Hyperfine interaction in hydrogen and nuclear spin-spin coupling in hydrogen deuteride

In the first part of this work a model for the Fermi contact interaction is proposed, in which the charge and the magnetic moment of the nucleus are uniformly distributed within a sphere of radius r0. This leads to a Schroedinger equation which is solvable without perturbation theory. The Schroedinger equation is exactly solved, in terms of an external solution (r > r0) and an internal solution, (r less than or equal to r0). The eigenvalues are determined by a transcendential equation following from the requirement that the wave function and its derivative be continuous across r = r0. In the mathematical limit r0 → 0, the usual Coulomb plus a delta function potential is obtained. Furthermore, it is shown that the magnetic perturbation energy goes to zero for a repulsive delta function and to negative infinity for an attractive delta function. In the second part of this work, these results are used to calculate the contribution from the Fermi contact interaction to the nuclear spin-spin coupling constant of HD. Employing the finite nucleus potential from Part I and a Heitler-London type of wave function, where the hydrogenlike orbitals are replaced by functions of the type derived in Part I, the problem of computing an energy term bilinear in the nuclear spins is reduced to a first order perturbation problem. The total energy is expressed as E = (psi,Hpsi)/(psi,psi). The integrals (psi,Hpsi) and (psi,psi) are then evaluated retaining only terms that are independent of, or bilinear in the nuclear spins. Upon expansion the energy term proportional to the two nuclear spins is evaluated, thus giving the coupling constant J