Electric-Octupole and Pure-Electric-Quadrupole Effects in Soft-X-Ray Photoemission

Abstract

Second-order [ O(k(2)), k = omega/c] nondipole effects in soft-x-ray photoemission are demonstrated via an experimental and a theoretical study of angular distributions of neon valence photoelectrons in the 100-1200 eV photon-energy range. A newly derived theoretical expression for nondipolar angular distributions characterizes the second-order effects using four new parameters with primary contributions from pure-quadrupole and octupole-dipole interference terms. Independent-particle calculations of these parameters account for a significant portion of the existing discrepancy between experiment and theory for Ne 2p first-order nondipole parameters.

Non-dipole effects in the angular distribution of photoelectrons in sequential two-photon atomic double ionization

“…Since the dominant non-dipole contribution comes from the interference of the E1 and E2 photoionization amplitudes, we neglect the M 1 photoionization amplitudes (which strictly vanish in the nonrelativistic single-configuration approximation). Our results for the photoelectron angular distribution in single-photon ionization are in a good agreement with other calculations [34,40,41] and experiment [37] (Figure 1; we denote the non-dipole parameters in one-photon single ionization without superscript). Note that, as revealed by Derevianko et al [41], the second-order non-dipole effects start to noticeably influence the photoelectron angular distribution of the Ne 2p ionization at the photon energies near to 1 keV.…”

“…These experiments were performed with synchrotron radiation from storage rings, thus due to the low intensity of the photon flux the probability of the second-step ionization (23) was negligible. Nevertheless, pronounced non-dipole effects in single ionization revealed in these experiments [36,37] point to potentially strong non-dipole effects in the 2PDI at the corresponding photon energies. Using the Free-electron LASer in Hamburg (FLASH), the angular distributions of the individual electrons e 1 and e 2 in the 2PDI process (22), (23) were measured in [15,22] while the angular correlation function between the two electrons was observed in [16].…”

“…Solid curves: present calculation; dotted curves: random phase approximation (RPA) [40,41]. Experimental data of [37] for the geometry suppressing the secondorder non-dipole effects.…”

Angular distribution in two-photon double ionization of helium by intense attosecond soft-x-ray pulses

“…It should be noted that the present deviation from a strictly aligned (k = 2) pattern is due to multiphoton effects and not due to retardation effects beyond the dipole approximation [29]. …”

Overview of core and valence photoemission

“…In general terms, it works better in the evaluation of total cross sections than in the calculation of photoelectron angular distributions. Recent measurements in small systems show that significant deviations from the dipole approximation can be found even in systems for which it has been traditionally applied [22]. Nevertheless, let us restrict ourselves to the calculation of the photocurrent in the dipole approximation.…”