Electron Continuum Wave Research Articles

Detailed electron impact fine-structure excitation cross-sections of Kr+ and linear polarization of its subsequently emitted photons

An extensive calculation for electron impact excitation cross-sections of Kr+ ion is performed using relativistic distorted wave theory. The transitions considered are from the ground state i.e. 4s24p5 (J=3/2) to the 4s24p5 (J = 1/2), 4s4p6 (J=1/2) levels and fine structure levels of 4s24p45s, 4s24p45p, 4s24p46s, 4s24p46p, 4s24p44d and 4s24p45d excited states. The transition matrix is evaluated using the relativistic multi-configuration Dirac-Fock bound state wave functions of the initial and final states of Kr+ ion obtained from the GRASP2K program. The 4s24p5, 4s4p6, 4s24p45s, 4s24p45p, 4s24p46s, 4s24p46p, 4s24p44d and 4s24p45d configuration state functions are used to calculate the required wave functions. The incident and scattered projectile electron continuum wave functions are calculated numerically by solving the Dirac equations using static potential of the target ion. Oscillator strengths and transition probabilities are calculated and reported for the dipole allowed transitions, making these available to check the accuracy of the bound state wave functions for future comparison purposes. The detailed excitation cross-sections and their corresponding excitation rate coefficients are reported for considered 116 fine-structure excitation transitions from the ground state 4s24p5 (J=3/2). Further, analytic fittings of the obtained cross-sections with respect to incident electron energy are also performed for all the transitions considered in the present work so that these can be directly used in any plasma model for diagnostics purposes. In addition, using the obtained magnetic sub-level cross-sections, the degree of linear polarization of the photon emissions from the decay of electron impact excited anisotropic states of Kr+ ion through the dipole allowed transitions is calculated and reported.

Single-center approach for photodetachment and radiative electron attachment: Comparison with other theoretical approaches and with experimental photodetachment data

A single-center method for calculating photodetachment cross section for anions and radiative electron attachment cross section for neutral molecules by microreversibility is presented. It uses the integral equation method to calculate the ejected electron's continuum wave function while the single-electron bound function of the anion is described by the Dyson orbital. It is compared with related theoretical approaches and benchmarked to the experimental photodetachment cross sections of ${{\mathrm{O}}_{2}}^{\ensuremath{-}}$, ${\mathrm{OH}}^{\ensuremath{-}}$, and ${\mathrm{CN}}^{\ensuremath{-}}$. The use of the plane-wave approximation of the ejected electron wave function combined with the Hartree-Fock frozen-core approximation of the Dyson orbital is also considered and its results are compared with those of our methods and with experiment. A good agreement between the calculated photodetachment cross sections and the experimental data is obtained for ${{\mathrm{O}}_{2}}^{\ensuremath{-}}$ and ${\mathrm{CN}}^{\ensuremath{-}}$ when using the three methods. For ${\mathrm{OH}}^{\ensuremath{-}}$, the calculated scattering-wave electron photodetachment cross sections agree well with two most recent sets of experimental data among the three available while the plane-wave results disagree with all the experimental and theoretical data. The different approaches to calculate the Dyson orbital are also discussed as well as the convergence of the calculations with respect to the choice of the one-electron basis set. The approximation of Dyson orbitals by Kohn-Sham orbitals appears to overestimate the photodetachment cross section.

Accurate theoretical study of PSq (q = 0,+1,−1) in the gas phase

Highly correlated ab initio methods were used in order to generate the potential energy curves and spin-orbit couplings of electronic ground and excited states of PS and PS(+). We also computed those of the bound parts of the electronic states of the PS(-) anion. We used standard coupled cluster CCSD(T) level with augmented correlation-consistent basis sets, internally contacted multi-reference configuration interaction, and the newly developed CCSD(T)-F12 methods in connection with the explicitly correlated basis sets. Core-valence correction and scalar relativistic effects were examined. Our data consist of a set of spectroscopic parameters (equilibrium geometries, harmonic vibrational frequencies, rotational constants, spin-orbit, and spin-spin constants), adiabatic ionization energies, and electron affinities. For the low laying electronic states, our calculations are consistent with previous works whereas the high excited states present rather different shapes. Based on these new computations, the earlier ultraviolet bands of PS and PS(+) were reassigned. For PS(-) and in addition to the already known anionic three bound electronic states (i.e., X(3)Σ(-), (1)Δ, and 1(1)Σ(+)), our calculations show that the (1)Σ(-), (3)Σ(+), and the (3)Δ states are energetically below their quartet parent neutral state (a(4)Π). The depletion of the J = 3 component of PS(-)((3)Δ) will mainly occur via weak interactions with the electron continuum wave.

Phase determination of harmonics by three-color photoionization of aligned molecules: TheH2+system

We investigate the harmonic phase dependence of photoionization of aligned $\mathrm{H}_{2}{}^{+}$ with three colors: two high-order (uv) harmonics of orders $(q+1)$ and $(q\ensuremath{-}1)$ in the presence of a ``dressing'' ir photon such that the absorption of the $(q\ensuremath{-}1)$ harmonic and one ir photon is resonant with the absorption of the $(q+1)$ harmonic and emission of one ir photon. The transition amplitudes for these two interfering paths are calculated for $\mathrm{H}_{2}{}^{+}$ for a wide range of uv photon energies, internuclear distances $R$, and orientations. The relative phase of the ionizing harmonic photons controls the interference between the paths in the total photoionization amplitude, thus allowing for its measurement. Calculations are obtained using the $\mathrm{H}_{2}{}^{+}$ electron continuum wave functions and Green's functions for two polarizations, parallel $(z)$ and perpendicular $(x)$ to the internuclear axis. It is found that the phase differences of the two transition amplitudes, which are made up of harmonic and molecular phases, exhibit a sharp peak when calculated as a function of harmonic order $q$, and internuclear distance $R$. This occurs for near-vanishing total photoexcitation amplitudes where the phase of the amplitude changes abruptly by $\ensuremath{\pi}$. The orientation dependence of the interfering three-photon photoionization amplitudes provides an additional degree of freedom for harmonic phase measurements using aligned molecules, because of the orientation dependence of the molecular phase inherent in such measurements.

Stable and metastable states of SN−

Highly correlated ab initio methods were used in order to generate the potential energy functions (PEFs) of the bound electronic states of the SN− anion and the long-range parts of the PEFs of its excited states and their mutual spin–orbit couplings. The SN (X2Π and a4Π) potential energy curves are also computed. In addition to the two bound electronic states of SN− (i.e. X3Σ− and 1Δ) already known, our calculations show that the 3Δ state is lying energetically below its quartet parent neutral state (a4Π). The depletion of the J = 3 component of SN−(3Δ) will mainly occur via weak interactions with the electron continuum wave. At large internuclear distances, SN−(5Π) state is predicted to possess a shallow polarization minimum supporting long-lived SN− ions. Finally, the reaction between S−(2Pu) and N(4Su) involves the electronic states of SN− and their mutual couplings, in competition with the autodetachment processes.

Ionization cross sections of helium and hydrogenic ions by antiproton impact

The antiproton-impact cross sections are calculated for hydrogenic ions, hydrogen negative ion, and helium at lower collision energies than reported before. The electronic wave function is expanded in terms of the atomic orbitals centered on the target nucleus in a semiclassical common trajectory method, which includes the trajectory bending effect. The absorption potential is used to circumvent an unphysical reflection of electronic continuum wave function during the collision. At low energies, the absorption potential is effective for the neutral target and the trajectory bending effect is important for the ionized target.

Associative detachment, dissociative attachment, and vibrational excitation of HCl by low-energy electrons

An improved nonlocal resonance model for electron-HCl collisions is constructed. The model takes account of the dependence of the dipole-modified threshold exponent on the internuclear distance. The long-range part of the ${\mathrm{HCl}}^{\ensuremath{-}}$ potential-energy function has been determined from the most accurate ab initio calculations which are available. Only the s-wave component of the electronic continuum wave function is taken into account. Cross sections for vibrational excitation, dissociative attachment, and associative detachment have been calculated. For all three collision processes, the cross sections calculated with this model are in better agreement with experiment than previous calculations. The calculations reproduce very well even fine details of the threshold structures in the vibrational excitation cross sections of HCl.

Quartet and sextet states of CS−

The potential energy and spin–orbit functions have been calculated for several electronic states of CS and CS−. Comparison with experimental data for CS shows very good agreement, making reliable predictions possible for the CS− molecule such as the existence of long-lived metastable states. The a 4Σ−, b 4Π, and a 6Π states were found to lie energetically below the triplet or quintet states of the CS molecule. The calculated spin–orbit integrals between the electronic states suggest that the depletion of the J=5/2 or 7/2 components in the Π states will mainly occur via weak interactions with the electron continuum wave.

Study of generalized spheroidal continuum wave functions applied to hydrogenic system in a half space

We apply the Killingbeck method to solve the generalized spheroidal electronic continuum wave functions of a hydrogen atom in front of the surface of an ideal insulator and a metal. We propose a dipole model to reduce the latter to one-electron two-center problem. Furthermore, we study the H 2 + and dipole electronic continuum wave functions in the whole space. The lowest partial wave solutions are obtained and their k-dependence is analyzed.

Vibrational branching ratios for single-photon ionization ofNa2

We report on an ab initio study of the single-photon ionization of ${\mathrm{Na}}_{2}$ from the electronic ground state (X${\mathrm{}}^{1}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+}$) and subsequent photodissociation of the resulting ion. The calculations are done as a function of internuclear distance (R=4.5--7.5 a.u.) and for a range of photoelectron energies 0.25--10 eV. The electronic continuum wave functions are determined using the so-called iterative Schwinger method, which is an ${\mathit{L}}^{2}$ method based on a single-center expansion of all relevant operators and wave functions. A Cooper minimum is found in the k\ensuremath{\pi}-continuum's p wave (l=1) around a photoelectron energy of approximately 4.5 eV. This does not, however, lead to significant observable implications for the total cross sections. The subsequent photodissociation of the ${\mathrm{Na}}_{2}^{+}$ ions is calculated using a numerical Numerov method, based on previously calculated data for the molecular potential-energy curves and dipole matrix elements. The spectrum resulting from photodissociation of ions created via photoionization of a thermal distribution of ${\mathrm{Na}}_{2}$ molecules is calculated and compared with the recent results of Kortyna et al. [Phys. Rev. A 50, 1399 (1994)]. Excellent agreement is found with the experimental values if the assumed initial temperature of the molecular beam is approximately 50 K, which is substantially colder than previously estimated. \textcopyright{} 1996 The American Physical Society.

Molecular photoionization cross sections by the Lobatto technique. II. core level photionization

The logarithmic derivative Kohn-Lobatto (LDKL) method for determining molecular electronic continuum wave functions is applied to the calculation of core level photoionization cross sections. The description of the photoionization process is based on a local effective potential obtained from density functional theory. However, the LDKL method avoids a shape approximation to the potential like the muffin-tin form underlying the continuum multiple scattering (CMS) method. Different from the procedure for the investigation of valence photoionization the influence of the attractive hole has to be taken into account explicitly. Slater's transition state potential in the local density approximation (LDA) leads to very satisfactory predictions of photoionization cross sections and asymmetry parameters. This is demonstrated for the well known cases of N 2 and CO. Applications to the inner shell photoionization of SF 6 illustrate that the LDKL method in the present LDA implementation affords an efficient and accurate treatment of larger molecules for which it offers an alternative superior to the widely used CMSXα method.

Molecular photoionization cross sections by the Lobatto technique. I. Valence photoionization

A method for the calculation of electronic continuum wave functions is presented which is based on the logarithmic derivative version of the Kohn (LDK) variational principle. The variational principle is cast into algebraic form by introducing a finite basis set that consists of spherical harmonic Gaussian-type functions (GTOs) and of Lobatto shape functions with the latter representing the translational part of the basis. A local effective potential which is obtained from density functional theory results in fairly accurate photoionization cross sections. Also studied are asymptotic corrections to the effective potential for the photoelectron which, in many cases, lead to improved results. The Lobatto procedure is applied to the diatomics N2 and CO and to benzene which may be regarded as a prototype for larger non spherical symmetric systems for which the method is targeted. For the two diatomics, results in excellent agreement with experiment have been found. For benzene the results are compared to those obtained by the Stieltjes–Tchebychev (ST) imaging technique and by the continuum multiple scattering (CMS) method which both have been applied to similar effective local potentials. Comparison with the ST imaging technique shows that the LDK Lobatto (LDKL) method provides qualitatively similar results, but the LDKL cross sections are of higher resolution and allow a more detailed analysis because of the explicit determination of the continuum wave function. For most of the valence orbitals of benzene the CMS method does not lead to satisfactory agreement with experiment due to the well-known deficiencies of this technique. The LDKL method implemented with a combined basis set does not suffer from the limitations of the ST and the CMS methods, but remains applicable to larger-size molecules.

Lanczos methods for hamiltonian spectra: Hilbert-space approximations to interaction-prepared states

Recent progress is reported in applications of iterative methods for calculations of molecular electronic continuum states. Vectors constructed in an appropriate Lanczos basis are seen to provide directly approximations to the interaction-prepared states of Fano and Cooper. Nondegenerate point-group-symmetry electronic continuum wave functions are constructed recursively in this way for complex molecules without explicit enforcement of the S-matrix, K-matrix or other asymptotic boundary conditions required in conventional scattering developments. A multi-channel Feshbach-Fano version of the approach employing an appropriately selected Q space of zeroth-order states provides a Lanczos formulation of complex photoionization spectra based on eigenfunctions of molecular point-group-symmetry type. Computational applications of the methods described are reported for the partial cross sections of selected (N 2, CO 2, C 2H 2) molecules.

Application of the Schwinger variational principle to electron-ion scattering in the static-exchange approximation

The authors present a method for applying the Schwinger variational principle to the scattering of low-energy electrons by molecular ions. Numerical procedures for its application in the static-exchange approximation are specifically discussed. As examples, the $s$- and $p$-wave phase shifts for $e$-${\mathrm{He}}^{+}$ are obtained. The procedure also provides the electron continuum wave functions which can be used to obtain photoionization cross sections. The resulting cross sections for photoionization of the ground and metastable states of the He are seen to be accurate.