Addendum: Spectral Distribution of Atomic Oscillator Strengths

Abstract

The following notes outline significant advances which have come to our attention since the original paper (RMP68) went to press. They are written in the context of RMP68 and cross referenced to its Sections, page numbers, Figures, and Bibliography. The material selection has been subjective, as it was in RMP68. (1) A rather successful effort has been made (CMcD68) to improve the calculated photoioniza-tion cross section of I.i over a 5-eV range above threshold by a successive-approximation, Brueckner-Gold-stone procedure. This procedure follows the general approach of Sec. 5.3 but starts from a Hartree-Pock approximation (Sec. 5.5c) which includes all intra-channel effects in zero order. The zero-order results fall ~20oro below the HC67 measurements; thereby they fail to reproduce the agreement reported by a supposedly equivalent calculation (Se67). This initial approximation also yields an ~10% discrepancy between the "length" and "velocity" results corresponding to Kqs. (2.3) and (2.8); this discrepancy is analyzed in detail consistent with the discussions in Secs. 5.4 and 5.5. An interesting feature of (CMcD68) is the progressive reduction of the gaps between calculated and experimental values, as well as between the length and velocity results, in the course of successive approximations. Simultaneous improvement of the ground-and continuum-state wave functions appears essential to this end (see below). (2) As stressed in Sec. 5.4, agreement between the "length" and "velocity" formulas l required by the consistency equation (2.6)) is present in an initial independent electron approximation but gets lost in successive approximations unless the improvements in the ground-and continuum-state wave functions fulfil conditions that remain unspecified. The violation of (2.6) which results from improving the continuum function ttlorte in accordance with (6.5) and (6.6) is illustrated by the following identity (St69) f: The right-hand side of (A1) should equal-tft-i(E-E,) (P, l s l e~) in order to satisfy (2.6) but in fact differs from it by inclusion of the factor (e-Ep)/(E Ep) in the inte-grand. This factor introduces a departure from unity, by excess or defect, to the extent that higher approximations in the expansion (6.5) of 4'@ include zero-order components P, with e much larger or smaller than E. (3) Light with ho=66.6 eU, an emission line of nitrogen , photoionizes He, leaving the ion in either its m=1 or +=2 state and thus produces photoelectrons of either 42.0 or 1.2 eV. The observed intensity ratio of these electron groups is 0.08&0.02 (Sa69). This ratio can be compared with a prediction from the profile of the 2s2p excitation line in Fig. 27(a). According to the discussion of Eq. (8.7), the ratio should be-', srq'p'F/~; taking q=2.8, p=1, 1'=0.038 eU from (MC65), and &It =dE,/ds=27. 2 eU/(1. 61)' in accordance with page 447, one obtains 0.07. (4) Newer evidence has emerged on the systematic variation along the periodic system of a prominent nonhydrogenic feature of the absorption spectrum, mentioned brieQy at the end of Sec. 4.8 and elsewhere in Secs. 4.6, 4.7, and 4.8. This evidence concerns the evolution and disappearance of the "resonance near threshold" of absorption by inner subshells throughout the first set of transition elements and throughout the rare earths. The new data concern the 3P(Mri, m) thresholds from Ti to Ni (SHK69) and'the 3d(Miv, v) threshold in Yb (CSW68); they are to be combined, respectively, with the Cu (HKSS68) data and with the extensive observations on the rare-earth 4d(Xiv, v)) thresholds (ZFGZh67, FZGZh67). The rare earths with lower Z show a gradual rise of absorption near the edge with extensive broad-line structures super-posed on it (FZGZh67); the gradual rise was attributed in RMP68 to the same centrifugal effect as in Xe (Sec. 4.7) and the lines to unspecified crystal-structure properties of the metal-film absorbers. The lower-Z transition elements also show a gradual rise which, however, is not matched by the corresponding absorption of Ar near its first threshold; some structure is observed, notably in Cr near the resonance maximum. These effects extend over a 5-10-eV spectral