Effective Ion Charge

Abstract

The impact parameter dependent energy transfer and random stopping power for ions carrying electrons were determined within the first-order Born approximation. The ion and atom were described by many-electron ground states. The excitations and ionizations of both collision partners were taken into account, but exchange of electrons was neglected. With the Bethe sum rule and closure relation, the random stopping was shown to have the Bethe form. For the Moliere form factors the anaJytical results were obtained. The effective charge was discussed in the random and channelling conditions. Comparison with some previous calculations was carried out.

Stopping and Straggling of Slow Atoms in Electron Gas

“…The important point is that we have to consider a stable in time, frozen charge distribution on the projectile. As was shown previously [10,11] the projectile charge in the Fourier space, which contribute to Eqs. and A -> Λ0 [6], as should be.…”

“…The decrease in C's with rs can be understood by noting that the energy absorbed by the electron gas on collective excitations drops as r^ 3/2 and the number of electrons subjected to the single particles excitations are related to the density of states below the Fermi energy EF . For the energy loss analysis the concept of effective charge is applied [10,11]. It relates stopping and straggling produced by a given projectile to the same charac^teristics produced by the projectile atomic nucleus.…”

“…The reason for that is the structure of the integral Eq. (8). It means that there is an additional contribution to the straggling caused by an extended charge projectile.…”

“…According to the density functional method when the ion moves in a solid the total energy E can be expressed in terms of local electron density p'(r) as a sum of the kinetic and the potential energies velocity VF, this screening can be approximately described in terms of the screened Coulomb potentials between electrons Vee, and between electron and nucleus Vne of the following form [6][7][8][9]:…”

Stopping of Slow H-, He-, Li- and Be-Like Projectiles in Electron Gas

“…The form factor Ζ 2 (z) is the Fourier transform of the spatial electron distribution on the projectile [6][7][8] The conduction electrons of a solid screen the quasi-static electric potential of a slow projectile due to dielectric response. Provided the speed of the atom is lower than the Fermi velocity VF, this screening can be approximately described in terms of the Coulomb potential between charges with the screening function exp(-rk TF ), where the Thomas-Fermi wave number kTF is related to the Fermi wave number as kTF = 4kF/πα 0 .…”