Coriolis splitting

The Rabi technique of radio frequency or microwave spectroscopy in atomic or molecular beams [10.14-10.17] has made outstanding contributions to the accurate determination of ground state parameters, such as the hfs splittings in atoms and molecules, small Coriolis splitting in rotating and vibrating molecules, or the narrow rotational structures of weakly bound van der Waals complexes [10.18]. Its basic principle is illustrated in Fig. 10.9. A collimated beam of molecules with a permanent dipole moment is deflected in a static... 

Coriolis splitting of rotational levels and to decide which of two theoretical... 

In an E vibrational state there is some splitting of rotational levels, compared with those of Figure 5.6(a), due to Coriolis forces, rather than that found in a If vibrational state, but the main difference in an E — band from an — A band is due to the selection rules... 

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>. 

It is reasonable to attempt an interpretation of depolarization for the state 2Pm within the energetically-isolated-state approximation. As the contribution to or 3/2) comes from large impact parameters, one may assume a rectilinear trajectory ( = 0) and use the random-phase approximation for R < Rm,Rm being the matching distance. The value of Rm itself is determined by the condition that the Coriolis coupling between molecular terms A% and is equal to the adiabatic splitting U B ) — t/04f). From equation (34) on the condition that AK Ae, we get U = U(B ) — U(A%) = AK(R), and using the polarization interaction equation (36) we finally obtain... 

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. 

Methane as the prototype of spherical tops was the subject of a great number of investigations, of which only some can be mentioned here. At high resolution the structure of rovibrational bands becomes very complicated due to tensorial splittings. Moreover Fermi and Coriolis resonances lead to interactions between fundamentals and overtone and combination bands of CH4 therefore theoretical models for the dyade 1/2 and 1 4 (Champion, 1977) and the pentade i/j, i/3, 2j> 2, 1 2 + and 21/4 (Lolck et al., 1982 and Poussigue et al., 1982) have been developed and sets of molecular con.stants were determined by adjustment to all available experimental high resolution IR and Raman... 

Under conditions of higher resolution, the far infrared spectrum of tetrahydro-furan was found to be quite complex (Fig. 4.29) with a number of bands split by Coriolis interaction. Assignments and analysis of the band origins led to a potential function... 

J > K with K = 0, 1, 2,ij. The inclusion of the Coriolis interaction introduces further splitting of the states with K / 0 (the so-called /-doubling) into states with e and / parity labels. 

In high-barrier cases quite often the splitting of a pair of nearly degenerate levels can be determined by treatment of the Coriolis resonances between the levels (see below). These splittings may be used to scale the energy levels however, even though they are very well determined, this... 

A Coriolis-like conpling parameter q " characterizing the interaction between the internal rotation of the methyl gronp and the overall rotation was determined from the -A splittings. 

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