We have calculated the second-order interaction between the spin-orbit coupling perturbation H~~r '(d V/dr)1 s acting on the core electrons and the exchange Coulomb interaction between the valence and core electrons. This calculation was previously carried out for two alkali nd states (Na 3d and Rb 4d), and was shown to result in the observed inversion of the fine-structure interval b, v for these d states. This calculation is extended to excited np states, and it is shown that the radial integrals have opposite sign to those for nd, resulting in a small increase of the calculated Av (by -10-20% in all cases). Specific results have been obtained for several excited np states of Na, K, Rb, and Cs, and give agreement to within 20-30% with the experimental fine-structure splittings b, v, pt.14 1595
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