Theoretical models of energy loss moments for solid targets bombarded by protons and correlated protons

ARISTA, N. R.; ARCHUBI, C. D.

Buenos Aires

Encuentro; DCM 2019; 2019

Most of the theoretical descriptions of thevicinage effect have been made using the dielectricformulation. This is a natural way to represent theelectrodynamical interactions in a dense mediumand is particularly useful to consider the interactionwith conduction or valence band electrons. Aninteresting dielectric model developed in thenineties by Kaneko [1] extends the possibilities ofthe dielectric approach to evaluate thecontributions of inner shells, opening in this waythe possibility of more comprehensive stoppingpower calculations. The so called wave-packetmodel (WPM) of Kaneko, based on the use ofgaussian distributions of electrons in momentumspace, provides a significant advantage in terms ofanalyticity as it yields closed analytical expressionsfor the dielectric function, with similar propertiesto those of the Lindhard dielectric model (LDM)corresponding to a free-electron gas, but usingmore appropriate velocity distributions for eachatomic shell.Our EWPM introduces modifications to theWPM originally proposed by Kaneko, using theLevine and Louie technique [2,3] to take intoaccount the energy gaps corresponding to thedifferent atomic levels of the target.On the other hand we extend the classicalelectrodynamics atomic-oscillator model of Bohrto a semiclassical impact parameter model (SIPM)for the case of correlated ions. To perform thisextension we consider short-distance correctionsand screening effects. This approach permits us toevaluate the rol of close and distant collisions onthe vicinage effect, showing the growingimportance of distant collisions with increasingenergies.We have performed specific calculations ofvicinage effects in energy losses and inner-shellionization for various accessible targets (C, Al, Si,Al₂O₃ and SiO₂), and compared the calculationswith existing experimental results. Inner-shell excitations produce an additionaldecrease in the vicinage effect. The present workstrongly suggests new experiments at intermediateand higher energies to test our new theoreticalpredictions and to reveal differences betweenmodels.