Time-dependent Close-coupling Calculations Research Articles

Electron-impact single and double ionization of W+

Electron-impact single and double ionization cross sections for the W+ atomic ion are calculated and compared with crossed-beams measurements. The single ionization cross sections include contributions from outer subshell direct ionization and excitation-autoionization. Agreement with crossed-beams measurements is improved when non-perturbative time-dependent close-coupling calculations are used instead of perturbative distorted-wave calculations for the direct ionization of the 6s and 5d outer subshells. The double ionization cross sections include contributions from outer subshell double direct ionization, inner subshell direct ionization, and excitation-autoionization. The double ionization cross sections are an order of magnitude smaller than the single ionization cross sections and in reasonable agreement with crossed-beams measurements.

R -matrix-with-time-dependence theory for ultrafast atomic processes in arbitrary light fields

We describe an ab initio and non-perturbative $R$-matrix with time-dependence theory for ultrafast atomic processes in light fields of arbitrary polarization. The theory is applicable to complex, multielectron atoms and atomic ions subject to ultrashort (particularly few-femtosecond and attosecond) laser pulses with any given ellipticity, and generalizes previous time-dependent $R$-matrix techniques restricted to linearly polarized fields. We discuss both the fundamental equations, required to propagate the multielectron wavefunction in time, as well as the computational developments necessary for their efficient numerical solution. To verify the accuracy of our approach, we investigate the two-photon ionization of He, irradiated by a pair of time-delayed, circularly polarized, femtosecond laser pulses, and compare photoelectron momentum distributions, in the polarization plane, with those obtained from recent time-dependent close-coupling calculations. The predictive capabilities of our approach are further demonstrated through a study of single-photon detachment from F$^{-}$ in a circularly polarized, femtosecond laser pulse, where the relative contribution of the co- and counter-rotating $2p$ electrons is quantified.

Analysis of multiple scattering contributions in electron-impact ionization of molecular hydrogen

We report a combined experimental and theoretical study on the low-energy (E0 = 31.5 eV) electron-impact ionization of molecular hydrogen (H2). Triple differential cross sections are measured for a range of fixed emission angles of one outgoing electron between and −130° covering the full 4π solid angle of the second electron. The energy sharing of the outgoing electrons varies from symmetric ( eV) to highly asymmetric (E1 = 1 eV and E2 = 15 eV). In addition to the binary and recoil lobes, a structure is observed perpendicular to the incoming beam direction which is due to multiple scattering of the projectile inside the molecular potential. The absolutely normalized experimental cross sections are compared with results from the time-dependent close-coupling (TDCC) calculations. Molecular alignment dependent TDCC results demonstrate that these structures are only present if the molecule axis is lying in the scattering plane.

Electron-impact single and double ionization of W

Electron-impact single and double ionization cross sections for the W atom are calculated using a semi-relativistic distorted-wave method. The cross sections include contributions from single direct ionization, double direct ionization and excitation-autoionization. Branching ratio calculations are made to determine whether an excitation may contribute to single or double ionization. We check the accuracy of the semi-relativistic distorted-wave calculations for direct ionization of various subshells by comparison with fully-relativistic distorted-wave calculations. We also check the accuracy of the perturbative distorted-wave calculations for direct ionization of the outer most subshells by comparison with non-perturbative time-dependent close-coupling calculations.

Double photoionization of helium from the 1s2p excited state

Time-dependent close-coupling (TDCC) calculations are carried out for the double photoionization of Helium in the excited state. TDCC results are presented for the total and energy differential cross sections for the term. TDCC results are presented for the total and energy differential cross sections for the levels. Differences found between the level resolved double photoionization cross sections are due to varying degrees of continuum correlation found in the outgoing two electrons.

Propensity for distinguishing two free electrons with equal energies in electron-impact ionization of helium

We report a combined experimental and theoretical study on the electron-impact ionization of helium at ${E}_{0}\phantom{\rule{0.28em}{0ex}}=\phantom{\rule{0.28em}{0ex}}70.6\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$ and equal energy sharing of the two outgoing electrons (${E}_{1}={E}_{2}=23\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$), where a double-peak or dip structure in the binary region of the triple differential cross section is observed. The experimental cross sections are compared with results from convergent close-coupling (CCC), $B$-spline R-matrix-with-pseudostates (BSR), and time-dependent close-coupling (TDCC) calculations, as well as predictions from the dynamic screening three-Coulomb (DS3C) theory. Excellent agreement is obtained between experiment and the nonperturbative CCC, BSR, and TDCC theories, and good agreement is also found for the DS3C model. The data are further analyzed regarding contributions in particular coupling schemes for the spins of either the two outgoing electrons or one of the outgoing electrons and the $1s$ electron remaining in the residual ion. While both coupling schemes can be used to explain the observed double-peak structure in the cross section, the second one allows for the isolation of the exchange contribution between the incident projectile and the target. For different observation angles of the two outgoing electrons, we interpret the results as a propensity for distinguishing these two electrons---one being more likely the incident projectile and the other one being more likely ejected from the target.

Sensitivity of cross sections to the diffuseness of the confining potential in time-dependent close-coupling calculations of the double photoionization of He@C60

Calculations of the photoionization of endofullerenes often use a square-well potential to represent the confining fullerene. The sensitivity of the photoionization cross sections to the form of this model potential is explored here by the use of a diffuse potential. The cross sections for single photoionization with excitation and double photoionization of He@C${}_{60}$ are found to show damping of the confinement resonance structure as the degree of diffuseness is increased using a commonly adopted well depth of 8.22 eV. For a deeper well depth of 11.00 eV, the double-photoionization cross section is found to be insensitive to the diffuseness of the confining potential, as has also been reported recently for the single photoionization of H@C${}_{60}$ and Xe@C${}_{60}$ [Dolmatov, King, and Oglesby, J. Phys. B 45, 105102 (2012)].

Strong Molecular Alignment Dependence ofH2Electron Impact Ionization Dynamics

Low-energy (E(0) = 54 eV) electron impact single ionization of molecular hydrogen (H(2)) has been investigated as a function of molecular alignment in order to benchmark recent theoretical predictions [Colgan et al., Phys. Rev. Lett. 101, 233201 (2008) and Al-Hagan et al., Nature Phys. 5, 59 (2009)]. In contrast to any previous work, we observe distinct alignment dependence of the (e,2e) cross sections in the perpendicular plane in good overall agreement with results from time-dependent close-coupling calculations. The cross section behavior can be consistently explained by a rescattering of the ejected electron in the molecular potential resulting in an effective focusing along the molecular axis.

Electron-impact ionization of Al

Perturbative distorted-wave and non-perturbative close-coupling methods are used to calculate electron-impact ionization cross sections for the ground state of the neutral Al atom. Configuration-average distorted-wave calculations are made for both direct ionization and excitation-autoionization contributions. The total perturbative results are found to be almost a factor of 2 higher than experiment over a wide energy range. On the other hand, the R-matrix with pseudo-states results for total ionization are found to be in good agreement with experiment. Comparison of time-dependent close-coupling calculations for the direct ionization with the R-matrix with pseudo-state calculations for total ionization reveals that both the direct ionization and excitation-autoionization contributions are strongly affected by correlation effects.

Double photoionization of helium including quadrupole radiation effects

Non-perturbative time-dependent close-coupling calculations are carried out for the double photoionization of helium including both dipole and quadrupole radiation effects. At a photon energy of 800 eV, accessible at current synchrotron light sources, the quadrupole interaction contributes around 6% to the total integral double photoionization cross section. The pure quadrupole single energy differential cross section shows a local maximum at equal energy sharing, as opposed to the minimum found in the pure dipole single energy differential cross section. The sum of the pure dipole and pure quadrupole single energy differentials is insensitive to non-dipole effects at 800 eV. However, the triple differential cross section at equal energy sharing of the two ejected electrons shows strong non-dipole effects due to the quadrupole interaction that may be experimentally observable.

Minima in the triple differential cross sections for the electron-impact ionization of helium

We examine unusual minima found in the triple differential cross sections for the electron-impact ionization of helium for configurations where the incident electron is out-of-plane with respect to the plane in which the outgoing electrons are detected. The position of the experimentally determined minima are confirmed by time-dependent close-coupling calculations. An analysis is made of the origin of the minima in the cross section, where it is found they are due to deep destructive interference between the partial-wave amplitudes which contribute to the differential cross section.

Low-energy collisions of antiprotons with atoms and molecules

Time-dependent close-coupling calculations were performed using the impact parameter method for antiproton and proton collisions with alkali-metal atoms and hydrogen molecules. The targets are described as effective one-electron systems using appropriate model potentials. The proton data verify the employed method while the results for antiprotons improve the literature on these systems considerably. Cross sections for ionization and excitation as well as electron-energy spectra and stopping power will be presented.

Double ionization ofH2by fast bare-ion collisions

A time-dependent close-coupling method is developed to treat the double ionization of ${\text{H}}_{2}$ by fast bare-ion collisions. At high incident energies, for which charge transfer to the projectile may be ignored, multipole expansions are made for the electron-electron and electron-projectile interactions in a fixed target nuclei coordinate system. The time-dependent Schr\"odinger equation for the six dimensional target electron wave function is reduced to a set of close-coupled equations on a four dimensional numerical lattice in $({r}_{1},{\ensuremath{\theta}}_{1},{r}_{2},{\ensuremath{\theta}}_{2})$ center-of-mass spherical polar coordinates. Time-dependent close-coupling calculations are carried out for $p+{\text{H}}_{2}$ collisions at an incident energy of 1.0 MeV. The ratio of double to single ionization is found to be 0.3%, which is in reasonable agreement with experimental measurements.

Collisions of antiprotons with hydrogen molecular ions

Time-dependent close-coupling calculations of the ionization and excitation cross section for antiproton collisions with molecular hydrogen ions are performed in an impact-energy range from 0.5 keV to 10 MeV. The Born-Oppenheimer and Franck-Condon approximations as well as the impact parameter method are applied in order to describe the target molecule and the collision process. It is shown that three perpendicular orientations of the molecular axis with respect to the trajectory are sufficient to accurately reproduce the ionization cross section calculated by [Sakimoto, Phys. Rev. A 71, 062704 (2005)] reducing the numerical effort drastically. The independent-event model is employed to approximate the cross section for double ionization and H+ production in antiproton collisions with H2.

Electron-impact ionization of ground and metastable neon

Electron-impact ionization of neutral neon continues to be of interest both from a fundamental and an applied perspective. Non-perturbative calculations are required for the electron-impact ionization of ground and excited states of neon. R-matrix with pseudostates (RMPS) calculations for the electron-impact ionization of the 1s22s22p6 ground state of Ne at higher incident electron energies are now made possible by the further partitioning of each individual LS partial wave across a greater number of processors. Furthermore, instead of a long sequence of parallel matrix diagonalizations, every partial wave diagonalization is now carried out concurrently. The ground-state cross section is found to be in excellent agreement with recent experimental measurements. The previous work of Ballance et al (2004 J. Phys. B: At. Mol. Opt. Phys. 37 4779), for the ionization of the 1s22s22p53s excited state of Ne, has been extended to examine the ionization of the 1s22s22p54s and 1s22s22p55s excited states. Very good agreement is found between R-matrix with pseudostates and time-dependent close-coupling calculations for the 1s22s22p54s excited state. The non-perturbative cross sections for low nl are used to scale semi-classical impact parameter cross sections to high nl. Ionization cross sections for the ground and all excited states will enable the accurate determination of the generalized collisional-radiative ionization rate coefficient for neutral Ne in finite plasmas.

Electron-impact single ionization of Mg andAl+

Theory and experiment are compared for the electron-impact single ionization of Mg and ${\text{Al}}^{+}$. Nonperturbative $R$ matrix with pseudostates (RMPS) and time-dependent close-coupling (TDCC) calculations have been carried out that exhibit large reductions from perturbative distorted-wave results of 38% for Mg and 20% for ${\text{Al}}^{+}$. Experimental single-ionization data available for Mg and ${\text{Al}}^{+}$ are in reasonable accord with distorted-wave data and lie substantially above the new theoretical results. Rate coefficients, necessary for the collisional-radiative modeling of Mg and Al plasmas were generated from the RMPS ionization cross sections. In the collisional-ionization region near the ionization threshold, the resulting rates were found to be up to two times lower for Mg and three times lower for ${\text{Al}}^{+}$ than the rates generated from experimental data.

Double photoionization of Be and Mg atoms using theR-matrix-with-pseudostates method

The $R$-matrix-with-pseudostates (RMPS) method is used to obtain total cross sections for double photoionization of Be and Mg atoms from their ground singlet and metastable triplet terms. Time-dependent close-coupling (TDCC) calculations are also carried out for the total and energy differential double photoionization cross sections of Mg from its ground term. The RMPS total ground-term cross sections for Be and Mg are in good agreement with results from TDCC and convergent close-coupling calculations at lower energies but are above them at higher energies. They are also in good agreement with the results of synchrotron measurements. The total cross sections for double photoionization from the triplet metastable terms of Be and Mg are found to be two to three times smaller than those from their singlet ground terms.

Photo-double ionization of H2

The Coulomb explosion of the hydrogen molecule, after absorption of a 76 eV photon, has been studied by momentum imaging the two electrons and the two protons. Absolute fully differential cross sections (FDCS) are compared with Time Dependent Close Coupling (TDCC) calculations and the first-order helium-like model in the coplanar geometry for equal electron energy sharing. While the helium-like model gives a consistent agreement in shape and magnitude with experimental data, the comparison with the TDCC calculations highlights the limit of this model when the molecular axis' orientation is along the polarization direction. New evidence of changes in the FDCS with internuclear separation is reported for the coplanar geometry.

Time-dependent close-coupling calculations of atomic and molecular collision processes

We report on our progress in understanding the dynamics of atomic and molecular collision processes using time-dependent close-coupling methods

Electron-impact ionization of the boron atom

Accurate knowledge of the electron-impact ionization of the B atom is urgently needed in current fusion plasma experiments to help design ITER wall components. Since no atomic measurements exist, nonperturbative time-dependent close-coupling (TDCC) calculations are carried out to accurately determine the direct ionization cross sections of the outer two subshells of B. Perturbative distorted-wave and semiempirical binary encounter calculations are found to yield cross sections from 26% lower to an order of magnitude higher than the current TDCC results. Unlike almost all neutral atoms, large excitation-autoionization contributions are found for the B atom. Nonperturbative $R$ matrix with pseudostates (RMPS) calculations are also carried out to accurately determine the total ionization cross section of B. Previous 60 LS-term RMPS calculations are found to yield cross sections up to 40% higher than the current more extensive 476 LS-term RMPS results.