Coriolis interactions

This Coriolis hypothesis is borne out by the V2 dependence of all of the other vibrational fine structure constants (42. 22 7n) [5]. All of these constants are nearly independent of V2 up to V2 = 36, where they suddenly begin to change rapidly. The 92 constant, which controls the Al = 2 interaction between l = 0 and l = 2 components of the same (V, V2,v3) vibrational state, is affected by the same Al == 1 Coriolis interaction that caused the rapid variation of Bo,U2,o. Figures 10 and 11 show the nearly identical V2 dependence of q2 and Bo. o- Figure 12, which is a plot of 2(1 2) versus Bo,U2,o, shows that despite the erratic i>2 dependences of both 2 and B, the 2 versus B plot is linear. This indicates that the changes in both constants originate in the same Coriolis interaction ... 

Figure 12. A plot of 42 vs. B(o.. O) for HCP. The nearly linear relationship indicates that B and 92 are both affected by the same A/ = 1 Coriolis interaction.

The higher bridge deformation vibration is split into two at about 696 and 666 cm 1. It also has rotational fine structure. The vp bands are at 170 and 145 cm-1. The individual bands are perpendicular bands with strong Q branches whose spacing is altered by Coriolis interaction between the two components of vp. An interesting treatment of the latter is given in79>. 

Figure 5.3 Correlation diagram of molecular terms for a pair of similar (excited and ground-state) alkali atoms. The right part of the figure corresponds to free atoms, the left part corresponds to the strong dipole-dipole interaction (Fdip A ). Dots mark crossings of terms coupled by the Coriolis interactions.

If atoms A and B are similar, adiabatic molecular terms are classified as A, . If only the dipole-dipole interaction is taken into account, adiabatic energies are given by equation (38) with S = 0. According to selection rules the only coupling between states will be due to the Coriolis interaction between 2 and II terms of the same parity. 

To understand this discrepancy let us estimate the characteristic distance Rm at which the off-diagonal element of the Coriolis interaction between E and II terms prevails over the difference in adiabatic energies ... 

It is a phase space rather than configuration space theory, so it can treat Hamiltonian systems containing unconserved angular momenta like Coriolis interactions which prevent the Hamiltonian from being written as a sum of the kinetic and potential energies [6,18]. The resulting hypersurfaces are dynamical in that they involve momenta as well as coordinates. 

Our second order Hamiltonian in Eq. (3.46) describes the effects of the large-amplitude inversion motion in the potential as well as in the kinetic energy part of the operator, and the effects of the centrifugal distortion and Coriolis interactions. 

Thus, for each value of / we have two 7x7 matrices, one connecting symmetric m a states with the antisymmetric states ( 1 2 + 1 4) and vice versa (Fig. 16). For special values of the rotational quantum numbers/, k, instead of a 7x7 matrix we have smaller blocks . This factorization is the analog of the factorization of the matrices describing Coriolis interactions in a C3V rigid molecule and can be used for a qualitative interpretation of the anomaly in Fjg. 17. For example, the/ =K levels in the —I component of the 1 4 level have basically the ground-state character of the rotational dependence of the inversion-splitting (Fig. 17) because they are obtained from the 1x1 block and therefore are unperturbed. 

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