Statistical weights of states

For the spin degeneracy we have seen that for the antiparallel form (parahydrogen) there is only one spin function (8.14) which corresponds to a value = o (equation 3.113). For the parallel form (orthohydr en) there are three spin functions (8.15) corresponding to the values of of + I, — I, and o (equations 3.114, 3.115, 3.116 et seq). Thus the statistical weight of states corresponding to even values of is ... 

Here, the energy levels are very close together and their discontinuous distribution can be replaced by a continuous one and so that that the statistical weight of states corresponding to the layer with a thickness of dz is ... 

It can be shown that H2CO is not a pyramidal molecule with one plane of symmetry by observing the 3 1 intensity alternation of the fine-line structure of some of its bands, which indicates that there are two planes of symmetry in the molecule. The 3 1 intensity alternation is due to the fact that the normal state energy levels with odd K have three times the statistical weight of states with even K. Therefore, subbands originating from even-K energy levels will be weak, while those from odd-K levels will be strong. 

Finally, let us consider molecules with identical nuclei that are subject to C (n > 2) rotations. For C2v molecules in which the C2 rotation exchanges two nuclei of half-integer spin, the nuclear statistical weights of the symmetric and antisymmetric rotational levels will be one and three, respectively. For molecules where C2 exchanges two spinless nuclei, one-half of the rotational levels (odd or even J values, depending on the vibrational and electronic states)... 

The formation of higher transition-metal borides depends on the competition and the statistical weight of the d and states of the metal atoms. Consequently, the acceptor metals Ni, Pd and Pt are expected to form metal-rich borides only i.e., besides the known PtBo.7 (anti-NiAs), Pt forms two borides, Pt 2B and Pt 4B, which... 

In Eq. (4.9), V is the frequency of radiation and a>. and (Ox are the statistical weights of the initial and final states. It should be remembered that Eq. (4.9) refers to the photoionization cross section, not the total photoabsorption cross section (see Sect. 4.2). 

Pj and Po = statistical weights of the respective states and are obtainable from Russell-Saunders coupling,... 

Table 2. Determination of statistical weight of the rovibronic states of in the MS group D3h(M) [3]...

The statistical mechanical theory of the helix-coil transition of DNA is improved by introducing approximate normalization factors for the unnormalized statistical weights of finding a given molecule of the assembly in a given microscopic state. 

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