Why the Salpeter approximation is not valid in the Sun

We review the derivation of the electrostatic screening effect from first principles. We show that under the conditions prevailing in the Sun the number of particles in the Debye sphere is of the order of unity. Consequently, fluctuations play a dominant role in the screening process and lead to an energy exchange between the scattering particles and the surrounding plasma that depends on the energy of the particles. Extensive molecular dynamics calculations show that low-energy particles gain on the average energy from the plasma while high-energy particles lose energy to the plasma, in contrast with the classical Salpeter picture in which all particles gain during the close approach to each other the mean Coulomb energy. Next, we adopt the Langevin equation for charged particles with the Rosenbluth potential. We show how the two completely independent methods, the molecular dynamics and Langevin equation, yield the same physical results. We then review the arguments for a static screening based on a static potential and show its basic assumptions and shortcomings. The particular assumptions leading to the Salpeter formula are discussed along with the approximations involved in its derivation. One of the tacit fundamental assumptions in the Salpeter approximation is that the scattering is fully elastic. The inelastic nature of the collisions which are dominant under the solar conditions is clarified. PACS numbers: 52.25.Gj, 52.20.Hv, 95.30.Cq, 26.65.+t, 26.20.+f