Centrifugal distortion terms

An obvious improvement to the theory, which should be most significant for the J = 13/2 levels, would be the inclusion of centrifugal distortion terms. There is, however, another interaction which might be significant, namely, the nuclear spin-rotation term. This is represented by an additional term in the effective Hamiltonian,... 

Further improvement in the agreement between experiment and theory, particularly for the higher J levels, would be obtained by the inclusion of centrifugal distortion terms. We will, however, defer discussion of these terms until we come to describe the results for the OH radical, where centrifugal distortion is much more important. Our reduction in the number of parameters required for a satisfactory quantitative interpretation of the radiofrequency electric resonance spectrum arises because of a number... 

Note that a centrifugal distortion term has been included the resolution and accuracy of pure microwave spectroscopy warrants this inclusion, even for the lowest rotational levels. 

The effective Hamiltonian used by Wayne and Radford was essentially that described earlier for 3S SO, with the addition of a centrifugal distortion term ... 

The constant term B .Ia(.Ia + 1) is absorbed into the term value Tv( 2) and is not considered to be part of the rotational Hamiltonian. There are matrix elements off-diagonal in v but these are small and are taken into account as centrifugal distortion terms. The result of (10.145) is that the first-order rotational energies of the two electronic states (for Ja = 3 /2) are given by... 

The centrifugal distortion terms in (11.44) were incorporated rather simply by making the replacements... 

The centrifugal distortion term involving yd is remarkably large, so much so that at N = 60, the order of the spin components actually changes sign. This is probably a unique observation. 

In Eq- (4.32) we shall provisionally neglect the centrifugal distortion terms. 

Another complication arises from the fact that the rotational constants are usually obtained as effective fitting parameters of a reduced rotational Hamiltonian [14]. Not only do the numerical values of the rotational constants depend on the exact form of the reduced Hamiltonian, they also contain small contributions from quartic and higher order centrifugal distortion terms. Watson [14] has proposed to always determine the so-called determinable combinations of these constants. The values of these combinations are independent of the form of the reduction, although they still contain small contributions from the distortion terms. Up to the quartic centrifugal distortion terms, the determinable combinations of the rotational constants are... 

Although centrifugal distortion is not a perturbation effect, a derivation of the form of the centrifugal distortion terms in Heff provides an excellent illustration of the Van Vleck transformation. If the vibrational eigenfunctions of the nonrotating molecular potential, V(R) rather than [V(R) + J(J + 1)H2/2/j,R2, are chosen as the vibrational basis set, then the rotational constant becomes an operator,... 

It is evident from Eq. (4.2.22) that the correct form of the centrifugal distortion terms is not given by the intuitive prescription replace Bv everywhere it appears in Eq. (4.2.20) by BV—DVJ(J+1). Alternative methods for evaluating the Eq. (4.2.21) perturbation summation have been proposed by Tellinghuisen (1973) and Kirschner and Watson (1973). 

The A-reduced form for the quartic and sextic centrifugal distortion terms is... 

The peaks representing the R branch get closer and closer together as / increases, a. Use equation 14.41 to estimate at what rotational state the rovibrational lines will cease to be separated from each other, and will start moving to lower energy. (This point is called the band head of the series of absorptions.) To simplify the problem, neglect the centrifugal distortion term. Use Bq = 10.44 cm and = 10.14 cm h... 

Xj.Xx.Xd centrifugal distortion terms of the quadrupole coupling, compare eq. (8)... 

Mo MhMn molecnlar dipole moment in the vibrational gronnd state centrifugal distortion terms of the dipole moment ju = Mo+MjJ J + ) + MkK ... 

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