INFRARED SPECTRUM OF SOLID HYDROGEN: THEORY OF THE INTEGRATED ABSORPTION COEFFICIENTS OF $W(\Delta J-6)$ TRANSITIONS

Abstract

The present work has been motivated by the $efforts^{1}$ to observe $W(\Delta J-6)$ transitions in the induced infrared spectrum of solid $H_{2}$. Transition with $\Delta J=6$ should occur due to the part of the dipole moment induced by the $2^{6}$ th electric multipole moment of $H_{2}$. Starting with the $expressions^{2-3}$ for the dipole moment induced in a molecule by the $2^{\ell}th$ multipole moment of its neighbour, expressions for the integrated absorption coefficients are derived for the $W_{v\leftarrow o}(o), W_{v\leftarrow o}(1)$, single transitions and the $W_{v\leftarrow o}(o), O_{v\leftarrow o}(0)$ double transition. On account of the higher order multipolar induction mechanism, these transitions are expected to be extremely weak. Their observation would provide the first experimental value for the $2^{6}$ th moment of $H_{2}$. We have also calculated the possible satellite structure around the $W_{v\leftarrow o}(O)$ line when the $para-H_{2}$ crystal contains traces of ortho impurity.