# Integer and half-integer channel spins for elastic scattering cross sections

## TL;DR

This paper provides analytical formulas for elastic scattering cross sections and partial amplitudes for nuclear particles with various channel spins, enabling detailed phase shift analysis using experimental data.

## Contribution

It introduces new analytical expressions for differential cross sections and partial amplitudes for channels with spins 1/2, 1, 3/2, 2, and 5/2, considering spin-orbit splitting.

## Key findings

- Analytical expressions for differential cross sections derived.
- Partial amplitudes formulated for arbitrary orbital angular momentum.
- Facilitates comprehensive phase shift analysis with experimental data.

## Abstract

We present the analytical expressions for the differential cross sections and independent partial amplitudes for elastic scattering of nuclear particles for channels with a spin value of 1/2, 1, 3/2, 2 and 5/2. The independent partial amplitudes are presented for arbitrary orbital angular momentum $l$ and taking into account spin-orbit splitting. The analytical expressions allow one to carry out full phase shift analyses using experimental data for differential cross sections for processes with channel spins 1/2, 1, 3/2, 2 and 5/2.