Permutational symmetry electron/nuclear spin effects

Let us discuss further the permutational symmetry properties of the nuclei subsystem. Since the electronic spatial wave function v /f (r, s R0) depends parametrically on the nuclear coordinates, and the electronic spacial and spin coordinates are defined in the BF, it follows that one must take into account the effects of the nuclei under the permutations of the identical nuclei. Of course,... 

Although H is nonrelativistic, relativistic effects manifest themselves in the realizable eigenstates through permutational symmetry. Spectroscopic states must be totally antisymmetric under the permutation of the labels of any two electrons. In addition, total anti symmetry/symmetry with respect to the permutations of the labels of fermionic/bosonic nuclei must be exhibited. For this reason, the set ]y jMn r,R s not deternuned by mj,Zj> alone but by mj,Zj,Sj>, where Sj> is the set of nuclear spins. 

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