Lifetime measurements and quantum-defect theory treatment of the k 3Πu− state of hydrogen molecule

Abstract

The experimental and theoretical lifetimes for rovibronic k 3Πu− states of H2 and D2 isotopomers have been investigated over a wide range of vibrational v′ and rotational N′ quantum numbers. Lifetimes have been measured by a delayed coincidence method, combined with direct electron-impact excitation of the ground state molecules and single photon counting techniques to detect induced fluorescence to the a 3Σg+ state. Pronounced pressure-dependence of the experimental lifetimes was observed and properly taken into account. The pure radiative lifetimes of the k 3Πu− states were estimated using theoretical transition dipole moments responsible for the visible k 3Πu→a 3Σg+ transition plus infrared emission on the higher-lying Λg3 states belonging to the 3s,d 3Λg complex. Both the predissociative and autoionization decay rates were predicted by the Fermi-Golden rule based on radial coupling matrix elements for the k 3Πu∼c 3Πu and k 3Πu∼X2Σg+(H2+) pairs of interacting states, respectively. The required electronic matrix elements as a function of internuclear distance R were derived in the framework of quantum-defect theory modified to allow explicit consideration of regular radial coupling effects. The relevant quantum-defect functions of all states treated were extracted from published highly accurate Born–Oppenheimer potential curves. Both the total theoretical radiative, predissociative plus autoionization rates and the calculated rovibronic term values agree well with their experimental counterparts. The N′-dependence of the experimental and theoretical lifetimes is found to be negligible for both isotopomers while a pronounced v′-dependence is observed for a H2 isotopomer. The vibrational predissociation is very weak comparing with radiative decay for both isotopomers whereas the autoionization rate is comparable with the radiative ones for the H2 v′⩾4 levels though it is still negligible for the D2 v′⩽6 levels.