Energy and shape relaxation in binary atomic systems with realistic quantum cross sections.

Area of Science:

• Kinetic Theory
• Statistical Mechanics
• Quantum Scattering

Background:

• Studying the time evolution of non-equilibrium particle distributions is crucial for understanding gas dynamics.
• Energetic particles in a thermal equilibrium background gas provide a model system for relaxation processes.

Purpose of the Study:

• To analyze the time evolution of non-equilibrium distribution functions for test particles in a background gas.
• To determine relaxation times to equilibrium using realistic quantum mechanical cross sections.

Main Methods:

• Solving the spatially homogeneous linear Boltzmann equation.
• Employing a moment method with Sonine polynomial expansion.
• Utilizing direct simulation Monte Carlo (DSMC) methods.
• Incorporating quantum mechanical differential cross sections.

Main Results:

• The moment method yields approximate eigenvalues and eigenfunctions of the Boltzmann collision operator.
• Reciprocals of eigenvalues quantify relaxation times to equilibrium.
• A single time scale, determined by the momentum transfer cross section, characterizes energy relaxation and distribution shape for hard sphere interactions.
• This single time scale also applies to realistic quantum cross sections dominated by small-angle scattering.

Conclusions:

• The momentum transfer cross section is a key parameter for predicting relaxation times in dilute gas systems.
• The findings are applicable to systems like energetic N in He and Xe in He.
• Both analytical (moment method) and numerical (DSMC) approaches validate the theoretical framework.