# The Schwinger Scattering of Twisted Neutrons by Nuclei

## TL;DR

This paper explores how the scattering of twisted neutrons, which carry orbital angular momentum, differs from traditional plane-wave neutrons, enabling new insights into nuclear amplitudes and potential applications in quantum tomography and fundamental physics.

## Contribution

It demonstrates that twisted neutrons alter scattering patterns and reveal dependencies on neutron helicity and nuclear amplitude phases, expanding the understanding of neutron-nucleus interactions.

## Key findings

- Angular distributions of scattered neutrons are modified with twisted neutrons.
- Dependence on neutron helicity and real part of nuclear amplitude is observed.
- Spin asymmetries are measurable at existing neutron facilities.

## Abstract

Thanks to J.~Schwinger, the process of elastic scattering of neutrons by nuclei is known to depend on the interference between a nuclear amplitude and an electromagnetic one for small scattering angles, resulting in spin asymmetries of a cross section or in polarization of the scattered neutrons. While this interference depends on the neutron's {\it transverse} polarization and on {\it an imaginary part} of the nuclear amplitude, this conclusion holds only for the incident plane-wave neutrons with a definite momentum. Here we show that this scattering is altered when the twisted neutrons, recently obtained experimentally, are used instead -- that is, neutrons with an orbital angular momentum. For bulk targets, the angular distributions of the scattered neutrons get modified, while scattering of a superposition of states with the different angular momenta also reveals dependence on the longitudinal polarization. For well-localized targets, the observables develop a dependence on the neutron's {\it helicity} and on {\it a real part} of the nuclear amplitude, providing full access to its phase already in the Born approximation. We argue that the corresponding spin asymmetries are measurable at existing neutron facilities. Thus, scattering of the twisted neutrons by nuclei can provide means for quantum tomography of the neutron states and become a useful tool for hadronic studies, low-energy nuclear physics, tests of fundamental symmetries, and neutron optics.