Analytical model of light ions reflection from solids

• Published in: Nuclear instruments & methods in physics research. Section B, Beam interactions with materials and atoms Beam interactions with materials and atoms, 2025-03, Vol.560, p.165610, Article 165610
• Main Authors: Afanas’ev, V.P., Lobanova, L.G.
• Format: Article
• Language: English
• Subjects: Light ions energy and angular distributions; Light ions reflection; Oswald-Kasper-Gaukler model
• ISSN: 0168-583X
• DOI: 10.1016/j.nimb.2024.165610

[Display omitted] •The analytical theory for describing the angular and energy distributions of medium energies light ions reflected from solids is constructed.•The analytical theory is based on the phenomenological method of electrons reflection from solids named Oswald-Kasper-Gaukler method (OKG).•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.•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.•Energy losses of ions in solids are calculated using Fokker-Plank approximation. 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 ωel(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(Z11/2 + Z21/2)-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