Inverse beta-decay of arbitrarily polarized neutrons in a magnetic field

TL;DR

This paper calculates the inverse beta decay cross section for polarized neutrons in a magnetic field, revealing dependence on neutrino direction and providing exact solutions for arbitrary neutron polarization.

Contribution

It introduces a method to compute the cross section using exact Dirac solutions in a magnetic field for any neutron polarization.

Findings

Cross section depends on neutrino direction even for unpolarized neutrons.

Exact solutions enable precise calculations in magnetic backgrounds.

Results have implications for neutron decay processes in magnetic environments.

Abstract

We calculate the cross section of the inverse beta decay process, $\nu_e+n\to p+e$, in a background magnetic field which is much smaller than $m_p^2/e$. Using exact solutions of the Dirac equation in a constant magnetic field, we find the cross section for arbitrary polarization of the initial neutrons. The cross section depends on the direction of the incident neutrino even when the initial neutron is assumed to be at rest and has no net polarization. Possible implications of the result are discussed.