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Inner-shell photodetachment of Na&minus, near the L-edge threshold was investigated using the R-matrix method. Significant structure was found in the cross section, and this structure is shown to be related to the complicated correlated electron dynamics endemic in negative ions. Comparison with experiment suggests that the absolute values of the measured cross section might be too small by a factor of two.

The effects of endohedral confinement on the correlation energy of Be, Mg, and Ca atoms have been investigated using modified Hartree-Fock and multiconfiguration Hartree-Fock methods where the endohedral system $(A@{\text{C}}_{60})$ is approximated as an atom enclosed in an attractive spherically symmetric potential well of inner radius $r\ensuremath{\sim}5.8$ a.u. and thickness of $\mathrm{\ensuremath{\Delta}}\ensuremath{\sim}1.89$ a.u., and correlation energies are studied as a function of the depth of the confining potential ($0\ensuremath{\le}{U}_{0}\ensuremath{\le}1$ a.u.) to give some idea as to how the correlation energy behaves in different endohedral environments. In general, we have found that as a function of well depth, starting from the free atom, valence electrons diffuse outward in the presence of the confining potential, which causes the electrons to be further apart, thereby decreasing the correlation energy; however, with further increase of well depth, the valence electrons become trapped in the confining well and, as a result of their being closer together, the correlation energy increases.

High-resolution measurements for inner-shell photoionization of Na are presented along with Breit?Pauli R-matrix calculations. The results show excellent agreement, and give insight into the nature and importance of the various relativistic and correlation effects on the inner-shell process.

R-matrix calculations of the photoionization of the core-excited 1s2s2p 4Po state of atomic lithium have been performed. The cross section is shown to be dominated by hollow atom resonances, in contrast to valence-excited Li where these hollow resonances are small modulations of the background continuum cross section in the higher energy region.

We have measured the angle-resolved energy dependence of the electrons emitted over the energy range of the triply excited 2s{sup 2}2p P{sup 2} lithium resonance using synchrotron radiation. We have also calculated the behavior of the angular distribution parameter {beta} using the R -matrix approximation. Experimental and theoretical results are in good agreement and show deep minima in the 1s2p P{sup 1,} {sup 3} ionic channels. The energy at which the minima occur does not coincide with the resonance energy, but is shifted towards higher energy. (c) 2000 The American Physical Society.

Calculations of inner-shell photoionization of ${1s}^{2}2p{}^{2}{P}^{o}$ and ${1s}^{2}3p{}^{2}{P}^{o}$ Li excited states have been performed using recent developments of the R-matrix code with a 29-term target representation for incident photon energies up to 165 eV, with particular emphasis on multiple electron processes. Partial and total cross sections are given for a number of excitation processes including the lower members of 19 hollow atom resonance series. The results are compared with recent experimental measurements of the lowest ${2s2p}^{2}{}^{2}{L}^{e}$ resonance of even-parity hollow lithium states produced by photoexcitation of laser-excited lithium atoms. Experiment and theory are in excellent agreement on a relative scale. The enhancement of the shake-up process increases with initial state excitation, up to 500% over that of the ground state for ${1s}^{2}3p{}^{2}{P}^{o}.$ Good agreement is also obtained for K-shell photoionization when comparing branching ratios with available experimental results.

Using multichannel quantum-defect theoretical methods, we have performed highly correlated R-matrix calculations for the photoionization excitation of neon in the (50{endash}53)-eV photon energy range, where numerous doubly excited resonances are found. By incorporating spin-orbit effects through an intermediate-coupling frame transformation, we have reproduced experimental observance of the significant breakdown of LS coupling in resonant angular distributions and fine-structure partial cross sections. Extreme sensitivity to the target structure in this weak process and strong interactions between neighboring Rydberg series of resonances make a detailed comparison for every resonance difficult, but many of the interesting spin-orbit features, beyond fine-structure splitting of series, are revealed. This method permits a quantitative analysis of LS-forbidden contributions to complex photoionization spectra and should prove useful for studying spin-orbit effects in light atomic systems. {copyright} {ital 1998} {ital The American Physical Society}

Photoion and photoelectron data for hollow lithium states were recently reported with increased spectral resolution. In order to reproduce and identify the important resonances due to ${2ln}^{\ensuremath{'}}{l}^{\ensuremath{'}}{n}^{\ensuremath{''}}{l}^{\ensuremath{''}}$ ${}^{2}{P}^{o}$ autoionizing states new photoionization calculations have been performed using the R-matrix code with a 29-term target representation for incident photon energies between 140 and 167 eV. Excellent agreement between theoretical and measured results over partial or total photoionization cross sections confirms the quality of the theoretical model. A determination of the resonance positions for each series converging to a ${2l2l}^{\ensuremath{'}}$ ${}^{1,3}L$ threshold of Li is proposed.

We here present an alternatve way to perform R-matrix calculations in which the eigenchannel parameters of multichannel quantum defect theory are calculated directly. Merits of our R-matrix calculations are twofold: (1) an analytical treatment of perturbed discrete Rydberg states, autoionizing states, and their adjacent continuum to avoid numerical calculations outside the R-matrix box; (2) clear assignment of overlapped resonances, e.g., to analyze the lithium inner-shell photoionization cross section, which has been of considerable interest in recent experimental measurements.

The photoionization cross section of the Ca atom, confined by a spherical annular potential, has been calculated using a modification to the Belfast R-matrix code for a variety of depths of the confining potential. The results show that the external potential affects the cross section, which is dominated by doubly excited autoionizing states, quite significantly, causing much of the oscillator strength to move into the discrete region of the spectrum. In addition, increasing well depth causes a level crossing between the first two excited states of Ca+, thereby changing the ordering of resonances dramatically. The calculation for free Ca shows excellent agreement with experiment. DOI: 10.1103/PhysRevA.87.013409

Absolute cross sections for photoionization of isotropically populated Ba(6s6p $^{1}$${\mathit{P}}_{1}$) to each accessible final J state (0, 1, and 2) have been determined from threshold to 370 nm using spectra obtained with four different combinations of linear and circular polarizations of the exciting and ionizing radiation. The effects of dealignment due to hyperfine interaction of the nuclear spin I=3/2 isotopes of barium have been taken into account. The results are generally in good agreement with R-matrix predictions of shapes and positions of autoionizing resonances as well as the magnitudes of the background (nonresonance) cross sections, but there are some discrepancies with oscillator strengths of the autoionizing states. It is shown that, to obtain the correct magnitude of the background cross section theoretically, the inclusion of electron correlation effects in the wave functions of both initial and final states is required. Data are also presented that verify the equivalence of obtaining the total photoionization cross section by properly combining two sets of data, each acquired with a different angle between linear polarization vectors, e.g., parallel and perpendicular, or by making a single measurement with the angle set at the ``magic'' angle, 54.7\ifmmode^\circ\else\textdegree\fi{}.

Photoionization cross-section calculations are performed on the ground state ([Ne]3${s}^{2}$3${p}^{6}$4$s$ ${}^{2}\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}^{e}$) and the first two excited states ([Ne]3${s}^{2}$3${p}^{6}$3$d$ ${}^{2}\phantom{\rule{-0.16em}{0ex}}{D}_{3/2}^{e}$ and [Ne]3${s}^{2}$3${p}^{6}$3$d$ ${}^{2}\phantom{\rule{-0.16em}{0ex}}{D}_{5/2}^{e}$) of Ca${}^{+}$ ions for photon energies from threshold to 45.0 eV using the relativistic (Breit-Pauli) $R$-matrix method. The discrete Ca${}^{2+}$ orbitals are generated using the computer program autostructure; 30 configurations are included in the configuration-interaction calculation for the states of Ca${}^{2+}$. The prominent 3$p$ \ensuremath{\rightarrow} 3$d$ giant resonances are analyzed and identified, and our results are compared with experimental results, and rather good agreement is found. Using results of our previous photoionization calculations on Sc${}^{2+}$ and Ti${}^{3+}$ ions, the strongest and broadest resonances in the photoionization cross section of those three ions (Ca${}^{+}$, Sc${}^{2+}$, and Ti${}^{3+}$), in terms of width and oscillator strengths, are compared to show the evolution as a function of nuclear charge.

Partial photoionization cross sections from the ^1S ground and the ^3P metastable states of the Be isoelectronic series to different final states including a number of satellite (ionization plus excitation) channels are studied using the R-matrix method. As expected, the ratio of each satellite partial cross section to the dominant partial cross section is found to be a monotonic decreasing function of Z for both the ground and the metastable states. The complicated patterns of these ratios as functions of photon energy are analyzed., 19 pages, 9 figures

The photoionization of the four-electron beryllium-like isoelectronic series from the neutral to Fe^{+22} has been studied for ground ^1S and metastable ^3P initial states. The wave functions of the final-state (target) ions were built using the CIV3 code. Both nonrelativistic LS-coupling R-matrix and relativistic Breit-Pauli (BP) R-matrix methods were used to calculate the cross sections in the photon-energy range between the first ionization threshold and the 1s^2 4f_{7/2} threshold for each ion. Our total cross sections compare well with experiment which is available for Be, B^+, C^{+2}, N^{+3}, and O^{+4}. The agreement between the present work and previous calculations is discussed in detail. The importance of relativistic effects is seen by the comparison between the LS and the BP results., Comment: 45 pages, 3 tables, 22 figures

Photoionization cross-section calculations are performed on potassiumlike transition metal ions (Ti{sup 3+}, V{sup 4+}, Cr{sup 5+}, Mn{sup 6+}, and Fe{sup 7+}) using both nonrelativistic (LS-coupling) and relativistic (Breit-Pauli) R-matrix methods for the ground ([Ne]3s{sup 2}3p{sup 6}3d {sup 2}D{sub 3/2}{sup e}) and the first excited ([Ne]3s{sup 2}3p{sup 6}3d {sup 2}D{sub 5/2}{sup e}) states of each of the five ions, along with the excited 4s {sup 2}S state of Ti{sup 3+}. Photon energies up to the first 3p ionization threshold are considered. The results show that for Ti{sup 3+}, the cross sections are dominated by the giant (3p{yields}3d) resonances which are analyzed and identified, while for the four other ions (V{sup 4+}, Cr{sup 5+}, Mn{sup 6+}, and Fe{sup 7+}), the 3p{yields}3d resonances lie below the ionization threshold, and the cross sections are dominated by 3p{sup 5}3dnd and 3p{sup 5}3dn's Rydberg series of resonances. Comparison of the Ti{sup 3+} results with available theoretical and experimental data shows good agreement.

Near-threshold resonances have been studied for Be-like ions with a focus on overlapping resonances among Rydberg series converging to different thresholds. The behavior of the overlapping as a function of Z and the approach to the limit of infinite Z are investigated. The 4s4p resonance is shown and discussed in detail as an example., Comment: 13 pages, 1 table, 2 figures

We demonstrate the successful implementation of genetic algorithm for the retrieval of atomic potentials using elastic differential cross sections (DCSs) between free electrons and atomic ions for electron energies from a few to several tens of electron volts. Since the DCSs over this energy region can be extracted from laser-generated high-energy photoelectron momentum spectra, the results suggest that infrared lasers can be used to image the target structure. Extending to molecular targets, in particular, to transient molecules created by an earlier pump pulse, our results suggest that few-cycle infrared probe lasers can be used for dynamic chemical imaging with temporal resolution of a few femtoseconds.

Photodetachment of the outer shells of the ground {sup 4}S{sup o} state of C{sup -} using an augmented R-matrix theoretical methodology has been studied from threshold to 13 eV. Total and partial cross sections and photoelectron angular distribution asymmetry parameters have been obtained. Excellent agreement between length and velocity formulations is found. The results resolve a discrepancy among earlier calculations, and a new shape resonance, 1s{sup 2}2s{sup 2}2p3s3p {sup 4}P, at a photon energy of 8.588 eV is predicted.

A fully quantum-mechanical modification to the R-matrix method is introduced to include the recapture of slow photoelectrons following Auger decay of an inner-shell vacancy state and is applied to the photodetachment of ${\mathrm{Li}}^{\ensuremath{-}}$ above the ${1s}^{\ensuremath{-}1}$ threshold. The results show excellent agreement with experiment and resolve a large discrepancy in the cross section near the $1s$ threshold between theory and experiment.

Calculations of 1 s electron inner-shell photoionization from the 1s 2 2p 2P a Li excited state were previously reported using the R-matrix code [Zhou et al., Phys. Rev. A 59, 462 (1999)]. These calculations included important resonances in the partial and total photoionization cross sections for incident photon energies (i) lower than 74 eV and due to the I snln'l' 2 L e >' autoionizing states for n = 2 and 3 and L = S, P, and D, and (ii) ) larger than 140 eV and due to the 2ln'l'n"l" 2Le autoionizing states. The latter resonances corresponding to 2ln'l'n"l" were recently analyzed by Zhou et al. [Phys. Rev. A 62, 012707 (2000)], using an eigenphase derivative technique along with quantum defect theory. The present paper proposes an analysis of the former resonances in the 58-74 eV incident photon energy range. The determination of the resonant positions for each series converging to a 1s2l 1 , 3 L or I s3l 1 , 3 L ionization threshold of Li is obtained using the same method as in Zhou et al. [Phys. Rev. A 62, 012707 (2000)]. The identifications are compared with theoretical results of Chung [Phys. Rev. A 57, 3518 (1998)] using the saddle-point method for energies below the Li + 1s2s 1 S threshold. Agreement is excellent in most cases and some discrepancies are discussed.

The photodetachment cross section of the $1s2s2p{}^{4}{P}^{o}$ metastable state of ${\mathrm{He}}^{\ensuremath{-}}$ in the region of the $1s$ threshold has been calculated using our enhanced R-matrix code with the asymptotic part upgraded to handle a negative-ion system. The results show a $1s$ photodetachment cross section with numerous structures, completely different from similar situations in atoms or positive ions. This is found to be due to the dominance of correlation of both initial and final states of the negative ion. Specifically, interchannel coupling and a newly identified multiconfiguration overlap effect are primarily responsible for the dramatic $1s$ photodetachment cross-section phenomenology. Comparison with a previous calculation has been made and, while there are some areas of excellent agreement, overall there are very serious discrepancies, as much as an order of magnitude.

Photoionization of multiply charged ions of the Ba isonuclear sequence up to Ba 6 + has been studied in a beam-beam experiment. A very strong increase in the resonance structures was observed when moving from Ba 2 + to Ba 6 + . Absolute values of the photoionization cross sections were measured for Ba 2 + and Ba 3 + ions. The interpretation of the results is provided using theoretical multiconfiguration Dirac-Fock and relativistic random phase approximation calculations, showing that the collapse of the nf orbitals occurs for Ba 4 + .

Photoionization of the ground ${1s}^{2}{2s}^{2}{}^{1}S$ state of atomic beryllium is studied in the energy region between the ${\mathrm{Be}}^{+}(2s)$ and ${\mathrm{Be}}^{+}(3d)$ thresholds using a noniterative variational R-matrix method combined with multichannel quantum-defect theory at the R-matrix surface. The autoionizing Rydberg series of resonances converging to the ${\mathrm{Be}}^{+}$ $(2p,$ $3s,$ $3p,$ and $3d)$ thresholds are identified and effective quantum numbers assigned. Also calculated are the photoelectron angular distribution asymmetry parameters \ensuremath{\beta} for the processes leaving the ion in the ${\mathrm{Be}}^{+}$ ${(1s}^{2}np,$ $n=2,3)$ states. The present photoionization cross sections extend earlier work and are in good agreement with previous calculations and experiments. There is excellent agreement between length and velocity gauges in our calculation.

Photoionization cross section of endohedrally confined calcium is computed using R-matrix method.

We apply a «cavity-type» method for the analysis of the learning ability of single- and multilayer perceptrons. We show that the mean-field equations obtained in this way, which are identical to the equations derived previously by the replica method, describe not only the properti of the optimal network, but also a learning process which leads to this network. We discuss the applicability of our ideas to the construction of learning algorithms. Our interpretation of the mean-field theory also leads naturally to a new concept, «flexibility,» which is a measure of the ability of the network to learn

Photoionization cross sections from the ground and metastable states of Be-like ions have been calculated using the Breit-Pauli R-matrix method. The resonances were identified and characterized with energy levels, widths and effective quantum numbers using the QB program. The general behavior of the resonances was analyzed along the sequence. Relativistic effects are identified by comparing the Breit-Pauli result with our calculated LS R-matrix result.