Free-bound electron exchange contribution to l-split atomic structure in dense plasmas

An analytical expression for the exchange energy between the bound electron in hydrogen-like ions and the free electrons of plasma is proposed. Two limiting cases are identified: 1) the low temperature limit where the energy depends linearly on density and on the ion charge as 1/Z² but does not depend on the temperature itself, 2) the high temperature limit where the energy depends on temperature as 1/T but does not depend on the ion charge. These two regimes are separated by a characteristic temperature (T ^â̂- = 4Z²Ry) which is a universal parameter depending only on the charge Z of the ions. We presented numerical results for aluminum: the exchange energy contributes about 15% to the total plasma energy and can reach an order of 10^-4 of the total transition energy. Comparison to the Local-density Approximation (Kohn-Sham) exchange energy shows a good agreement.