Accurate Hartree-Fock vibrational branching ratios in 3σg photoionisation of N2

The authors report vibrational branching ratios for resonant photoionisation of N2 leading to the X2 Sigma g+ state of N2+. Their theoretical values are obtained from an accurate solution of the adiabatic-nuclei frozen-core Hartree-Fock model of molecular photoionisation. In contrast to other theoretical results the present results are in very good agreement with experimental measurements. Differences between the present and previous calculations are discussed

Application of the Schwinger variational principle to electron scattering

The authors present the results of the first rigorous application of the Schwinger variational principle to electron scattering with the inclusion of exchange. The results of this application to e-He scattering in the static-exchange approximation show that the Schwinger method provides accurate solutions of the scattering problem with small basis set expansions

Variational treatment of electron-polyatomic molecule scattering calculations using adaptive overset grids

The Complex Kohn variational method for electron-polyatomic molecule scattering is formulated using an overset grid representation of the scattering wave function. The overset grid consists of a central grid and multiple dense, atom-centered subgrids that allow the simultaneous spherical expansions of the wave function about multiple centers. Scattering boundary conditions are enforced by using a basis formed by the repeated application of the free particle Green's function and potential, $\hat{G}^+_0\hat{V}$ on the overset grid in a "Born-Arnoldi" solution of the working equations. The theory is shown to be equivalent to a specific Pad\'e approximant to the $T$-matrix, and has rapid convergence properties, both in the number of numerical basis functions employed and the number of partial waves employed in the spherical expansions. The method is demonstrated in calculations on methane and CF$_4$ in the static-exchange approximation, and compared in detail with calculations performed with the numerical Schwinger variational approach based on single center expansions. An efficient procedure for operating with the free-particle Green's function and exchange operators (to which no approximation is made) is also described

Polarization and ellipticity of high-order harmonics from aligned molecules generated by linearly polarized intense laser pulses

We present theoretical calculations for polarization and ellipticity of high-order harmonics from aligned N$_2$, CO$_2$, and O$_2$ molecules generated by linearly polarized lasers. Within the rescattering model, the two polarization amplitudes of the harmonics are determined by the photo-recombination amplitudes for photons emitted parallel and perpendicular to the direction of the {\em same} returning electron wave packet. Our results show clear species-dependent polarization states, in excellent agreement with experiments. We further note that the measured polarization ellipse of the harmonic furnishes the needed parameters for a "complete" experiment in molecules.Comment: 4 pages, 4 figure

Probing molecular frame photoionization via laser generated high-order harmonics from aligned molecules

Present photoionization experiments cannot measure molecular frame photoelectron angular distributions (MFPAD) from the outermost valence electrons of molecules. We show that details of the MFPAD can be retrieved with high-order harmonics generated by infrared lasers from aligned molecules. Using accurately calculated photoionization transition dipole moments for fixed-in-space molecules, we show that the dependence of the magnitude and phase of the high-order harmonics on the alignment angle of the molecules observed in recent experiments can be quantitatively reproduced. This result provides the needed theoretical basis for ultrafast dynamic chemical imaging using infrared laser pulses.Comment: 5 pages, 4 figure

Quantitative Rescattering Theory for high-order harmonic generation from molecules

The Quantitative Rescattering Theory (QRS) for high-order harmonic generation (HHG) by intense laser pulses is presented. According to the QRS, HHG spectra can be expressed as a product of a returning electron wave packet and the photo-recombination differential cross section of the {\em laser-free} continuum electron back to the initial bound state. We show that the shape of the returning electron wave packet is determined mostly by the laser only. The returning electron wave packets can be obtained from the strong-field approximation or from the solution of the time-dependent Schr\"odinger equation (TDSE) for a reference atom. The validity of the QRS is carefully examined by checking against accurate results for both harmonic magnitude and phase from the solution of the TDSE for atomic targets within the single active electron approximation. Combining with accurate transition dipoles obtained from state-of-the-art molecular photoionization calculations, we further show that available experimental measurements for HHG from partially aligned molecules can be explained by the QRS. Our results show that quantitative description of the HHG from aligned molecules has become possible. Since infrared lasers of pulse durations of a few femtoseconds are easily available in the laboratory, they may be used for dynamic imaging of a transient molecule with femtosecond temporal resolutions.Comment: 50 pages, 15 figure

Iterative approach to the Schwinger variational principle applied to electron—molecular-ion collisions

We present a study of electron—molecular-ion collisions. The scattering equations are solved using an iterative approach to the Schwinger variational principle. These equations are formulated using the Coulomb Green's function to properly treat the long-range Coulomb tail of the molecular-ion potential. We apply this approach to electron—hydrogen-molecular-ion collisions in the static-exchange approximation. We obtain elastic differential cross sections, and also use the continuum states from these calculations to compute the photoionization cross section of the hydrogen molecule. The iterative method used here converged rapidly in all calculations performed

Padé-approximant corrections to general variational expressions of scattering theory: Application to 5σ photoionization of carbon monoxide

We discuss a method for systematically correcting results obtained using variational expressions in scattering theory. The approach taken is to compute a sequence of Padé approximants of the form [N/N] for the error in an initial variational estimate obtained using a basis-set expansion. The relationship between the Padé-approximant approach and the iterative Schwinger method for correcting variational estimates is also examined. We discuss a large class of general variational expressions to which the Padé-approximant approach can be applied. The variational expressions considered include those for the wave function, for photoionization transition matrix elements, as well as for scattering matrix (K-matrix) elements. We have applied this approach to the 5σ photoionization of CO using the frozen-core Hartree-Fock and fixed-nuclei approximations. We find that the Padé-approximant method converges rapidly and reliably. Both total photoionization cross sections and photoelectron angular distributions from threshold to 40 eV are presented and compared to previous experimental and theoretical results. We find major quantitative discrepancies between the present results for the total cross section and previous theoretical results

Studies of differential and total photoionization cross sections of carbon dioxide

The photoionization of CO2 has been studied using accurate frozen-core Hartree-Fock final-state wave functions. The Hartree-Fock continuum equations were solved using the iterative Schwinger variational method. We present differential and total cross sections for photoionization leading to the X 2Πg, A 2Πu, B 2Σu+, and C 2Σg+, states of CO2+ as well as for oxygen and carbon K-shell photoionization. The present cross sections are compared to experimental data and are found to be in generally good agreement. The theoretical cross sections exhibit features due to a narrow shape resonance in those channels where the continuum wave functions have σu symmetry. The relation between these results and experimental cross sections is discussed. The present fixed-nuclei results have also been compared to published theoretical results obtained using the Stieltjes-Tchebycheff moment theory approach and the continuum multiple-scattering method