Energies, transition probabilities, predissociation rates, and lifetimes of the ${{\rm{H}}}_{2}$, HD, and ${{\rm{D}}}_{2}$ $c{}^{3}{{\rm{\Pi }}}_{u}^{-}$ state

Abstract

Transition probabilities of H 2 , HD, and D 2 Pc u 3 − S + a g 3 electric dipole, Pc u 3 − S + b u 3 discretecontinuum magnetic dipole, and electric quadrupole transitions have been calculated using accurate energies and ro-vibrational wave functions obtained from precise ab initio potential energy curves. The predissociation rates of the Pc u 3 (v N , ) levels by direct and indirect spinspin and spin-orbit coupling between Pc u 3 − S + b u 3 fine structure levels, have been also determined. The present investigation achieved good agreement with measured lifetimes of the Pc u 3 fine structure levels without adjustment. A comparison of the calculated and observed lifetimes of metastable H 2 , HD, and D 2 suggests that the Pc u 3 − S + b u 3 magnetic dipole and electric quadrupole transition moments underestimate the spontaneous emission rate of the metastable levels by ∼370 s −1 . The measured and calculated lifetimes of H 2 , HD, and D 2 fine structure levels are in very good agreement after the adjustment of 370 s −1 to the spontaneous decay rate of the Pc u 3 − S + b u 3 transition. The calculated energies, transition probabilities, and predissociation rates obtained in the present work, along with the P c u 3 state excitation function, are sufficient to determine the P c u 3 state emission cross section, the kinetic energy distribution of H(1s) atoms, and the energy deposition rate of the S + X g 1 − P c u 3 excitation. In a previous investigation by Berg and Ottinger (1994 J. Chem. Phys. 100 8746), the authors were forced to insert a large scale factor into the predissociation rate in order to reconcile with measured lifetimes. Errors introduced in the approximations made in the previous investigations are discussed in the text. The H 2 P c u 3 state has the second largest triplet state excitation cross section. Predissociation and spontaneous emission of the P c u 3 state plays an important role in the energy deposition of H 2 -dominated atmospheres.

Isotope dependence of thec3Πu−b3Σ${}_{u}^{+}$ andD1Π${}_{u}^{+}$−B′1Σ${}_{u}^{+}$ predissociation rates of molecular hydrogen

“…In contrast, the F 1 and F 3 components of the N level can only couple to the F 2 component of the N+1 and N−1 levels, respectively. Second and more importantly, the spin-orbit and spin-spin interactions add in the F 2 component but cancel in the F 1 and F 3 components (Liu et al 2017a). The overall predissociation rate also decreases with the reduced mass, which is a consequence of the strong μ dependence of the FCFs and the c u 3 P + −b u 3 S + coupling via the second order process.…”

“…Accurate calculation of some high (v, N) levels of the a g 3 S + and c u 3 P states of the heavy isotopologues such as DT and T 2 requires the potential up to 600 to 1000 a 0 . The three term extrapolation based on the last 3 points of the potential around 44 a 0 used in our previous work (Liu et al 2012(Liu et al , 2016(Liu et al , 2017a) is insufficient. The H 2 b u 3 S + long range potential of Ovsiannikov and Mitroy (2006) and the a g 3 S + , c u 3 P , B¢ u 1 S + and D u 1 P long range potentials of Vrinceanu and Dalgarno (2008) are used to extend V(R) to the required ranges of R (see also Liu et al 2017b).…”

“…This investigation strongly suggests that approximate isotope relations should be applied with caution to the predissociation rate. Liu et al (2017a) for the corresponding lifetimes of the H 2 , HD and D 2 molecules b Statistical average of the decay rates of the F 1 , F 2 , and F 3 components of DT and T 2 based on the 2J+1 degeneracy.…”

“…Except for the small difference in the V (R) of the a g 3 S + , b u 3 S + and c u 3 P states, the calculation of the three types of transition probabilities and FCFs is identical to those in Liu et al (2017a). As noted in Liu et al (2017b), small changes in V rad (R) and V rel (R) and the addition of the V nad (R) introduce negligible changes (0.1%∼1.0%) in transition probabilities, FCFs and predissociation rates from those of Liu et al (2017a). Other than the small V(R) changes noted above, the predissociation rates of the HT, DT and T 2 c u 3 P -(v, N, J) levels are also calculated in the same ways as in the earlier work (Liu et al 2017a).…”

“…For the same (N, J) level, the ratio of first order predissociation rates of two isotopologues is related to the FCF ratio: ) . Table 5 shows the c u 3 Ppredissociation rates of the fine structure levels of the v=0-4 and J=1−9 states for HT, DT and T 2 molecules, calculated using the same method as that of Liu et al (2017a). The F 2 component has a larger rate than the F 1 component, which, in turn, is greater than the F 3 component.…”