Comments on the radial distribution of charged particles in a magnetic field

TL;DR

This paper provides a detailed numerical analysis of the point spread function for charged particles in magnetic fields, addressing efficiency modulations and singularities relevant to high-precision beta decay experiments.

Contribution

It offers a precise numerical representation of the point spread function and compares it with previous approximations, enhancing understanding of radial distributions in magnetic fields.

Findings

Numerical PSF representation matches well with previous models.

Identifies and discusses singularities in the radial distribution.

Improves accuracy of particle detection efficiency modeling.

Abstract

Magnetic guiding fields in combination with energy dispersive semiconductor detectors have been employed already more than 50 years ago for in-beam internal conversion electron spectroscopy. Even then it was recognized that efficiency modulations may appear as function of the electron energy, arising when electrons hit a baffle or miss the sensitive area of the detector. Current high precision beta decay experiments of polarized neutrons with conceptional similar experimental devices resulted in a detailed study of the point spread function (PSF). The latter describes the radial probability distribution of mono-energetic electrons at the detector plane. Singularities occur as function of the radial detector coordinate which have been investigated and discussed by Sjue at al. (Rev. Scient. Instr. 86, 023102 (2015)), and Dubbers (arXiv:1501.05131v1 [physics.ins-det]). In this comment a rather precise numerical representation of the PSF is presented and compared with approximations in the mentioned papers.