Free-bound electron exchange contribution to l-split atomic structure in dense plasmas
1 Sorbonne Universités, Pierre et Marie Curie UPMC, LULI, UMR 7605, case 128, 4 place Jussieu, 75252 Paris Cedex 05, France
2 ExtreMe Matter Institute EMMI, GSI, Planckstr. 1, 64291 Darmstadt, Germany
3 Ecole Polytechnique, Laboratoire pour l'Utilisation des Lasers Intenses LULI, Physique Atomique dans les Plasmas Denses PAPD, 91118 Palaiseau, France
4 Russian Research Center, “Kurchatov Institute”, Moscow 123182, Russia
a e-mail: email@example.com
Published online: 15 November 2013
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∗ = 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.
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