Quantitative theory of channeling particle diffusion in transverse energy in the presence of nuclear scattering and direct evaluation of dechanneling length

Abstract

A refined equation for channeling particle diffusion in transverse energy taking into consideration largeangle scattering by nuclei is suggested. This equation is reduced to the Sturm-Liouville problem, allowing one to reveal both the origin and the limitations of the dechanneling length notion. The values of the latter are evaluated for both positively and negatively charged particles of various energies. New features of the dechanneling dynamics of positively charged particles are also revealed. First, it is demonstrated that the dechanneling length notion is completely inapplicable for their nuclear dechanneling process. Second, the effective electron dechanneling length of positively charged particle varies more than twice converging to a constant asymptotic value only at the depth exceeding the latter.

Quantum features of high energy particle incoherent scattering in crystals

“…This problem is readily solved by the quantum treatment of transverse particle motion [25,26], being, however, both really necessary and practically feasible only at the electron and positron energies of a few dozen MeV and less. However, most of the current investigations are conducted at GeV [13,14,27] and higher [1][2][3][4][5][6][7][8][9][10][15][16][17][28][29][30][31][32][33][34] energies, at which the quantum description of particle motion in the averaged crystal field becomes both redundant and cumbersome, revealing the necessity for the introduction of classical particle motion features into the treatment of their incoherent scattering by the inhomogeneously distributed nuclei. Till now, a redefinition of the scattering impact parameter upper limit R → u 1 [28][29][30][31]35] has been used, which did not take into consideration any incoherent scattering dependence on the transverse particle coordinate, giving, thus, a qualitative estimate only.…”

Steering of Sub-GeV electrons by ultrashort Si and Ge bent crystals

“…Furthermore, even if these values were ob-tained in the same way as L dech DSim , the depedence of L ′ dech DSim on the penetration depth evidently differ from the exponent function. Indeed, one has to remember that the dechanneling of negative particles is mainly due to strong scattering with nuclei that has an intrinsic non-slow diffusive nature [35].…”

“…Electron dechanneling lenght has already been experimentally measured with Si straight [36,37,38] and bent [15,16,17,18] crystals. In contrast to positrons, electrons dechannel faster [15,16,17,18,33,34,35]. Indeed, negatively charged channeled particles oscillate around atomic planes, thereby being more subject to the strong scattering with lattice nuclei.…”

On the ionization loss spectra of high-energy channeled negatively charged particles

“…The channeling motion of a particle in a crystal can break down due to its incoherent scattering either on thermal vibrations of the atoms (mostly for negative particles) or on the subsystem of the atomic electrons (mostly for positive particles). In the case of negatively charged particles the decrease in the number of channeled particles with a e-mail: trofymenko@kipt.kharkov.ua (corresponding author) b e-mail: kirillin@kipt.kharkov.ua the crystal thickness behaves almost exponentially [6]. The distance on which the number of channeled particles in the incident beam decreases by a factor of e (due to the particle transition to the over-barrier regime of motion) is known as the dechanneling length l d .…”