Pure Hunds cases

Let the diatomic (or linear) molecule satisfy the conditions for the Hund s case (a) coupling scheme (see Section 1.2, Fig. 1.3(a)), where the electronic orbital and spin angular momenta are coupled with the internuclear axis. The magnetic moment which is directed along the internuclear axis and corresponds to the projection Cl of the total angular momentum J upon the internuclear axis, has the value 

Account has been taken here of the fact that the Lande factor gi which is connected with the electronic orbital momentum precisely equals unity gi = —1, whilst the spin-connected one equals gs = —2.0023. The recommended gs and hb values can be found in Table 4.1. The discrepancy of the gs value from two is due to quantum electrodynamical correction. It is important to mention that, in agreement with the definition of Cl = A+2 as a positive value (see Section 1.2) and gi, gs as negative (see Section 4.1), we have from (4.54) that if 2 A, but 7S2 7/A, hq can take a positive value because Hu and Cl possess the same direction (positive Lande factor go). In other cases g,Q is negative, (J-Q being directed opposite to Cl as shown in Fig. 4.24 (negative go). 

Let us consider some simple examples. For a singlet state 1IIq=i with A = 1, 5 = 2 = 0 we have a negative moment value hq = giUB determined only by the orbital motion of electrons. It thus precisely equals the Bohr magneton. For the doublet state 2IIn, where Cl can be 3/2 or 1/2, is determined both by the orbital and by the spin contribution. Thus, for Cl = 3/2, A = 1, 2 = 1/2 according to (4.54) we obtain Hn = (gi + gs/2)HB —= —2.00116. Of particular interest is the state 2n1/2 with Cl = 1/2, A = 1 and 2 = —1/2 where hq = (gi - gs/2)/j,B, and hq is determined only by the anomalous quantum electrodynamical 

For instance, for the n state we have gj = —1/[J(J+1)], as was immediately confirmed for the case of alkali dimers and applied, in particular, to Na2(H1nu) [290] and to K2(51nu) [312] in order to determine the lifetime from the Hanle effect. 

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]. 

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No Rydberg state ever exactly corresponds to a pure Hund s case, except at n = 00 or 3, but rather to a situation in an intermediate Hund s case, and it is necessary to choose, to describe it, a basis set corresponding to any one of the pure Hund s cases. The energy terms to be added in each Hund s case are different depending on this choice of basis set. To clarify these choices, consider first the simple case of atoms. 

If a lattice consists of a small, very compact ion and a large, easily polarizable ion, the effect of the deformation may be so great that the purely heteropolar type of bond is lost and a lattice results whose properties resemble those of a molecular lattice. Hund has investigated this problem and found that layer lattices result generally in these cases, in... 

Einstein Coefficients. Using the spectroscopic constants for the X v = 0 and A Ilj, v = 0 states derived from the A<-X absorption spectrum [8] and assuming Hund s case (b) to hold for these states, the Einstein A coefficients were calculated for 23 purely rotational transitions between the X v = 0, N = 0 to 5 levels and for 79 purely rotational transitions between the A Ilj, v = 0, N = 1 to 5 (and A-doublets) levels [9]. 

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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