Gravitational Corrections to the Energy-Levels of a Hydrogen Atom

TL;DR

This paper investigates how internal gravitational fields from the atomic nucleus affect hydrogen atom energy levels, calculating relativistic energy shifts for various states using Schwarzschild metric.

Contribution

It provides the first detailed calculation of gravitational corrections to hydrogen energy levels considering relativistic effects and angular momentum dependence.

Findings

Energy shifts depend on total angular momentum quantum number.

Relativistic gravitational corrections are significant for precise atomic energy measurements.

Results are obtained using Schwarzschild metric for the internal gravitational field.

Abstract

The first order perturbations of the energy levels of a hydrogen atom in central internal gravitational field are investigated. The internal gravitational field is produced by the mass of the atomic nucleus. The energy shifts are calculated for the relativistic 1S, 2S, 2P, 3S, 3P, 3D, 4S and 4P levels with Schwarzschild metric. The calculated results show that the gravitational corrections are sensitive to the total angular momentum quantum number.