Electron shielding of the nuclear magnetic moment in hydrogen-like atom

TL;DR

This paper provides exact calculations of wave function corrections in hydrogen-like atoms due to magnetic fields and nuclear magnetic moments, revealing how the electron shields the nuclear magnetic moment.

Contribution

It introduces exact solutions for wave function corrections in hydrogen-like atoms under magnetic influences, advancing understanding of nuclear magnetic shielding effects.

Findings

Exact correction to ground state wave function in magnetic field

Wave function projections for arbitrary principal quantum number n

Calculated shielding of nuclear magnetic moment by the electron

Abstract

The correction to the wave function of the ground state in a hydrogen-like atom due to an external homogenous magnetic field is found exactly in the parameter $Z\alpha$. The $j=1/2$ projection of the correction to the wave function of the $ns_{1/2}$ state due to the external homogeneous magnetic field is found for arbitrary $n$. The $j=3/2$ projection of the correction to the wave function of the $ns_{1/2}$ state due to the nuclear magnetic moment is also found for arbitrary $n$. Using these results, we have calculated the shielding of the nuclear magnetic moment by the $ns_{1/2}$ electron.