Computational forms for binary particle interactions at different levels of anisotropy

TL;DR

This paper develops computational models for binary particle interactions at various anisotropy levels, improving simulation accuracy by including anisotropic effects and validating with electron-positron annihilation spectra.

Contribution

It introduces new computational forms of the collision integral for relativistic interactions at multiple anisotropy levels, including a novel isotropic form, enabling more precise modeling.

Findings

Validated the isotropic emission spectrum against analytical results.

Extended spectral calculations to axisymmetric distributions.

Produced two-dimensional spectral maps for enhanced insight.

Abstract

Particle interactions are key elements of many dynamical systems. In the context of systems described by a Boltzmann equation, such interactions may be described by a collision integral, a multidimensional integral over the momentum-phase space of the interaction. This integral is often simplified by assuming isotropic particle distributions; however, such an assumption places constraints on the dynamics of the system. This paper presents computational forms of the collision integral for relativistic, binary interactions at three levels of anisotropy, including a novel form in the isotropic case. All these forms are split into two parts, an absorption and an emission spectrum, which may be pre-calculated via numerical integration for simulation purposes. We demonstrate the use of these forms by comparison with the analytically integrated, isotropic emission spectrum of electron-positron annihilation, which are shown to agree to numerical precision. The emission spectrum is then further extended to axisymmetric particle distributions, where two-dimensional spectral maps can be generated to provide new insight.