Section 4.2.2.7. Absorption-edge locations

Only a small number of absorption-edge locations have been directly measured to high accuracy using the currently acceptable protocols. Some of the available data were obtained in order to provide wavelength determinations for spectra from highly charged and/or exotic atoms (Bearden, 1960; Lum et al., 1981). This small group was, however, significantly expanded very recently by an important set of new measurements, extending to Z = 51, that are well coupled to the optical wavelength scale (Kraft, Stümpel, Becker & Kuetgens, 1996) The resulting experimental database is summarized in Table 4.2.2.3. The effort that would be needed to expand the experimental database in a systematic way is quite large. Thus, we make use of a procedure, not previously used for this purpose, that combines available electron binding energy data with emission-line locations from our expanded reference set of emission-line data and emission lines that have been rescaled to be consistent with the optically based scale. At the same time, calculation of the location of absorption thresholds within the theoretical framework (see below) has been undertaken and will be made available in the longer publication and on the web site.

Table 4.2.2.3| top | pdf | Directly measured and emission + binding energies (see text) K-absorption edges in Å Numbers in parentheses are standard uncertainties in the least significant figures. Z Symbol Directly measured Emission + binding energies References 23 V 2.269211(21) 2.26893(11) (a) 24 Cr 2.070193(14) 2.07014(17) (a) 25 Mn 1.8964592(58) 1.896457(42) (a) 26 Fe 1.7436170(49) 1.743589(98) (a) 27 Co 1.6083510(42) 1.60836(17) (a) 28 Ni 1.4881401(36) 1.48823(25) (a) 29 Cu 1.3805971(31) 1.38060(16) (a) 30 Zn 1.2833798(40) 1.28338(15) (a) 39 Y 0.7277514(21) 0.727750(23) (a) 40 Zr 0.6889591(31) 0.688946(30) (a) 41 Nb 0.6531341(14) 0.653112(29) (a) 42 Mo 0.61991006(62) 0.619906(64) (a) 45 Rh 0.5339086(69) 0.533951(10) (a) 46 Pd 0.5091212(42) 0.509156(11) (a) 47 Ag 0.4859155(57) 0.4859168(91) (a) 48 Cd 0.4641293(35) 0.464135(12) (a) 49 In 0.4437454(48) 0.443740(11) (a) 50 Sn 0.4245978(29) 0.424590(13) (a) 51 Sb 0.4066324(27) 0.406612(12) (a) 68 Er 0.2156801(75) 0.2156762(50) (b) 82 Pb 0.1408821(74) 0.1408836(11) (c) References: (a) Kraft et al. (1996); (b) Lum et al. (1981); (c) Bearden (1960).

The feature of absorption spectra customarily designated as `the absorption edge' has been variously associated with: the first inflection point of the absorption spectrum; the energy needed to produce a single inner vacancy with the photo-electron `at rest at infinity'; or the energy needed to remove an electron from an inner shell and place it in the lowest unoccupied energy level. A general discussion of this question has been given by Parratt (1959). If we choose the second alternative, then it is easy to see that, with some care for symmetry restrictions, one can estimate the absorption-edge energy by combining the binding energy for any accessible outer shell with the energy of an emission line for which the transition terminus lies in the same outer shell. Of course, this procedure does not focus on the details of absorption thresholds, the locations of which are important for a number of structural applications. On the other hand, our choice gives greater regularity with respect to nuclear charge and facilitates use of electron binding energies, since they are referenced to the Fermi energy or the vacuum.

Electron binding energies have been tabulated for the principal electron shells of all the elements considered in the present table (Fuggle, Burr, Watson, Fabian & Lang, 1974; Cardona & Ley, 1978; Nyholm, Berndtsson & Mårtensson, 1980; Nyholm & Mårtensson, 1980; Lebugle, Axelsson, Nyholm & Mårtensson, 1981; Powell, 1995). The number of values available offers the possibility of consistency checking, since the K and L shells are connected by emission lines to several final hole states, each of which has (possibly) been evaluated by photoelectron spectroscopy. For each of the elements for which well qualified reference spectra are available, we evaluated edge location estimates using several alternative transition cycles and used the distribution of results to provide a measure of the uncertainty. Comparison of edge estimates obtained by this procedure with experimental data provides a quantitative test of the utility of the chosen approach to edge location estimation. In Table 4.2.2.3, the numerical results in the column labelled `Emission + binding energies' were obtained by combining emission energies and electron binding energies using all possible redundancies. The estimated uncertainties indicated were obtained from the distribution of the redundant routes. As can be seen, the results are in general agreement with the available directly measured values. Accordingly, we have used this protocol to obtain the edge locations listed in the summary tables below.