Energy Loss of Charged Particles in Crystals

Abstract

The theory of charged particle energy Ioss by collisions as a function of impact parameter in a crystal is developed on the basis of the quantum dielectric formalism. Simple and convenient formulae taking into account the energy zone structure of crystals are obtained for nonrelativistic and relativistic particles. The relation between energy loss and local electron density is studied. For the first time i t is shown strictly that the hyperchanneled particle energy loss in the axial channels is less than that in corresponding plane channels.

Monte Carlo Simulation Analysis of Proton‐Energy Spectra for Axial Channeling in Silicon in the Intermediate Energy Region

“…It should be noted that the contribution to stopping from single-particle excitations is larger than that from the local part. This can be explained by the non-local feature of the single-particle excitation for low and intermediate ion energies [2]. It was shown in [21] that for Si in our energy region CI amounts to 0.5.…”

“…Neglecting the second term and setting I = hw, makes (4) identical with Lindhard's expression (1). In the low energy region, and in the intermediate region, which contains the stopping power maximum, the expression for S(v) in [2] is rather complicated and its application in Monte Carlo calculations of ion channeling is inappropriate.…”

“…The Fourier components of the electron density f ( G ) were taken from the analysis of X-ray diffraction experiments [29]. Similar as in [2] for f ( l l 1 ) we have used the more reliable value from [30].…”

“…In [20 to 221 more accurate expressions for the local stopping power are given taking into account the real crystal structure. Burenkov et al [2] used the dielectric formalism to calculate the local stopping power. For high particle velocity they obtained the following expression: where and G is the inverse lattice vector.…”

Nonlinear, Band-Structure, and Surface Effects in the Interaction of Charged Particles with Solids

“…Hence, early theoretical investigations were based on semiempirical treatments of the electronic excitations in the solid [30,31,32,33,34]. Attemps to introduce the full electronic band structure in the evaluation of the electronic stopping power of alkaline metals for low projectile velocities include a one-band calculation [35] as well as a calculation based on a linear combination of atomic orbitals [36].…”