Odd-even staggering in the J and L distributions of atomic configurations

In atomic spectra, there are more even than odd J values and more J values of the (2n + 1/2) type (1/2, 5/2, 9/2, etc) than of the (2n + 3/2) type (3/2, 7/2, etc). The former phenomenon is linked with the excess of LS terms with an even value of (L + S), compared with those with an odd value. An exact formula is derived from the Pauli principle, although none is available for the total number of levels of an electronic configuration. The latter phenomenon, which is essentially independent of the Pauli principle, can be computed using the statistical method. Fluctuations also appear in the number of LS terms according to the parity of L, for any given half-integer spin S. Other exact formulae are derived. The ratios of the excesses to the total numbers of levels decrease more rapidly in configurations of increasing complexity for integer than for half-integer J values.