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Predissociation by tunnelling

Barriers caused by avoided crossings between two states of the same symmetry are known to occur in several molecules which are isovalent with GeH+. For example AlH has a well known barrier which occurs at large internuclear distances. This causes a breaking off in the rotational structure above v$^{\prime }$=1, J$^{\prime }$=7 for the $^{1}\Pi $ state when recorded in emission [74], whereas in absorption, the v$^{\prime }$=1, J$^{\prime }$=16 has been observed (for J$^{\prime }$ $\geq$ 12 the lines have a marked increase in width) [74]. Due to the differences between absorption and emission detection techniques, it is more difficult to observe the emission spectra for the broad, low intensity lines lying above J$^{\prime }$=7.

For GaH, which is isoelectronic with GeH+, the $^{1}\Pi $ state (in the absence of any interactions between electronic states) would have an extremely shallow minimum [75]. Due to a higher lying $^{1}\Pi $ potential an avoided crossing is induced in the lower $^{1}\Pi $ state. Rotational levels of the v$^{\prime }$=0 state lie trapped behind the barrier in the lower $^{1}\Pi $ state. Lifetime broadened lines are found in the absorption spectrum [76], where identification to rotational levels is impossible due to the large linewidths. Identification of the diffuse R and Q band heads in GaH was possible following a study of the corresponding band of GaD, where broad, but individual, rotational lines could clearly be resolved. A barrier due to an avoided crossing in the isovalent species SiH+, CH+ and GeH+ is not expected to be as high due to the ion-induced dipole having a weak attractive effect between the potential surfaces. The dissociation asymptotes of the two lowest $^{1}\Pi $ states of GaH are separated by 33,000 cm-1, whereas those of GeH+ are separated by 61,000 cm-1. Therefore the mutual repulsion in GeH+ between the $^{1}\Pi $  states will be reduced in comparison with GaH.

A shape resonance is a level in which a molecule can become classically bound, due to a centrifugal barrier preventing dissociation. A centrifugal barrier is caused by orbital motion of the nuclei. Through quantum mechanical tunnelling (the radial wavefunction penetrates the barrier), the molecule can dissociate. A centrifugal energy term is added to the potential of the potential of the non-rotating molecule [V$_{\rm el}$(R)]:


\begin{displaymath}
{\rm V_{eff}(R) = V_{el}(R) + \frac{\hbar^{2}}{2\mu R^{2}}\left[J(J+1)-\Omega^{2} \right]}
\end{displaymath} (3.15)

As can be seen from Equation 3.15 , for large values of J, V$_{\rm eff}$ can support a number of bound rotational states which lie above the dissociation limit of V$_{\rm el}$. Molecules which exhibit such rotational barriers include H2+ [77], CH+ [48,49,78,79] and HeH+ [45] .


next up previous contents
Next: Feshbach resonances Up: Predissociation Previous: Born Oppenheimer Approximation   Contents
Tim Gibbon
1999-09-06