Half-integer nuclear spins

The NMR spectra of quadrupole nuclei with half-integer nuclear spins 7> 1/2 consist of the central transition (CT), +1/2 <-> —1/2, and the so-called satellite transitions, ( 1/2 <-> 3/2), + 3/2<-> 5/2), etc. In the case of strong quadrupolar interactions, it is practically impossible to excite the whole spectrum non-selectively (i.e., the CT is often selectively observed). Therefore, the second moments, caused by quadrupolar interactions in Eqs. (6) and (10), are those of the CT only. 

Fig. 3. Line shape function of the central transition of a quadrupole nucleus with a half-integer nuclear spin, calculated for /Jq=0 in the limiting case of rapid magic angle spinning assuming that the electric quadrupole interaction is the dominating line broadening interaction...

I/ I+ ) for atoms with half-integer nuclear spin... 

The highest half-integer nuclear spin of a stable nucleus is / = 9/2. The energy of a nuclear quadrupole energy level is given as = e qQxjlA where x is a solution of the secular equation... 

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)... 

We now compare the results calculated for the fundamental frequency of the symmetric stretching mode with the only available experimental datum [78] of 326 cm . The theoretical result is seen to exceed experiment by only 8.3%. It should be recalled that the Li3 and Li3 tiimers have for lowest J the values 0 and respectively. Thus, the istopic species Li3 cannot contribute to the nuclear spin weight in Eq. (64), since the calculations for half-integer J should employ different nuclear spin weights. Note that atomic masses have been used... 

J = 1,3,5 — are antisymmetric with respect to the nuclear coordinates. It follows that homonuclear diatomic molecules with anti-symmetric nuclear spin wave functions (nuclei with half-integer I = 1/2, 3/2...) can combine only with symmetric rotational functions (even J = 0,2,4...), while those with symmetric nuclear spin wave functions (even I) can combine only with antisymmetric rotational functions... 

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