Rotational Spectroscopy - Quadrupole Splitting

Quadrupole Splitting

When a nucleus has a spin quantum number, I greater than 1/2 it has a quadropole moment. Then, coupling of nuclear spin angular momentum with rotational angular momentum causes splitting of the rotational energy levels; if the quantum number J of a rotational level is greater than I, 2I+1 levels are produced, but if J > I 2J+1 levels result. The effect is known as hyperfine splitting. For example, with 14N (I = 1) in in HCN, all levels with J > 0 are split into 3. The energy of the sub-levels are proportional to the nuclear quadrupole moment and a function of F and J. where F = J+I, J+I-1, ..., 0, ... |J-I|. Thus, observation of nuclear quadrople splitting permits the magnitude of the nuclear quadrupole moment to be determined. This is an alternative method to the use of nuclear quadrupole resonance spectroscopy. The selection rule for rotational transitions becomes