Hyperfine-interaction-induced g/u mixing and its implication on the existence of the first excited vibrational level of the state of and on the scattering length of the H + H collision.

calculations of the energy level structure of that include relativistic and radiative corrections to nonrelativistic energies and the diagonal part of the hyperfine interaction have predicted the existence of four bound rovibrational levels [( = 0, = 0 - 2) and ( = 1, = 0)] of the first electronically excited ( ) state of , the ( = 1, = 0) level having a calculated binding energy of only = 1.082 219 8(4)·10 E and leading to an extremely large scattering length of 750(5) a for the H + H collision [J. Carbonell , J. Phys. B: At., Mol. Opt. Phys. , 2997 (2004)]. We present an investigation of the nonadiabatic coupling between the first two electronic states ( and ) of induced by the Fermi-contact term of the hyperfine-coupling Hamiltonian. This interaction term, which mixes states of total spin quantum number = 1/2, is rigorously implemented in a close-coupling approach to solve the spin-rovibronic Schrödinger equation. We show that it mixes states of gerade and ungerade electronic symmetry, that it shifts the positions of all weakly bound rovibrational states of , and that it affects both the positions and widths of its shape resonances. The calculations demonstrate that the = 1/2 hyperfine component of the A ( = 1, = 0) state does not exist and that, for = 1/2, the s-wave scattering lengths of the H + H(1s) collision are -578(6) a and -43(4) a for the = 0 and = 1 hyperfine components of the H(1s) atom, respectively. The binding energy of the = 3/2 hyperfine component of the A ( = 1, = 0) state is not significantly affected by the hyperfine interaction and the corresponding scattering length for the H + H(1s, = 1) collision is 757(7) a.