By W.R. Hindmarsh and D. ter Haar (Auth.)
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S 2 The average values are evaluated by the methods already used, bearing in mind that S j and S2 precess relatively rapidly about S, S more slowly about J and J very slowly about F. Sj I . S i = I . J HYPERFINE STRUCTURE and similarly 57 I . S2 = i l . J where we have put Si = ^2 for S states. F o r states, J = 0 and I . J = 0. 12) Next we treat the case where one of the electrons is in an 5:-state and the other not. Here we neglect the contribution of the non-5 electron t o the hyperfine interaction.
This discrepancy is partly because Racah used a value of ΔΓΟ/ΓΟ some 10 times too large, and partly because his value of |iA(0)|^ was also too large. 15)) for |i/^(0)|^ is on the whole much more reliable than the results of numerical calculations. The modification known as the Goudsmit -Fermi-Segré expression (see Paper 12) is better still: When such values are used, and the electron configuration responsible for the spectral lines concerned correctly identified, there is order of magnitude agreement between theory and observation.
F ) ( S . G) = i f t . G + iihS. 4) therefore cancel, and we have (c) The total interaction We now write down the total magnetic hyperfine energy: = + Wefind ;Ό·+1) This confirms that the interaction is proportional to I . J , and we have therefore given a satisfactory interpretation of the occurrence of the Lande interval rule for hyperfine structure. Quantitative predictions of the magnitude of the effect can be made provided Qj, which gives the value of the magnetic dipole moment of the nucleus, is known, and r " ^ can be evaluated.