The relationship of electron Fermi energy with strong magnetic fields

TL;DR

This paper derives a concise expression for electron Fermi energy in strong magnetic fields, showing it scales as B^{1/4}, and explains high X-ray luminosities of magnetars based on this theory.

Contribution

It introduces a new analytical expression for electron Fermi energy in strong magnetic fields using Dirac delta functions.

Findings

Electron Fermi energy scales as B^{1/4} in strong magnetic fields.

The theory explains high soft X-ray luminosities of magnetars.

Provides a concise mathematical formulation for Landau level quantization.

Abstract

In order to depict the quantization of Landau levels, we introduce Dirac $\delta$ function, and gain a concise expression for the electron Fermi energy, $E_{F}(e) \propto B^{1/4}$. The high soft X-ray luminosities of magnetars may be naturally explained by our theory.