Improved separation of soft and hard components in multiple Coulomb scattering

TL;DR

This paper introduces a novel method for separating soft and hard components in multiple Coulomb scattering, improving the accuracy of angular distribution functions by deforming the Fourier integral path into the complex plane.

Contribution

The authors present a new approach that decomposes the scattering distribution into positive soft and hard components, incorporating Rutherford asymptotics and power corrections.

Findings

The soft component closely resembles a Gaussian distribution.

The hard component captures large-angle scattering with Rutherford asymptotics.

The method provides detailed insights into the interplay of components at intermediate angles.

Abstract

Evaluation of the angular distribution function of particles scattered in an amorphous medium is improved by deforming the integration path in the Fourier integral representation into the complex plane. That allows us to present the distribution function as a sum of two positive components, soft and hard, the soft component being close to a Gaussian, and the hard component vanishing in the forward direction, while including the Rutherford asymptotics and all the power corrections to it at large scattering angles. Detailed properties of those components, and their interplay at intermediate deflection angles are discussed. Comparison with the Moli\`{e}re theory is given.