Numerical experiments in screening theory

Abstract

In an attempt to clarify the behavior of the screening phenomenon in N-body systems at thermodynamics equi- librium, under the particular conditions at the core of the Sun, we define the screening energy and summarize the two main types of methods to calculate it: (a) by using classical mean field in Statistical Mechanics and (b) ab initio, by using molecular dynamics and first principles only. We invent a pair interaction with a finite parametrized range and strength, and carry out a numerical experiment which demonstrates the difference between the two aforementioned methods and underlying assumptions as a function of the range of the interaction (or equivalently the number of particles in the interaction zone). We study the effect that fluctuations in the number of particles in the screening/neutralizing cloud have on the screening, and the deviations from mean field results which ensue. We also demonstrate that the classical mean field theory is inaccurate under the conditions prevailing in stellar cores and essentially over estimates the screening. We show how the molecular dynamics results tend to the mean field Statistical Mechanics limits when the number of particles in the neutralizing domain increases.