Quantum and classical dynamics of neutron in a magnetic field

TL;DR

This paper analyzes the quantum and classical behavior of neutrons in magnetic fields, providing solutions to the Pauli equation, exploring neutron motion in multipole magnets, and proposing experiments to verify finite and infinite neutron trajectories.

Contribution

It offers a rigorous solution to the neutron Pauli equation in multipole magnetic fields and discusses experimental verification and applications in neutron storage rings.

Findings

Existence of finite and infinite solutions for neutron trajectories.

Predictions align with Stern-Gerlach experimental results.

Proposed experiments for verifying neutron motion types.

Abstract

The paper presents solution of quantum problem of neutron propagation in the magnetic field with multipole field expansion. Rigorous solution of the Pauli equation for neutron reveals existence of two solutions, finite and infinite, for any multipole configuration. As an example, we present detailed study of neutron motion in quadrupole and sextupole magnets. Our predictions agree with the results of Stern-Gerlach experiment for neutrons. To verify existence of finite and infinite motion, we discuss an experiment which could be performed in the Budker Insitute of Nuclear Physics using existing equipment. We conclude with considerations of neutron storage ring with straight section and discrete magnets focusing the beam.