Nuclear Spins and Wave Function Symmetry

If the nuclei in a diatomic molecule have nonzero spins, the wave function in Eq. (22.2-35) must be multiplied by a nuclear spin wave function to be a complete wave function. 

In the case of homonuclear diatomic molecules (molecules with two nuclei of the same isotope of the same element), the wave function must not pretend to distinguish between the nuclei, which are indistinguishable from each other. The wave function must be symmetric with respect to interchange of the nuclei if they are bosons and must be antisymmetric with respect to interchange of the nuclei if they are fermions. 

The spin angular momentum of a nucleus is denoted by I and has the same general properties as any angular momenmm. Its magnitude takes on the values 

The angular momentum vector I is me vector sum of me spin angular momenta of all of me nucleons in me nucleus. A given nucleus can have different spin states, just as 

If / = 1/2, as is the case with H, and some other nuclei, there must be an odd number of nucleons. The nuclei are fermions and the total wave function must be antisymmetric. Each nucleus can occupy nuclear spin functions like those of electrons, denoted by a for spin up and p for spin down, and the diatomic molecule has singlet and triplet nuclear spin states like those of two electrons. The triplet nuclear spin functions for such a diatomic molecule are symmetric  

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Section 22.3 Nuclear Spins and Wave Function Symmetry... 

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