Electrodynamics for Nuclear Matter in Bulk

Abstract

A general approach to analyze the electrodynamics of nuclear matter in bulk is presented using the relativistic Thomas-Fermi equation generalizing to the case of N ≃ (m Planck /m n ) 3 nucleons of mass m n the approach well tested in very heavy nuclei (Z ≃ 10 6 ). Particular attention is given to implement the condition of charge neutrality globally on the entire configuration, versus the one usually adopted on a microscopic scale. As the limit N ≃ (m Planck /m n ) 3 is approached the penetration of electrons inside the core increases and a relatively small tail of electrons persists leading to a significant electron density outside the core. Within a region of 10 2 electron Compton wavelength near the core surface electric fields close to the critical value for pair creation by vacuum polarization effect develop. These results can have important consequences on the understanding of physical process in neutron stars structures as well as on the initial conditions leading to the process of gravitational collapse to a black hole. PACS numbers:It is well know that the Thomas-Fermi equation is the exact theory for atoms, molecules and solids as Z → ∞ [1]. We show in this letter that the relativistic Thomas-Fermi theory developed for the study of atoms for heavy nuclei with Z ≃ 10 6 [2]- [12] gives important basic new information on the study of nuclear matter in bulk in the limit of N ≃ (m Planck /m n ) 3 nucleons of mass m n and on its electrodynamic properties. The analysis of nuclear matter bulk in neutron stars composed of degenerate gas of neutrons, protons and electrons, has traditionally been approached by implementing microscopically the charge neutrality condition by requiring the electron density n e (x) to coincide with the proton density n p (x),It is clear however that especially when conditions close to the gravitational collapse occur, there is an ultra-relativistic component of degenerate electrons whose confinement requires the existence of very strong electromagnetic fields, in order to guarantee the overall charge neutrality of the neutron star. Under these conditions equation (1) will be necessarily violated. We are going to

Electron–positron pairs in physics and astrophysics: From heavy nuclei to black holes

“…For this purpose, a Bogoliubov transformation from the time-independent number basis (a k , b † k ) (526,527) to a time-dependent number basis [ã k (t),b † k (t)] is introduced [437,455,456],…”

“…The major difficulties appear to be connected with the fact that all fundamental interactions, the gravitational, the electromagnetic, the strong, the weak interactions appear to participate in essential way to this process which appear to be therefore one of the most interesting fundamental process of theoretical physics. Current progress is presented in the following works [527,528,529,530,531,532,533,534,535,536,537,538]. What is important to recall at this stage is only that both the supernovae and GRBs processes are among the most energetic and transient phenomena ever observed in the Universe: a supernova can reach energy of ∼ 10 52 ergs (hypernovae) on a time scale of a few months and GRBs can have emission of up to ∼ 10 55 ergs [539] in a time scale as short as of a few seconds.…”

On Magnetic Fields in Rotating Nuclear Matter Cores of Stellar Dimensions

“…Now let us review the main assumptions and results of those works. According to 13 and 18 the protons are distributed at constant density n p within a radius…”

“…al. 13 . According to that work the system consisting of degenerate neutrons, protons and electrons in beta equilibrium is globally neutral and expected to be kept at nuclear density by self gravity.…”

Neutral Nuclear Core vs Super Charged One

“…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 , n p (r) = n p θ(R c − r),…”