Hund s cases a and

Figure 7.16 (a) Hund s case (a) and (b) Hund s case (c) coupling of orbital and electron spin... 

Changes in the degeneracy patterns between, for example, Hund s cases (a) and (c) can be attributed to monodromy. 

The case of intermediate coupling of momenta (between Hund s cases (a) and (6)), as well as that of breaking weak field approximation axe discussed in [294]. The molecular (/-factors for Hund s case (c) coupling are discussed in [92, 364]. 

The transformation of general Hund s case (a) and case (b) functions under space-fixed inversion... 

Figure 9.8. Correlation between the Hund s case (a) and case (b) rotational levels of a 2Tl state. The diagram is not drawn to scale for a good case (a) molecule the spin-orbit splitting is very much larger than the rotational level spacing.

Figure 3.1a Natural rotational quantum numbers for Hund s cases (a) and (b). Reduced term value plots for 2S (B = 1.0 cm-1) and 2nr (B = 1.0 cm-1, A = 20.0 cm-1), (a) Plot °f — BJ(J + 1) versus J(J + 1) displays case (a) limiting behavior for the 2II state at very low J. The dotted lines illustrate the B2/A corrections to the near case (a) effective B-values (See Section 3.5.4). The 2S state does not exhibit case (a) behavior even at low J (at J = 0 the limiting slopes of the 2S Fi and h l curves are —oo and +oo).

Equations (6.1.30) and (6.1.61) axe valid when the initial and final states are in Hund s case (a). In the case of orbitally degenerate 5 0 states, if either or both of the initial and final states are intermediate between Hund s cases (a) and (b), interference effects can occur, as illustrated by Gauyacq, et al., (1987) for the NO C2n—X2n three-photon transition. 

The transition intensities at the X2n1 /2 and X2n3/2 thresholds are equal, if the ion-core is at the Hund s case (a) limit. Experimentally, in conventional photoelectron spectra from the X1E+ ground state of HC1, the intensity ratio 2n1/2/2n3/2 is equal to 1.06 0.05 (Yencha, et al., 1989). This slight deviation from 1 can be explained because the 2n state is intermediate between Hund s cases (a) and (b) (Wang and McKoy, 1991). 

For the fragments OH and H from H2O, the internal motion of OH is not only rotation and vibration, but also electronic motion. In addition, rotational and electronic motions are coupled in OH with the coupling being intermediate between Hund s cases a and b. Although the other product is an atom, the spin of the electron of the H-atom has to be coupled to the partner product OH. This is why in most cases, (l6) does not describe the asymptotic motion of the products correctly. Instead, linear combinations of such wavefunctions have to be used in the general case. Nevertheless we first discuss the simplified case of decoupled motion. 

One now has a choice of how to construct a basis set in which to set up the Hamiltonian, and the best basis is the one which most nearly diagonalizes the Hamiltonian matrix. However, nature does not care which basis we choose and a full calculation in any basis yields the same results which basis is chosen is purely a matter of convenience. In diatomic molecules the choices of basis for the inclusion of spin most normally used were first considered by Hund, and are called Hund s cases a and b (see Figure 5 for explanation). 

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