Bethe’s notation

Other groups may be handled in a similar manner to O in Example 8.1-1. For improper rotations, the two rules formulated previously hold also for double groups (Box 8.1). If the group contains the inversion operator, even or odd parity is indicated by a superscript of + or —in Bethe s notation and by a subscript g or u in Mulliken-Herzberg notation. 

Actually, different B values were found from interconfigurational versus intra-configurational transitions. To account for this, the notations B y B33, emd Bgi have been introduced (19), the subscripts being related to Bethe s notation of d orbitals in cubic symmetry, ysfe) and ysffs). The transitions Bg(t%g) of a [Pg.177]

We will now summarize the conclusion of the Kirkwood-Bethe theory. Fig 15 shows the computed peak pressure and computed reduced tunc constant for TNT plotted VS the inverse reduced distance. The dotted lines are a power function fit thru the computed peak pressures. The x s are drawn in by the writer to compare computed and measured reduced time constants (taken from Fig 7.9, p 240 of Ref 1). Comparison of other computed and measured shock parameters on the basis of the power functions shown below (in Cole s notation and in English units) is made in Table 11 (from p 242 of Ref 1)... 

Though the Mulliken-Griffith nomenclature is used here, the sub-scripts 3 and 5 on various quantities are reminescences of Bethe s original notation y3 and y5 for the two sub-shells. 

To generate an irreducible G subspace, for particular cases, f needs to be chosen with care. In the case of the kubic harmonics, first defined by Bethe in 1929 suitable functions are the mononomials x y"zP, which we identify in Elert s notation as (mnp). The kubic harmonics up to level 4 and their maps onto the irreducible representations of the cubic groups are listed in Table 3.9. 

The different notations for the IRs of Oh and Td are given in Appendix B. For the acceptors, the Bethe-Koster notation is used and for donors, the Mulliken s one. 

Using Bethe s T-notation for the underlying double group Cf, that is isomorphous to D. ... 

Relative to the 5f - ground term. The values of J are indicated. Relative to the 5f J-9/2 ( l) ground level. Bethe notation is used for these Kramer s doublets. 

Fig. 3.5/ and 6d manifolds in an octahedral field and their correlation with free ion one-electron levels. Note that the crystal field lowers the energy of the 6d levels (relative to 5J) prior to splitting. Bethe notation is used for the Kramers s doublets and Mulliken notation for the spin-free Hamiltonian states, as usual. 

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