A semiclassical theory of atomic quantum defects is given in terms of a ’’radial action defect’’ derived in the context of Hamilton–Jacobi theory. This derivation leads to the relation δl(E) =πμl(E) between the semiclassical (WKB) phase shift and the semiclassical quantum defect, a result identical in form to that of Seaton for the analogous fully quantum mechanical quantities. The semiclassical theory is used to compute quantum defects for the l=0→3 Rydberg states of Li and the l=0→4 states of Na and K, with good results.
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Jaffé et al. (1977) studied this question.
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