Theoretical radiative lifetime of the metastable c3Πu state of H2

Magnetic dipole and electric quadrupole interactions are considered here as the mechanism for the forbidden radiative transition from the metastable c3Πu state of H2 to the dissociative b3Σu+ state. The discrete vibrational wavefuncion for the c3Πu state is generated from Browne’s potential. The continuum vibrational wavefunction for the b3Σu+ state is generated from an exponential type pontential function, which fits closely with Kolos and Wolniewicz’s potential. By virtue of this exponential type potential function, the phase integral and the exponential integral of the continuum vibrational wavefunction become integrable and an analytical expression is given for the vibrational wavefunction of b3Σu+. The electronic wavefunctions, used here to calculate the transition moments, are two-center wavefunctions previously derived by Chiu (for c3Πu) and by Hirschfelder and Linnett (for b3Σu+). It is found that the translational expansion of the magnetic dipole operator (originally at the center of mass) at the atomic centers generates an additional gradient operator, which contributes significantly towards the magnetic dipole transition probability. From the total transition probability which is a sum of that due to magnetic dipole transition and that due to electric quadrupole transition, a lifetime of τ=1.76 msec is calculated for the lowest vibrational level of the c3Πu state. For a comparison, the δ-function approximation is used for the continuum vibrational wavefunction. This approximation gives rather good agreement with the accurate calculation.