Scattering of a spin-1/2 particle off a spin-0 target in a simple three-dimensional basis

TL;DR

This paper develops a three-dimensional momentum-spin basis formulation for scattering of a spin-1/2 particle off a spin-0 target, simplifying the integral equations and providing explicit relations for spin observables.

Contribution

It introduces a simplified integral equation framework using azimuthal symmetry and derives explicit formulas for spin observables in this context.

Findings

Reduced the number of integral equations by exploiting symmetry.

Derived explicit expressions for spin observables.

Presented a comprehensive set of integral equations for the T-matrix.

Abstract

Scattering of a spin-1/2 particle off a spin-0 target is formulated based on a simple three-dimensional momentum-spin basis. The azimuthal behaviour of both the potential and the T-matrix elements leads to a set of integral equations for the T-matrix elements in two variables only, namely the momentum's magnitude and the scattering angle. Some symmetry relations for the potential and the T-matrix elements reduce the number of the integral equations to be solved by a factor of one half. A complete list of the spin observables in terms of the two-dimensional T-matrix elements is presented.