Neutral Nuclear Core vs Super Charged One

Abstract

Based on the Thomas-Fermi approach, we describe and distinguish the electron distributions around extended nuclear cores: (i) in the case that cores are neutral for electrons bound by protons inside cores and proton and electron numbers are the same; (ii) in the case that super charged cores are bare, electrons (positrons) produced by vacuum polarization are bound by (fly into) cores (infinity).Equilibrium of electron distribution in neutral cores. In Refs. [1, 2, 3], the Thomas-Fermi approach was used to study the electrostatic equilibrium of electron distributions n e (r) around extended nuclear cores, where total proton and electron numbers are the same N p = N e . Proton's density n p (r) is constant inside core r ≤ R c and vanishes outside the core r > R c ,where R c is the core radius and n p proton density. Degenerate electron density,where electron Fermi momentum P F e , Fermi-energy E e (P F e ) and Coulomb potential energy V coul (r) are related by,The electrostatic equilibrium of electron distributions is determined bywhich means the balance of electron's kinetic and potential energies in Eq. (3) and degenerate electrons occupy energy-levels up to +m e c 2 . Eqs. (2,3,4) give the relationships:

Supercritically charged objects and electron-positron pair creation

“…( 15) and (16). Note that for the ultra-relativistic cases with ϕ(r) m e , an analytical solution is obtained for ϕ(r) [105]. The values of R and Z for various types of objects are fixed according to the results indicated in Figs.…”