Calculation of mean excitation energy and stopping cross section in the orbital local plasma approximation

Extension of the kinetic theory of stopping, in the Oddershede-Sabin (OS) [At. Data Nucl. Data Tables 31, 275 (1984)] orbitally decomposed form, from gas phase to films and crystals generates the need for orbital mean excitation energies calculated within the local-spin-density approximation (LSDA) to density-functional theory (DFT), the preeminent theoretical model for such extended systems. In LSDA, the orbitals and orbital energies used in the construction of the electron density have no standing for estimation or calculation of excitation energies. As an alternative we propose an orbital density generalization of the local plasma approximation (LPA) of Lindhard and Scharff [K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 27, No. 15 (1953)] that we test by calculation of mean excitation energies Ik for each atomic orbital k within the LSDA for all atoms with Z<37. Stopping cross sections for a representative sample (about half) of these elements have been calculated using these Ik values. The results do not differ substantially from those of OS (who used Ik values from Dehmer, Inokuti, and Saxon [Phys. Rev. A 12, 102 (1975)]; Inokuti, Baer, and Dehmer [ibid. 17, 1229 (1978)]; Inokuti, Dehmer, Baer, and Hanson [ibid. 23, 95 (1981)]), with the discrepancy generally less than 15%. Comparison of the LPA and OS orbital mean excitation energies exhibits a number of striking systematic features, including (1) the orbital Iks corresponding to the orbital lying highest in energy generally differ by less than 40% between the two calculations; (2) the difference at lower energies can be as much as a factor of 3; (3) the ratio IkOS/IkLPA shows, within columns of the Periodic Table, a monotonically decreasing variation as a function of Z for the highest-energy orbital but a smooth variation as a function of Z for the lower-energy orbitals. There seem to be characteristic patterns for each different orbital. Although the two methods give very different Iks for core orbitals, there is little effect on the resulting stopping cross sections because the valence orbital Ik dominates the stopping for low projectile energies, the energy range of interest here. We give a brief analysis of the sensitivity of the stopping to shifts in Ik values.