Analytical model of light ions reflection from solids

IF 1.4 3区物理与天体物理 Q3 INSTRUMENTS & INSTRUMENTATION

Nuclear Instruments & Methods in Physics Research Section B-beam Interactions With Materials and Atoms Pub Date : 2025-01-11 DOI:10.1016/j.nimb.2024.165610

V.P. Afanas’ev, L.G. Lobanova

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Abstract

The paper presents an analytical theory for describing the angular and energy distributions of medium energies light ions reflected from solids. This analytical theory is based on the phenomenological method of electrons reflection from solids named Oswald-Kasper-Gaukler method (OKG), which was successfully verified for electron spectroscopy. It is shown, that OKG method is based on the solution of boundary value problem for the transfer equation using the invariant imbedding method in the small-angle approximation. The main advantage of OKG method is an opportunity for the description of atomic particles reflection processes from solids by means of spherical harmonics method. Presented analytical formulas determine all scattering characteristics of reflected particles using dimensionless parameter, which is the ratio of the residual range to the transport length, and differential elastic cross section ω_el(n₀,n). Energy losses of ions in solids are calculated using Fokker-Plank approximation. Differential elastic cross sections are calculated in first Born approximation using Kr-C potential. The value of the parameter which determines the differential elastic cross section on small angles is determined by the ratio of the de Broglie wavelength of incidence particle to the screening radius a = 0.8853a₀(Z₁^1/2 + Z₂^1/2)^-2/3, where a₀ – first Bohr radius and was corrected in the range determined in Moliere works.

For elastic scattering of protons, the path length distribution function (PLDF) was found. The function was tested by comparison with the results of computer simulations performed using the binary-collision simulation program SPIM-L. Analytical results are also compared with experimental angular and energy spectra of 0.1–30 keV protons reflected from Be, C, Al, Ti, Ni, Cu and W targets. Satisfactory agreement between the theoretical and experimental results was found.

For the ions initial energies of hundreds of eV energy spectra of reflected protons were compared with results of computer simulation by means of MARLOWE program. The satisfactory agreement between the analytical, experimental and simulation results means the opportunity of the description not only electron scattering processes, but also the processes of light ions reflection from solids by means of OKG method.

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来源期刊

Nuclear Instruments & Methods in Physics Research Section B-beam Interactions With Materials and Atoms 物理-核科学技术

CiteScore

2.80

自引率

7.70%

发文量

231

审稿时长

1.9 months

期刊介绍： Section B of Nuclear Instruments and Methods in Physics Research covers all aspects of the interaction of energetic beams with atoms, molecules and aggregate forms of matter. This includes ion beam analysis and ion beam modification of materials as well as basic data of importance for these studies. Topics of general interest include: atomic collisions in solids, particle channelling, all aspects of collision cascades, the modification of materials by energetic beams, ion implantation, irradiation - induced changes in materials, the physics and chemistry of beam interactions and the analysis of materials by all forms of energetic radiation. Modification by ion, laser and electron beams for the study of electronic materials, metals, ceramics, insulators, polymers and other important and new materials systems are included. Related studies, such as the application of ion beam analysis to biological, archaeological and geological samples as well as applications to solve problems in planetary science are also welcome. Energetic beams of interest include atomic and molecular ions, neutrons, positrons and muons, plasmas directed at surfaces, electron and photon beams, including laser treated surfaces and studies of solids by photon radiation from rotating anodes, synchrotrons, etc. In addition, the interaction between various forms of radiation and radiation-induced deposition processes are relevant.