Bose-Einstein statistics, permutational function

As mentioned above, we assume that the molecular energy does not depend on the nuclear spin state For the initial rovibronic state nuclear spin functions available, for which the product function 4 i) in equation (2) is an allowed complete internal state for the molecule in question, because it obeys Fermi-Dirac statistics by permutations of identical fermion nuclei, and Bose-Einstein statistics by permutations of identical boson nuclei (see Chapter 8 in Ref. [3]). By necessity [3], the same nuclear spin functions can be combined with the final rovibronic state form allowed complete... 

Explicitly, the Pauli principle states that the wave function of an ensemble of particles with half-valued spin, which obey Fermi-Dirac quantum statistics and are therefore called/emions, must change its sign upon exchange of any two coordinates in the wave function. A fermionic many-particle wave function is then said to be antisymmetric under pair exchange of coordinates. By contrast, the wave function of a set of particles with integer spin, which obey Bose-Einstein quantum statistics and are therefore called bosons, does not change its sign upon pair permutation of any two coordinates in the function. 

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