Alternative square-integrable (${\mathit{L}}^2$) basis functions, the oscillating Hermite Gaussian functions (OHGF’s), are proposed for describing the continuum orbitals in ${\mathit{L}}^2$ calculations on molecules. Each function is the product of a Hermite Gaussian function (HGF), which gives the proper dumping and angular factor, and a radial trigonometric function, cos(kr), which describes the oscillating asymptotic behavior of a continuum orbital. Analytic expressions for the one- and two-electron integrals involving s-type OHGF’s and many-center s-type HGF’s are derived and their numerical implementation is discussed in detail. The present proposal of adopting a mixed basis set of OHGF’s and many-center HGF’s for the ${\mathit{L}}^2$ description of bound and continuum molecular states is compared with the other types of basis functions currently employed. With respect to these, it requires a greater computational effort in the integral evaluation, but it also allows an accurate description of the electronic continuum in general polyatomic systems.

By differentiation of the expressions for the basic s-type integrals previously presented, analytic expressions are here derived for integrals, relevant for quantum-chemistry calculations, involving oscillating Hermite Gaussian functions (OHGF’s) and many-center Hermite Gaussian functions (HGF’s) of any order. The OHGF is the product of a HGF and a radial trigonometric factor cos(kr), and has been proposed for describing the continuum orbitals in ${\mathit{L}}^2$ calculations on molecules. The resulting expressions are compact and particularly suitable for numerical implementation on a computer, while the increase in the computational effort of the integral evaluation with respect to the s-type functions is estimated to be of the same order as that found in the standard case of simple Gaussian functions. Applications of the OHGF basis to the calculation of continuum states are presented and compared to the exact results for test cases: the hydrogen atom and the ${\mathrm{H}}_2^{+}$ molecule, in order to discuss advantages and limitations of the proposed approach.

A high-efficiency cascade-photon-coincidence lifetime-measuring apparatus has been used to study the 5d ${}_{}{}^4{}_{}{}^{}$${\mathit{F}}_{9/2}$→5p ${}_{}{}^4{}_{}{}^{}$${\mathit{D}}_{7/2}^{\mathit{o}}$→5s ${}_{}{}^4{}_{}{}^{}$${\mathit{P}}_{5/2}$ cascade in Kr ii and the 6d ${}_{}{}^4{}_{}{}^{}$${\mathit{F}}_{7/2}$→6p ${}_{}{}^4{}_{}{}^{}$${\mathit{D}}_{5/2}^{\mathit{o}}$→6s ${}_{}{}^4{}_{}{}^{}$${\mathit{P}}_{3/2}$ cascade in Xe ii. A neutral atomic beam was excited and ionized by electron impact, and the spontaneously emitted photons were collected by an ellipsoidal mirror and detected by fast photomultipliers provided with narrow-band interference filters. The spectrum of time delays was acquired by a time-to-amplitude converter and multichannel pulse-height analyzer. The lifetime of the Kr ii 5p ${}_{}{}^4{}_{}{}^{}$${\mathit{D}}_{7/2}^{\mathit{o}}$ state was found to be 7.004±0.053 ns. This is in agreement with two previous high-precision measurements and represents an improvement in precision by a factor of 3.6. The Xe ii 6p ${}_{}{}^4{}_{}{}^{}$${\mathit{D}}_{5/2}^{\mathit{o}}$ lifetime was found to be 9.494±0.067 ns. This result agrees with several measurements of lower accuracy, but is in clear disagreement with two previous measurements claiming high precision, which disagree with each other as well.

The information which is contained in an averaged form in the first-order reduced density matrix is sufficient to build a close approximation to the second-order reduced density matrix and consequently to the system energy. This is achieved by using the anticommutating relation of fermion operators and the commutating relation of the pair-of-fermions operators. Three test calculations are reported and analyzed.

We report theoretical calculations for the ${\mathrm{\beta }}_{2\mathit{p}}$-asymmetry parameter in the photoionization of He(1${\mathit{s}}^2$) above the N=2 ionization threshold. We use an extension of a method recently proposed [I. Sánchez and F. Martín, Phys. Rev. A 44, 7318 (1991)] that makes use of a Feshbach partitioning of the final-state wave function and an ${\mathit{L}}^2$ representation of the coupled continuum states. Partial differential cross sections at emission angles 0° and 90° are also provided. Our results are in good agreement with the experimental data, thus showing the accuracy of the present method to study electron angular-distribution properties.

In this work we report an improved experimental determination of K-shell binding energies from Be-like ${\mathrm{Ne}}^{6+}$, B-like ${\mathrm{Ne}}^{5+}$, and C-like ${\mathrm{Ne}}^{4+}$ ground-state multiply charged ions using high- resolution Ne-K Auger-electron spectroscopy. The derived energy differences, namely, ${\mathrm{Ne}}^{6+}$ E(1${\mathit{s}}^2$2${\mathit{s}}^2$) ${}_{}{}^1{}_{}{}^{}$S–${\mathrm{Ne}}^{7+}$ E(1s2${\mathit{s}}^2$${)}^2$S, ${\mathrm{Ne}}^{5+}$ E(1${\mathit{s}}^2$2${\mathit{s}}^2$2p) ${}_{}{}^2{}_{}{}^{}$P°–${\mathrm{Ne}}^{6+}$ E(1s2${\mathit{s}}^2$2p) ${}_{}{}^3{}_{}{}^{}$P°, and ${\mathrm{Ne}}^{4+}$ E(1${\mathit{s}}^2$2${\mathit{s}}^2$2${\mathit{p}}^2$) ${}_{}{}^3{}_{}{}^{}$P–${\mathrm{Ne}}^{5+}$ E(1s2${\mathit{s}}^2$2${\mathit{p}}^2$${(}^3$P)) ${}_{}{}^4{}_{}{}^{}$P are 1099.1, 1048.5, and 1001.8 eV, respectively. These energies are accurate to within ±0.1 eV. Theoretically, we have studied relativistic binding energies of ${\mathrm{Ne}}^{\mathit{q}+}$ (q=6, 5, and 4) by using the (i) saddle-point technique, (ii) 1/Z method, and (iii) multiconfiguration Dirac-Fock model. Excellent agreement with experiment is obtained.

The effect of electronic state mixing on tunneling dynamics is studied. To this aim the theoretical description of the differential photodissociation cross section is extended to include rotational and vibrational couplings. The mixing of bound and quasibound electronic states is reflected in resonance widths. The anisotropy of the photofragments reflects mixing of dissociative continua. It is shown that inclusion of these nonadiabatic couplings is required to reproduce the recently reported [Siebbeles, Schins, Los, and Glass-Maujean, Phys. Rev. A 44, 343 (1991)] differential photodissociation cross section of ${\mathrm{H}}_2$ for excitation around the ${\mathit{scri}}^3$${\mathrm{\Pi }}_{\mathit{g}}$ (v’=5, N’=1,2) resonances. Nonclassical photofragment anisotropies are found for coherent excitation of different rotational resonances (v’=5, N’=1, and N’=2) and of different rovibrational resonances (v’=5, N’=1 and v’=4, N’=2). The latter is strongly connected to the molecular excitation mechanism and has therefore no parallel in collision experiments.

Whole-atom differential coherent scattering cross sections were measured for 59.5-keV γ rays scattered at 90° by Cu, Mo, Ag, Cd, Sn, Pr, Sm, Gd, Dy, Ho, Yb, Ta, W, Pb, Th, and U employing a reflection-geometry setup and an effective graded shielding arrangement. A 2-${\mathrm{cm}}^3$ hyperpure Ge detector was used for detecting coherently scattered γ rays. The measured cross sections are compared with the theoretical values based on the numerical partial-wave calculations for the available cases. Form factors corresponding to 3.395-Å ${}_{}{}^{\mathrm{-}1}{}_{}{}^{}$ photon-momentum transfer were extracted from the measured cross sections. The results were compared with the different formalisms of form-factor theory and their relative appropriateness is discussed.

We have applied the complex Kohn variational method to the study of molecular-photoionization processes. This requires electron-ion scattering calculations enforcing incoming boundary conditions. The sensitivity of these results to the choice of the cutoff function in the Kohn method has been studied and we have demonstrated that a simple matching of the irregular function to a linear combination of regular functions produces accurate scattering phase shifts.

An analytic method is presented for the calculation of various indices that characterize statistical fluctuations in ionization yields, specifically for the incidence of an ion such as a proton or α particle at a high speed. A general expression for the Fano factor for ion incidence is derived, and the relation to the Fano factor for electron incidence is clarified. For an illustration, the theory is applied to protons incident on argon. The resulting Fano factor for protons of energies between 0.1 and 2 MeV is nearly the same as that for electrons at the same speeds, and it is considerably lower than the values measured with α particles.

We analyze the electron emission spectrum into backward angles for projectile ionization in 0.5-MeV/u ${\mathrm{H}}^0$ and ${\mathrm{He}}^{+}$ on He collisions. The energy and angular distributions of the ejected electron are calculated taking into account both scattering correlations and two-center effects. Two-center effects are treated using the continuum-distorted-wave approximation and the classical-trajectory Monte Carlo method. Correlation effects are described in terms of a Born series including contributions up to second order. Both contributions are found to enhance significantly the electron-loss cross section in near-symmetric projectile-target collision systems. We find improved agreement with experiment for ${\mathrm{He}}^{+}$ on He collisions. Extensions to heavier targets are also discussed.

We used distorted-wave and multiconfigurational Dirac-Fock methods to calculate direct and indirect contributions to cross sections for electron-impact ionization of ${\mathrm{C}}^{3+}$, ${\mathrm{N}}^{4+}$, ${\mathrm{O}}^{5+}$, and ${\mathrm{F}}^{6+}$. The features due to excitation autoionization and resonant excitation double autoionization observed in recent cross-beam measurements [G. Hofmann et al., Z. Phys. D 16, 113 (1990)] are well reproduced in our results. Our cross sections are also in good agreement with reported results of nonrelativistic close-coupling calculations [S. S. Tayal and R. J. W. Henry, Phys, Rev. A 42, 1831 (1990); 44, 2955 (1991)] over most of the energy range studied. We examine the effects of radiative decay on the intermediate states, and we show that neglect of certain channels in the close-coupling calculation results in overestimation of the cross sections in the region of the 1s2s2pnl resonances.

We have calculated electron-impact ionization cross sections for Li-like ${\mathrm{Ar}}^{15+}$, ${\mathrm{Fe}}^{23+}$, ${\mathrm{Kr}}^{33+}$, and ${\mathrm{Xe}}^{51+}$ ions for incident electron energies between 3 and 4 times the ionization threshold using the relativistic distorted-wave and the multiconfiguration Dirac-Fock methods. The calculations include direct-ionization, excitation-autoionization and resonant-excitation-double-autoionization processes. There are many narrow resonances due to the excitation of the 1s2s3lnl’ states. The effect of indirect processes persists to very highly charged ions in the isoelectronic sequence.

Lowest-order QED theory using distorted-wave states is applied to the calculation of positron-impact ionization cross sections for highly charged atomic ions. Electron and positron ionization cross sections for atomic ions are predicted to differ by substantial amounts in the threshold region. For highly charged ions like ${\mathrm{U}}^{90+}$, the smaller positron ionization cross section is more strongly affected by transverse photon interactions than the corresponding electron ionization cross section. At twice the threshold for ${\mathrm{U}}^{90+}$ ionization, the annihilation terms are found to reduce the positron cross section by about 12%.

The electron loss to the continuum (ELC) process was investigated in ${\mathrm{He}}^{+\mathrm{-}}$(He,Ar) collisions at 1.41- and 2.41-a.u. impact velocities. The cusp-shaped energy distributions of electrons ejected into the forward direction were measured in coincidence with the scattered ${\mathrm{He}}^{2+}$ projectile ions. The shape of these cusps was studied by fitting the multipole series expansion [Meckbach, Nemirovsky, and Garibotti, Phys. Rev. A 24, 1793 (1981)] of the measured spectra using ${\mathit{B}}_{\mathit{n}\mathit{j}}$, the nth-order expansion coefficients of the jth-order Legendre polynomials, as fitting parameters. The observed skewness of the spectra (nonzero ${\mathrm{\beta }}_1$=${\mathit{B}}_{01}$/${\mathit{B}}_{00}$ values) indicates the importance of the higher-order theories in the description of the distribution of ELC electrons. A dip at the top of the peak (‘‘cusp inversion’’), reflected by a positive ${\mathrm{\beta }}_2$=${\mathit{B}}_{02}$/${\mathit{B}}_{00}$ value, was observed in the 1.41-a.u. ${\mathrm{He}}^{+\mathrm{-}}$He collision.

We present a comprehensive survey of the behavior of all correlations ${\mathit{C}}_{\mathit{i}\mathit{j}}$ between the polarization of the incoming photon and the spin of the outgoing photoelectron, for ejection from all subshells of uranium, for electron energies from 1 eV to 100 keV. The correlations for ns-subshell photoionization are reported here. The numerical results for these polarization correlations are obtained within the independent-particle approximation in a relativistic self-consistent atomic field (Dirac-Slater type), including all significant multipole contributions. We confirm that at low photon energies (up to ∼1 keV), which means relatively low kinetic energy ɛ for the photoelectron and ejection from a subshell of high n, dipole predictions are generally valid, reproducing the full numerical results, including the abrupt changes in the shape of the ${\mathit{C}}_{\mathit{i}\mathit{j}}$ curves as functions of the ejection angle θ. As photon energy increases, the correlation coefficients become complicated functions of θ, losing symmetry around θ=90°. For higher ɛ, the correlation coefficients of different n tend to merge into a common curve as a function of θ, although the shape of the curve keeps changing as ɛ increases, as we have previously reported for angular distributions.

A set of complex scaling schemes which enable one to calculate resonance positions and widths is introduced. Although these scaling procedures are not equivalent to the complex-coordinate method, they change the asymptotic behavior of resonance wave functions from exponentially diverging to square integrable. Coupled to a Padé-approximation-extrapolation procedure, these nonsimilarity transformations enable one to obtain the complex resonance energies of the original Hamiltonian. A study of these scaling schemes, their influence on the spectrum, and the limitations of the method is presented. The use of some of these procedures, especially a kinetic-energy-scaling scheme where ħ→ħ${\mathit{e}}^{\mathrm{-}\mathit{i}\mathrm{\phi }}$, is most attractive from the computational point of view, and permits the use of currently existing programs for the calculation of potential-energy matrix elements.

Calculated total, differential, and momentum-transfer cross sections are reported for the vibrationally elastic scattering of electrons from ${\mathrm{H}}_2$O and ${\mathrm{NH}}_3$ molecules in the range of energy 0.5–20 eV. The total cross sections are approximated by a sum of the rotationally elastic ones and the rotational transition from ground to first excited state (00→10). The first-order Born approximation with the rotating-molecule model is used in the calculation of the first rotational excitation cross section. The experimental value of the dipole moments of ${\mathrm{H}}_2$O and ${\mathrm{NH}}_3$ are used in this step of the calculation. Spherically approximate molecular wave functions are applied to calculate the spherical part of the interactions of the incident electron with the molecule and the rotationally elastic-scattering cross section, in which the static and exchange interactions are calculated exactly within the accuracy of the molecular wave function and a parameter-free correlation-polarization potential is used to account for the polarization effect. The agreement of the differential cross sections with the experimental data is good at small angles and reasonably good at intermediate and large angles. Good agreement with measured values is obtained for the momentum-transfer cross sections. Total cross sections are reported with theoretical results on the e-${\mathrm{NH}}_3$ system below 10 eV. The possible sources of the discrepancies between the current theoretical and experimental results are analyzed for the total cross sections at very low energies by a quantitative consideration of the contributions of very strong forward scattering at near-zero angles to the total cross sections.

Triple-differential ionization cross sections ${\mathit{d}}^3$σ/d${\mathrm{\vartheta }}_{\mathit{p}}$${\mathit{dcphi}}_{\mathit{p}}$${\mathit{dp}}_{\mathrm{rec}}$, the momentum distributions of singly charged recoil ions transverse to the beam direction as a function of the projectile polar (${\mathrm{\vartheta }}_{\mathit{p}}$), and azimuthal (${\mathit{cphi}}_{\mathit{p}}$) scattering angle were measured in order to elucidate the dynamics of 3-MeV ${\mathrm{H}}^{+}$ on He single ionization. For projectile polar deflections 0.2 ≤${\mathrm{\vartheta }}_{\mathit{p}}$≤1 mrad and azimuthal scattering angles $0^{\mathrm{°}}$≤${\mathit{cphi}}_{\mathit{p}}$≤360°, the kinematic regimes where two-body interactions dominate the three-body momentum exchange of the single-ionization reaction were separated experimentally.

Within many-body perturbation theory (MBPT), the correlated decay of an inner-shell vacancy, namely, the double Auger effect, is considered. Expressions for the amplitude and probabilities are obtained in the lowest order of MBPT. The approximate formulas, in particular the ‘‘shakeoff’’ model, are discussed. The calculations are performed for the 1${\mathit{s}}^{\mathrm{-}1}$→2${\mathit{s}}^{\mathrm{-}2}$2${\mathit{p}}^{\mathrm{-}1}$+${\mathit{q}}_1$+${\mathit{q}}_2$ transition in Ne. It is shown that the angular distribution of electrons ejected in the double Auger decay of an s hole is asymmetric, depending strongly on the angle of their relative motion.