# Kinetics of relativistic electrons undergoing small recoils in periodic structures and matter

Source: [Kinetics of relativistic electrons undergoing small recoils in periodic structures and matter](<https://www.sota2.com/research/paper/68fa37661e209131ce8b1c8b>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T22:21:49.710Z

Authors: E. Bulyak, N. Shul'ga

Published: 2017-11-27T08:05:47.000Z

## Abstract

We developed a general method for evaluating the energy spectrum evolution of relativistic charged particles that have undergone small quantum losses, such as the ionization losses when the electrons pass through matter and the radiation losses in the periodic fields. These processes are characterized by a small magnitude of the recoil quantum as compared with the particle's initial energy. The \`detector' function for arbitrary recoil spectrum is derived in addition to the straggling function. These functions are determined by the average number of scattering events undergone by the particle over the length of the detector (ionization losses) or the periodic field and the specific spectrum of the recoil. Moments for both the straggling function and the detector function are derived. The minimum average number of recoils, above which both functions depend only upon the mean energy of recoil quantum, is estimated. The average of this number is about 10 recoil events.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1711.09571>)

[PDF](<https://arxiv.org/pdf/1711.09571.pdf>)