Stark–Lo Surdo effect on magnetic moments of a one-electron atom in the ground state

Magnetic multipole moments of a non-relativistic hydrogen-like atom in the ground state, subjected to an external weak, static, and uniform electric field, are analyzed within the framework of the non-relativistic first-order quantum-mechanical perturbation theory. The electron wave function is taken to be a two-component Pauli spinor. It is shown that while for an isolated atom the only non-vanishing magnetic moment is the dipole one, the electric field induces in the atom an additional magnetic quadrupole moment. Both moments are due solely to the spin-magnetisation component of the electron current density; the convective component of the current density makes no contribution in either case. Explicit expressions for the spherical and Cartesian components of the induced magnetic quadrupole moment tensor, as well as its coordinate-independent representation, are presented.