Theoretical and experimental demonstration of the existence of quadrupole Cooper Minima

Calculations and measurements of the Xe 5s and 5p nondipole photoelectron asymmetry parameters are obtained which present clear evidence of the existence of quadrupole Cooper minima, i.e., minima in quadrupole matrix elements as a function of energy, in the photoionization process. This verifies earlier predictions of quadrupole Cooper Minima. ‡ Present address: Laboratoire de Chimie Physique-Matière et Rayonnement, UMR 7614, 75231 Paris Cedex 05, France § Present address: Physics Department, Western Michigan University, Kalamazoo, Michigan 49008, USA ‖ Present address: Institute of Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, 02-668 Warsaw, Poland ¶ Present address: University of California, Lawrence Livermore National Laboratory, Livermore, California 94550, USA Existence of quadrupole Cooper Minima 2 Laboratory studies of nondipole effects in photoionization have seen a recent renaissance owing to the unparalleled brightness of modern light sources that have made such precision investigations possible [1]. Studies of low-energy nondipole effects in atomic photoionization reveal information about quadrupole-allowed ionization channels and the elusive quadrupole ionization process itself because the nondipole angulardistribution parameters depend upon interferences between quadrupole and dipole matrix elements [2, 3, 4, 5]. Atoms, owing to their relative simplicity, are the ideal target for these studies because they generally allow for unambiguous interpretation of the results. In addition, atoms are simple enough to perform calculations approaching exactness. These investigations have significantly altered our understanding of nondipole effects in photoionization [1, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], which were previously thought to be of importance only at photon energies of many keV [20, 21, 22]. Furthermore, the effects of correlation in the quadrupole photoionization channels in the form of interchannel coupling and quadrupole ionization plus excitation (satellite) channels were inferred as a result of combined experimental and theoretical studies [17]. In addition, for dipole photoionization, studies in regions of the well-known Cooper minima [23], i.e., zeros or near-zeros in dipole matrix elements, have proved extremely useful as benchmarks because the various photoionization parameters take on welldefined values at these minima. Moreover, the quantitative details of matrix element minima are extremely sensitive to many-body correlations. Similar considerations must also apply for quadrupole Cooper minima. In this letter, we report experimental evidence for the existence of a quadrupole Cooper minimum, the result of a combined laboratory and computational investigation of nondipole effects in Xe valence-shell photoionization. Note that quadrupole Cooper minima have been predicted for some time [24], but without experimental confirmation. This investigation is an example of how a combined experimental/theoretical study can yield significantly more insight than the sum of individual experimental and theoretical investigations. The differential cross section for photoionization, including the lowest-order nondipole contribution, is given by [3, 4, 25, 26, 27]