For all states with ,
there is a degeneracy associated with the two possible values
.
This arises due to the interaction between the rotational and electronic motion and is particularly significant for
electronic states.
Consider the case of a
state. The
state can interact with a nearby
state, leading to a shift in the energies for both the
and
electronic states. The degeneracy of the
and
levels is then removed. It can be considered that this splitting arises due to the inability of the electrons to follow the nuclear motion as the rotation increases, leading to a mixture between the
state with electronic states of different
.
The two electronic states,
and
have different symmetries and are labelled accordingly [72] :
For example, consider the origin of the lambda doubling in GeH+ pictorially. Figure 3.4 shows interactions between the possible orientations of the p orbital of the germanium ion and the hydrogen s orbital [48]. The germanium and hydrogen nuclei lie along the z axis. If the electrons were able to follow the motion of the nuclei exactly with no `slip', the two
orbitals would be degenerate. However, with increasing molecular rotation, the electrons tend to `lag' behind the nuclei. The py orbital (e-component) takes on a partly
,
whereas the pz orbital has
character. The distinction between these characteristics becomes impossible with increasing rotation, thus the degeneracy of the
state is lifted. The px orbital (f-component) remains unaffected with increased molecular rotation as it lies out of the plane of rotation.
The selection rules for electric dipole transitions obey the selection rule
which in terms of e and f levels correlates to:
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(3.1) | ||
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(3.2) |
For GeH+ the e component of the state is shifted (by rotational-electronic coupling to the
state) with respect to the f component and can be expressed as:
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(3.3) |
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