title: Note: Precise radial distribution of charged particles in a magnetic guiding field.
abstract: Current high precision beta decay experiments of polarized neutrons, employing magnetic guiding fields in combination with position sensitive and energy dispersive detectors, resulted in a detailed study of the mono-energetic point spread function (PSF) for a homogeneous magnetic field. A PSF describes the radial probability distribution of mono-energetic electrons at the detector plane emitted from a point-like source. With regard to accuracy considerations, unwanted singularities occur as a function of the radial detector coordinate which have recently been investigated by subdividing the radial coordinate into small bins or employing analytical approximations. In this note, a series expansion of the PSF is presented which can numerically be evaluated with arbitrary precision.
authors.affiliation: Institute for Nuclear Physics, Johannes Gutenberg-University Mainz, D-55099 Mainz, Germany.
authors.forename: H
authors.initials: H
authors.lastname: Backe