Top-left panel: root mean square positron momentum vs time-density with depletion of the distribution excluded or included. The horizontal line is the thermal r.m.s. momentum ~0.0528 a.u.;
Bottom-left panel: the fraction of positrons remaining vs time-density;
Top-right panel: the momentum-transfer and elastic-scattering cross sections, and product of positron momentum and momentum-transfer cross section, which is proportional to the mean-squared momentum transfer;
Bottom-right panel: evolution of positron distribution in time-density (counter shows time-density in units of ns amg), excluding and including annihilation. Solid black line is the Maxwell-Boltzmann distribution at T=293 K
Description of the videos:
In all cases the positrons are initially distributed uniformly in energy (triangular in momentum) up to the positronium-formation threshold. In all cases the momentum distribution rapidly bunches above the minimum in the momentum-transfer quantity B(k)= k σ nkB
T m/M. The peak then cools through the minima, roughly maintaining its form, eventually merging with the low-momentum peak formed by positrons with initial momenta below the minimum, before finally evolving towards a Maxwell-Boltzmann distribution (solid black line in bottom right panel).