Hyperfine Splittings andgFValues of MetastableH2

The energy arising from the hyperfine interaction, the interaction with the magnetic field, and the cross term between them has been studied for ortho-${\mathrm{H}}_2$ in the $c{}_{}{}^3{}_{}{}^{}\pi _u^{}{}_{}{}^{}$ state. The cross term gives rise to a first-order correction of the $g_F$ values which accounts for the discrepancies between the theoretical zeroth-order $g_F$ and the experimental values. The interactions are expressed as products of irreducible spherical tensors, and Racah's method is used to derive all the diagonal and off-diagonal matrix elements. The case of the rotational level $N=1\mathrm{}$ is presented in detail. The coupling constants of hyperfine structure have been evaluated by using a single-configuration electronic wave function for the $c{}_{}{}^3{}_{}{}^{}\pi _u^{}{}_{}{}^{}$ state of ${\mathrm{H}}_2$.