L.A. LaJohn

Cooper minima: a window on nondipole photoionization at low energy

Photoionization of Mg 3s is studied near the Cooper minimum in dipole channels using the relativistic-random-phase approximation. While the importance of first-order nondipole effects on photoelectron angular distributions at low energies is well known, it is reported here for the first time that in the energy region near the dipole Cooper minimum, quadrupole transitions are not just important, but actually dominate the total photoionization cross section. Studies of dipole?dipole, dipole?quadrupole and quadrupole?quadrupole interference terms in the photoelectron angular distribution show that in the region of dipole Cooper minimum even the calculation of the dipole angular distribution parameter, ?, requires the inclusion of quadrupole channels. The significance of second-order [O(k2r2)] nondipole terms, primarily due to the contributions from electric quadrupole?quadrupole interference terms at photon energy as low as ~11 eV, are shown to induce dramatic changes in the photoelectron angular distribution over a small energy range.

Circumstances in which radiation is not absorbed, forbidding photoionization: four classes of matrix element zeros

Abstract We compare a new class of photoionization matrix element zeros, which we will call relativistic high-energy zeros (RHEZ), occurring at energies on the order mc 2 , to three well-studied classes of zeros, which include Cooper minima, point Coulomb relativistic zeros (PCRZ) and higher energy nonrelativistic Coulomb zeros (HENRCZ). RHEZ differ from the other three types of zeros in several ways. For example, the position of the zero with respect to photon energy in dipole RHEZ matrix elements is completely independent of n , Z , the central potential V , and retardation; has a simple dependence on the bound state l quantum number. Despite the fact that RHEZ occur at such high energies the dipole RHEZ do have some physical consequences.

The need to include multipole effects beyond the dipole approximation in the description of photoionization both at nonrelativistic and relativistic energies

Abstract We may ask what information characterizes low energy photoionization and what further information is accessible when photoionization is studied at higher energies, as in the X-ray and γ-ray regimes. For a “complete” experiment it is in fact not generally sufficient, even at low energy, to determine the energy dependence of the usual dipole parameters. Rather, such parameters should be determined for each multipole, or alternatively, the energy and angle dependence of angular distributions and polarization correlations. However it is known that in some circumstances, particularly for total cross sections from s-subshells, relativistic and higher multipole contributions tend to cancel well into the γ-ray regime, leaving a non-relativistic dipole description useful. Conversely, it has been shown that in some circumstances quadrupole effects remain of some importance at low energy in angular distributions, even for light elements and even at threshold. In general, and neglecting small relativistic effects, except for bound state normalization the high energy photoeffect matrix element is given by the matrix element in the nuclear point Coulomb potential. Consequently, at all energies the dependence of the photoionization matrix element on atomic properties is given by dipole and quadrupole terms, plus small octapole contributions, within an accuracy of 1%. This result, demonstrated within independent particle approximation, is expected to remain valid when many-electron correlations are included.

Beyond Dipole Effects in Atomic Processes

We attempt to answer the question: to what extent does physics beyond the nuclear point Coulomb level enter into observable properties of non-dipolar matrix elements in atomic processes such as photoionization, Rayleigh scattering and bremsstrahlung? We characterize these processes in terms of nuclear point Coulomb properties plus low multipole screening contributions. Except in photoeeect, the atomic form factor is also needed. In photoionization no higher than octupole, in Rayleigh scattering no more than quadrupole, screening contributions need to be included to achieve accuracy within a few percent. Similar considerations apply to bremsstrahlung. Here we summarize the importance of higher multipole physics in atomic processes. For both photoionization and Rayleigh scattering we have examined the importance of higher multipole screening contributions to Coulombic matrix elements in physical observables. For photoionization this leads to a simple parameterization. But in Rayleigh scattering we must rst partition the amplitude as the sum of the form factor (for which screening eeects of higher multipoles are very important) and the anomalous scattering factors, in which screening contributions are only important in the lowest multipoles. For photoionization we have demonstrated that, within the independent particle approximation (IPA), the only atomic information needed beyond nuclear Coulomb properties are 1 (1) the bound state normalization constant, (2) the diierence between reduced and nuclear point Coulomb reduced multipole matrix elements and (3) the corresponding diierences between screened and Coulombic phase shifts associated with these transitions 1]. Furthermore no more than the rst three multipoles of these screening contributions (beyond Coulomb properties) are ever needed to achieve an accuracy for physical observables that is within a 2% error limit. In the case (Z > 50) of moderate to high Z (for inner shells) and very high Z (Z > 75, all shells) multipole screening contributions (which will be designated by j where j is the 2 j-pole) up to octupole are needed for an accurate (within 2%) description of photoionization. Conversely, in the case of low Z outer shells (Z < 15 and E b < 15 ev) with l > 0 only 1 plus Coulomb properties are needed to describe photoionization. The behavior of j can be summarized as j R j?1