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

Abstract

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 beta 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 much the accuracy of such measurements, even for rather large radii of gyration. This finding can considerably simplify the layout of the respective spectrometers.

arXiv comment24 pages, 12 figures

References in corpus (8)

• Improved Determination of the Neutron Lifetime
• The neutron and its role in cosmology and particle physics
• Determination of the Weak Axial Vector Coupling from a Measurement of the Beta-Asymmetry Parameter A in Neutron Beta Decay
• Characterization of a ballistic supermirror neutron guide
• Precision Measurement of the Neutron Beta-Decay Asymmetry
• Measurement of the neutron $\beta$-asymmetry parameter $A_0$ with ultracold neutrons
• Storage of ultracold neutrons in the UCN$\tau$ magneto-gravitational trap
• Neutron Beta Decay Studies with Nab

Cited by in corpus (8)

• The neutron and its role in cosmology and particle physics
• Measurement of the Weak Axial-Vector Coupling Constant in the Decay of Free Neutrons Using a Pulsed Cold Neutron Beam
• Constraints on the Dark Matter Interpretation $n\to \chi +e^{+}{e}^{-}$ of the Neutron Decay Anomaly with the PERKEO II experiment
• Limit on the Fierz Interference Term b from a Measurement of the Beta Asymmetry in Neutron Decay
• Design of the Magnet System of the Neutron Decay Facility PERC
• Magnetic guidance of charged particles
• Radial distribution of charged particles in a magnetic field
• Undetected Electron Backscattering in PERKEO III