Nuclear-Mass and Anomalous-Moment Corrections to the Hamiltonian for an Atom in a Constant External Magnetic Field

Abstract

The Hamiltonian for a many-particle system in a homogeneous magnetic field is constructed by a straightforward extension of previous work on hydrogenic atoms by Grotch and Hegstrom. Relativistic-correction terms of order ${\alpha }^2{\mu }_{B}H$ are identical to those obtained many years ago by Abragam and Van Vleck and by Perl and Hughes. In addition, higher-order terms due to the anomalous moments and to nuclear motion are explicitly formulated in the present work. These terms are of orders ${\alpha }^3{\mu }_{B}H$ and ${\alpha }^2\left(\frac{m}{M}\right){\mu }_{B}H$, respectively, and are coming to be within the range of present experimental measurements.