Electric-Dipole–Quadrupole Interference of Overlapping Autoionizing Levels in Photoelectron Energy Spectra

Nondipole effects in soft X-ray photoemission

“…The lower-energy valence results also agreed fairly well with IPA predictions and provided direct evidence for experimentally significant breakdowns in the DA below 1 keV. At an even lower photon energy ð13 eVÞ; a third group demonstrated small ðo0:5%Þ nondipole effects in atomic Cd can be observed due to interference between different-parity autoionization resonances (Martin et al, 1998).…”

“…The most general question concerning the significance of nondipole effects is their relevant photon-energy range, particularly to guide experimentalists when, if ever, it is safe to assume the DA in interpreting results. While in specific cases nondipole effects have been observed at very low photon energies, Martin et al (1998) observed a small nondipole effect around 13 eV and Hemmers et al (2003) found significant effects as low as 26 eV; it remains to be seen how widespread low-photon-energy nondipole effects really are. Significant efforts to provide guidelines to the photoemission and related communities should be a high priority for future work.…”

“…However, because the influence of quadrupole matrix elements in the firstorder nondipole correction comes through dipolequadrupole interference terms, measurements of nondipole anisotropy in angular-distributions of photoelectrons can be used as a tool to investigate highermultipole resonances excited by photons. Martin et al (1998) were the first to show the observation of resonant dipole-quadrupole interferences was possible by measuring the forward/backward anisotropy of Cd photoelectrons, setting at the same time a low-energy record on the observation of nondipole effects. Noting (e,2e) experimental results on cadmium ''are the equivalent of nondipole photoionization,'' the authors calculated the dipole-quadrupole interference between the Cd 4d 9 5s 2 5pðJ ¼ 1Þ and 5p6p 3 P 2 ðJ ¼ 2Þ autoionizing levels at 12:992 eV photon energy.…”

“…The pioneering experimental work of Martin et al (1998) and Kr. assig et al (2002) occurred in parallel with theoretical studies on such effects at low photon energy.…”

“…with the Fano expression of the radial matrix elements R l as a function of q l ; the Fano profile line index, the authors were able to extract the profile indexes q 1 and q 2 for the ð2s2pÞ 1 P 1 and ð2p 2 Þ 1 D 2 autoionizing resonances, the phase-shift difference ðd 2 À d 1 Þ; and the matrixelement ratio R 2 =R 1 : Cadmium and helium are not unique in any way, and the occurrence of such dipole-quadrupole interferences Martin et al (1998) showing the experimental dipole-quadrupole interference spectrum given by the difference of CIS spectra taken by two electron detectors. The ordinate is normalized to the dipole spectrum at 13 eV: The solid curve is a calculation appropriate to photoionization, and the dotted curve is a calculation with the phase appropriate for electron scattering.…”