decades [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The reason for this phenomenon is related to the fact that the plasma shields the nuclear attraction of the bound electron that in turn shifts the energy level toward the continuum. As the overlap of the bound electron with the free electrons depends on the bound electron configurations, different shifts are encountered for upper and lower levels thereby inducing the so-called plasma polarization shift (PPS) [16].Although the PPS and some relations to the bound orbital quantum numbers have been indicated, no general rules could be established to predict plasma screening effects in dependence on the bound electron characteristics. To reveal such dependences is an urgent need in order to provide a clear picture about the plasma influence on the energy levels and in order to study the behavior of the spectral fine structure that is also at the origin of the spectral line shift [5,11].In this work the self-consistent field ion sphere model (SCFISM) [17][18][19][20] is used. Generally, two basic screening

High-resolution measurements of Cl15+ line shifts in hot, solid-density plasmas

“…Our measured values at the highest density disagrees with the analytical line shift model developed by Li and Rosmej [28] by a factor of two. Even though the measured shifts between 4 and 6 eV are lower than predicted by this model, they are at least four times larger than the lower limits placed early on on the shift by pioneering work [5], which estimated that the shifts are at least as large as 5% of the line width (> 1 eV in our case).…”

“…show the predictions from the ion-sphere model proposed by Li and Rosmej (green traces) [28]. This model predicts a linear dependence on the electron density.…”

“…The experimental data are from Orion shots (left to right) 10140, 10141, 10143,and 10142. The calculated shift is based on the analytical expression given by[28] and is given for plasma temperatures (solid green lines) between 600 and 1000 eV in 100 eV increments. The temperatures associated with these measurements are estimated to lie between 600 and 650 eV.…”

A study of density effects in plasmas using analytical approximations for the self-consistent potential

“…The analytical expressions obtained agree with results from direct numerical integration of energies and wavefunctions. Moreover, beyond the hydrogen-like case, the current formalism may be generalized to more complex ions, in the spirit of other works such the work by Li and Rosmej [29]. Finally, to deal with more complex ions, the analytical potential proposed here may be included in parametric potential codes such as FAC [30], as mentioned in our previous work.…”

Stark shift and width of x-ray lines from highly charged ions in dense plasmas

“…For example, a recent measurement of both shift and width of the K β transition of He-like Cl from the ORION laser facility indicated significant disagreement with existing theoretical models [12]. Specifically, it was shown that the recent theoretical line shift model of Li and Rosmej [13] overestimated the energy shift by about a factor of two at electron densities that are inferred from the line widths according to the standard theory of Stark broadening. Clearly, additional theoretical developments are needed to put a potential density diagnostic based on line shifts on a solid footing, and, of course, to provide reliable atomic data for the modeling of the radiative properties of astrophysical and laboratory plasmas.…”