Saha Equation for the Photo-Ionization of Hydrogen Atoms in Partially Ionized Relativistic Hydrogen Plasma and the Effect of Gravity on the Binding of Hydrogen Atoms in Rindler Space

TL;DR

This paper derives a modified Saha equation for hydrogen ionization in a relativistic plasma under gravity, showing how gravitational fields influence hydrogen atom binding and ionization equilibrium.

Contribution

It introduces a new Saha ionization formula in Rindler space, accounting for gravity's effect on hydrogen atom binding and plasma ionization.

Findings

Neutral hydrogen decreases with temperature

Neutral hydrogen increases with gravitational field strength

Binding energy of electrons increases with gravity

Abstract

We have studied Saha equation for photo-ionization of hydrogen atoms in partially ionized relativistic hydrogen plasma in Rindler space. Following the principle of equivalence, we have obtained the abundances of neutral hydrogen atoms, hydrogen ions and the electrons in dynamic equilibrium of the photo-ionization reaction of neutral hydrogen atoms and electron capture process by hydrogen ions (de-ionization process) and also investigated their variations with temperature of the plasma and the uniform gravitational field in the Rindler space or equivalently the uniform acceleration of the observer. Hence obtained the Saha ionization formula for partially ionized hydrogen plasma in Rindler space. It has been observed that the abundance of neutral hydrogen atoms decreases with the increase in temperature of the plasma, which is the usual picture, whereas it increases with the increases in the strength of uniform gravitational field. The second part of this observation shows that the binding of the electrons inside hydrogen atoms increases with the increase in the strength of gravitational field or equivalently an observer with very high acceleration will see less amount of ionized hydrogen atoms compared to inertial observer.