Practical theoretical expressions for ions embedded in Debye and quantum plasmas

An accurate theoretical expression is proposed for the atomic structure under external confinement. The analysis is based on the tensor expression for the Breit-Pauli Hamiltonian in which the Racah wave functions are expanded in terms of the linear combinations of the multi-Slater wave functions. The variables are separated into radial and angular parts, where the variational parameters in the trial wave functions are obtained by solving the radial Schrodinger equation and the expressions of the angular part are worked out using an irreducible theory of complex system. Relativistic corrections are derived directly, which are treated as a sum of five terms: mass correction, one-body Darwin correction, two-body Darwin correction, spin-spin contact interaction correction, and orbit-orbit interaction correction. Energies and radiative decay rates of Be-like Fe22+ and Kr32+ ions in the presence of two kinds of plasma environments are presented for demonstration purposes, one is the Debye plasma which is described by a standard Debye-Huckel potential and the other is the quantum plasma which is treated under an exponential cosine screened Coulomb potential. Independent self-consistent calculations within the fully relativistic frame by incorporating the above two potentials are also performed using the Flexible Atomic Code to verify the validity of the proposed expressions. Results are given over a wide range of screening lengths. Relativistic effects in energy spectra are studied for the first time and are found to be rather important, especially in the high-Z system. Comparisons between our two sets of results and other theoretical predictions when available are made. Some behavior of the respective properties with respect to the plasma shielding strength is discussed. The present study should be beneficial for the analysis of spectra in astrophysical and fusion plasmas.