Three-photon detachment of electrons from the fluorine negative ion

Absolute three-photon detachment cross sections are calculated for the fluorine negative ion within the lowest-order perturbation theory. The Dyson equation of the atomic many-body theory is used to obtain the ground-state 2p wavefunction with correct asymptotic behaviour, corresponding to the true (experimental) binding energy. We show that in accordance with the adiabatic theory this is crucial for obtaining absolute values of the multiphoton cross sections. Comparisons with other calculations and experimental data are presented.

R-matrix Floquet theory of multiphoton processes:VI. The negative halide ions

The R-matrix Floquet approach is applied to study the negative F and Cl ions in a light field. Detachment rates are obtained for detachment processes involving up to three photons. The results obtained in the present approach are compared to other experimental and theoretical results. For two- and three-photon processes reasonable agreement with other calculations has been found, while for two-photon detachment the results agree with the experimental cross sections. The three-photon results are in less good agreement with experiment although the larger error bars make accurate comparisons more difficult. The changes in the detachment behaviour for these ions are compared to each other as well as to the detachment behaviour of H.

R-matrix Floquet theory of multiphoton processes:XIII. Resonances in H multiphoton detachment

The results of calculations investigating the effects of autodetaching resonances on the multiphoton detachment spectra of H are presented. The R-matrix Floquet method is used, in which the coupling of the ion with the laser field is described non-perturbatively. The laser field is fixed at an intensity of 10 W cm, while frequency ranges are chosen such that the lowest autodetaching states of the ion are excited through a two- or three-photon transition from the ground state. Detachment rates are compared, where possible, to previous results obtained using perturbation theory. An illustration of how non-lowest-order processes, involving autodetaching states, can lead to light-induced continuum structures is also presented. Finally, it is demonstrated that by using a frequency connecting the 1s and 2s states, the probability of exciting the residual hydrogen atom is significantly enhanced.

R-matrix-Floquet theory of multiphoton processes:VIII. A linear equations method

A new linear equations method for calculating the R-matrix, which arises in the R-matrix-Floquet theory of multiphoton processes, is introduced. This method replaces the diagonalization of the Floquet Hamiltonian matrix by the solution of a set of linear simultaneous equations which are solved, in the present work, by the conjugate gradient method. This approach uses considerably less computer memory and can be readily ported onto parallel computers. It will thus enable much larger problems of current interest to be treated. This new method is tested by applying it to three-photon ionization of helium at frequencies where double resonances with a bound state and autoionizing states are important. Finally, an alternative linear equations method, which avoids the explicit calculation of the R-matrix by incorporating the boundary conditions directly, is described in an appendix.

Partial and total multiphoton detachment rates for H- in a perturbative B-spline-based approach

An ab initio approach has been applied to study multiphoton detachment rates for the negative hydrogen ion in the lowest nonvanishing order of perturbation theory. The approach is based on the use of B splines allowing an accurate treatment of the electronic repulsion. Total detachment rates have been determined for two- to six-photon processes as well as partial rates for detachment into the different final symmetries. It is shown that B-spline expansions can yield accurate continuum and bound-state wave functions in a very simple manner. The calculated total rates for two- and three-photon detachment are in good agreement with other perturbative calculations. For more than three-photon detachment little information has been available before now. While the total cross sections show little structure, a fair amount of structure is predicted in the partial cross sections. In the two-photon process, it is shown that the detached electrons mainly have s character. For four- and six-photon processes, the contribution from the d channel is the most important. For three- and five-photon processes p electrons dominate the electron emission spectrum. Detachment rates for s and p electrons show minima as a function of photon energy. © 1994 The American Physical Society.

Multiphoton inner-shell ionization of the carbon atom

We apply time-dependent R-matrix theory to study inner-shell ionization of C atoms in ultra-short high-frequency light fields with a photon energy between 170 and 245 eV. At an intensity of 10¹⁷ W/cm², ionization is dominated by single-photon emission of a 2l electron, with two-photon emission of a 1s electron accounting for about 2-3% of all emission processes, and two-photon emission of 2l contributing about 0.5-1%. Three-photon emission of a 1s electron is estimated to contribute about 0.01-0.03%. Around a photon energy of 225 eV, two-photon emission of a 1s electron, leaving C⁺ in either 1s2s2p³ or 1s2p⁴ is resonantly enhanced by intermediate 1s2s²2p³ states. The results demonstrate the capability of time-dependent R-matrix theory to describe inner-shell ionization processes including rearrangement of the outer electrons.

Single- and multiphoton detachment of K

Single- and multiphoton detachment rates have been calculated for K- using the R-matrix Floquet approach. Single-photon detachment rates, obtained at a laser field peak intensity of 10(9) W cm(-2), are discussed and compared with other theoretical work. Two-photon detachment rates at the same intensity have also been obtained, and similarities with results from earlier calculations for Li- and Na- are discussed. Three-photon rates are also presented at this laser intensity, and are compared and contrasted with those arising in the single-photon case, since both involve resonance structure with P-1(o) symmetry. The influence of resonances such as the 5s(2) S-1(e) doubly excited state and excitations of the residual atom are also considered.

Configuration-interaction effects in and intensity dependence of F- multiphoton detachment

Two- and three-photon detachment rates have been obtained for F- using several expansions in the R-matrix Floquet approach. These rates are compared with other theoretical and experimental results. The use of Hartree-Fock wavefunctions for the ground state of F with addition of continuum electrons does not lead to agreement with experiment for two- and three-photon detachment. By adding correlation terms, agreement with experiment and other theoretical results is improved considerably, demonstrating the importance of electron correlation effects. However, convergence with respect to the wavefunction expansion cannot be established, we also study the intensity dependence of multiphoton detachment rates for F- at the Nd-YAG frequency. Due to the ponderomotive shift the three-photon detachment channel closes at an intensity of 8.5 x 10(11) W cm(-2) and the influence of this channel closure on the multiphoton detachment peaks is illustrated by determining the heights of the excess-photon peaks obtained using a Gaussian laser pulse.

Direct Photodetachment of F‾ by mid-infrared few-cycle femtosecond laser pulses

The recent adiabatic saddle-point approach of Shearer et al. [ Phys. Rev. A 84 033409 (2011)] is extended to multiphoton detachment of negative ions with outer p-state electrons. This theory is applied to investigate the strong-field photodetachment dynamics of F- ions exposed to few-cycle femtosecond laser pulses, without taking into account the rescattering mechanism. Numerical calculations are considered for mid-infrared laser wavelengths of 1300 and 1800 nm at laser intensities of 7.7 × 1012, 1.1 × 1013, and 1.3 × 1013 W/cm2. Two-dimensional momenta saddle-point spectra exhibit a distinct distribution in the shape of a “smile” in the complex-time plane. Electron momentum distribution maps of direct electrons are investigated. These produce a distinct pattern of above-threshold detachment (ATD) concentric rings due to constructive and destructive quantum interference of electrons detached from their parent ions. Probability detachment distributions presented, capturing the influence of saturation effects that are found to become more significant with increasing laser intensity at a fixed wavelength. ATD photoangular distributions as functions of laser intensity and wavelength near channel closings are also investigated and found to be sensitive to initial-state symmetry. Nonmonotonic structures observed in the ejected photoelectron energy spectra are attributed to interference effects from coherent electronic wave packets. Additionally the profiles of all the photoelectron emission spectra show strong dependence on the carrier-envelope phase, indicating that it is a reliable parameter for characterizing the wave form of the pulse.

Did children’s perceptions of an after-school social learning program predict change in their behavior?

This research explored the influence of children’s perceptions of a pro-social behavior after-school program on actual change in the children’s behavioral outcomes over the program’s duration. Children’s perceptions of three program processes were collected as well as self-reported pro-social and anti-social behavior before and after the program. Statistical models showed that: Positive perceptions of the program facilitators’ dispositions significantly predicted reductions in anti-social behavior; and positive perceptions with the program activities significantly predicted gains in pro-social behavior. The children’s perceptions of their peers’ behavior in the sessions were not found to a significant predictor of behavioral change. The two significant perceptual indicators predicted a small percentage of the change in the behavioral outcomes. However, as after-school social learning programs have a research history of problematic implementation children’s perceptions should be considered in future program design, evaluation and monitoring.

Singly, doubly and triply resonant multiphoton processes involving autoionizing states in magnesium

Using the R-matrix Floquet theory we have carried out non-perturbative, ab initio one- and two-colour calculations of the multiphoton ionization of magnesium with the laser frequencies chosen such that the initial state of the atom is resonantly coupled with autoionizing resonances of the atom. Good agreement is obtained with previous calculations in the low-intensity regimes. The single-photon ionization from the 3s3p P excited state of magnesium has been studied in the vicinity of the 3p S autoionizing resonance at non-perturbative laser intensities. Laser-induced degenerate states (LIDS) are observed for modest laser intensities. By adding a second laser which resonantly couples the 3p S = and 3p3d P autoionizing levels, we show that, due to the small width of the 3p3d P state, LIDS occur between this state and the 3s3p P state at intensities of the first laser below 10 W cm . We next investigate the case in which the first laser induces a resonant two-photon coupling between the ground state and the 3p S autoionizing state, while the second laser again resonantly couples the respective 3p S and 3p3d P autoionizing states. At weak intensities, our calculations compare favourably with recent experimental data and calculations. We show that when the intensity of the first laser is increased, the effect of an additional autoionizing state, the 4s5s S state, becomes significant. This state is coupled to the 3p3d P autoionizing level by one photon, inducing a triply resonant processes. We show that LIDS occur among the three autoionizing levels and we discuss their effect on the decay rate of the ground state. We consider dressed two- and three-level atoms which can be used to model the results of our calculations.