Mass effects in the theoretical determination of nuclear-spin relaxation rates for atomic hydrogen and deuterium.

Abstract

The normal method for calculating very precise eigenvalues for ${\mathrm{H}}_{2}$ and its isotopes is to solve the Schr\"odinger equation using a reduced mass calculated from the bare nuclear mass with the mass-independent Born-Oppenheimer potentials and with mass-dependent adiabatic and nonadiabatic correction terms that account for the finite mass of the nuclei. On the other hand, scattering calculations have used reduced masses calculated from the masses of the separated atoms to solve the Schr\"odinger equation with mass-dependent adiabatic potentials, but with no explicit treatment of electronically off-diagonal nonadiabatic corrections. We have extended the conventional bound-state methods based on bare nuclear masses into the continuum by introducing an effective local potential to account for the electronically off-diagonal nonadiabatic mass-dependent corrections. Good agreement is found with previously calculated eigenvalues of ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$. The scattering length for the ground state $^{1}\mathrm{\ensuremath{\Sigma}}_{\mathrm{g}}^{+}$ of ${\mathrm{H}}_{2}$ is very sensitive to the nonadiabatic corrections, but is in good agreement with that previously calculated using a reduced mass based on the separated atomic masses. Using quantum close-coupling methods, we also find good agreement with previously calculated collision-rate coefficients in the T\ensuremath{\rightarrow}0 limit for collisions of H with H and D with D.