Energy and polarizability of atoms in a weak magnetic field: Hydrogenic atoms

The ground-state wave function of a hydrogenic atom is approximated by ψ₀(H)=exp-[k(x²+y²+sz²)1/2]1/p, and the expectation value of the Hamiltonian, including diamagnetic and spin-orbit terms in a magnetic field Hz, is minimized with respect to k, s, and p so as to determine these Hz-dependent parameters, and the energy is evaluated. In the presence of an infinitesimal electric field Eₜ, in the t direction, the wave function is taken to be ψ₀(H)(1+bt+cρt), where ρ=(x²+y²+sz²)1/2. The energy is minimized with respect to b and c, and the coefficient of Eₜ² is identified as -(1/2)αₜ, the polarizability component, which contains diamagnetic and weakly spin-dependent terms. Comparison with experiments of Castner and Lee on donors in Si is briefly discussed.