The point spread function of electrons in a magnetic field, and the decay of the free neutron

Experiments in nuclear and particle physics often use magnetic fields to guide charged reaction products to a detector. Due to their gyration in the guide field, the particles hit the detector within an area that can be considerably larger than the diameter of the source where the particles are produced. This blurring of the image of the particle source on the detector surface is described by a suitable point spread function (PSF), which is defined as the image of a point source. We derive simple analytical expressions for such “magnetic” PSFs, valid for any angular distribution of the emitted particles that can be developed in Legendre polynomials. We investigate this rather general problem in the context of neutron β-decay spectrometers and study the effect of limited detector size on measured neutron decay correlation parameters. To our surprise, insufficient detector size does not affect the accuracy of such measurements much, even for rather large radii of gyration. This finding can considerably simplify the layout of the respective spectrometers.