OBSERVATION OF THE S-3(0) TRANSITION IN SOLID PARAHYDROGEN AND A THEORY OF SOLID-STATE ROVIBRATIONAL LINE WIDTHS

The S-3(0) transition (nu = 3 <-- 0, J = 2 <-- 0) in solid parahydrogen has been observed at 12058.98 cm(-1) with a width of 0.25 cm(-1) (fwhm). The line width of this transition is broader than that of the pure rotational S-0(0) transition. Although line widths usually narrow with vibrational excitation due to diminished coupling among molecules and a larger mismatch between the energies of the excitons and phonons, all observed S-nu(0) (nu = nu <-- 0, J = 2 <-- 0, for nu = 1, 2, 3) transitions exhibit line widths which are larger than that of the pure rotational transition. This has led us to develop a new theory of solid-state line widths. The S-nu(0) line widths are herein shown to be a result of the mixing of the simultaneous state Q(nu)(0) + S-0(0) manifold (nu = nu <-- 0, J = 0 <-- 0 and nu = 0 <-- 0, J = 2 <-- 0, respectively, for two neighboring molecules) into the zeroth-order S-nu(0) manifold. The derived transition moment illustrates that only states with a total exciton momentum, k, of zero are accessed, The Line widths of all S-nu(0) transitions are reproduced theoretically by considering the consequences of simultaneously placing two excitons, Q(nu)(0) and S-0(0), in the lattice. Although both can propagate independently, the interactions allowing the propagation of rotational energy among lattice sites is much stronger than that for vibrational energy. As a result, the rotational excitation hops much more quickly than that of vibration, By considering the roton's dephasing due to the presence of the simultaneously-created Q(nu)(0) excitation, one can calculate the contribution of this coherence relaxation (i.e., T-2 relaxation) process to the overall frequency uncertainty of each S-nu(0) transition. Due to this scattering, the crystal state irreversibly decays from \Q(nu)(0) + S-0(0))(k=0) to \Q(nu)(0) + S-0(0))k not equal 0, thus rendering the state unmeasurable by changing the phase relationship between the initial and final states. All Delta J = 2 rovibrational Line widths have been calculated using this method; our theoretical line widths closely reproduce those observed experimentally.