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The dynamics of strong-field (\ensuremath{\sim}${10}^{14}$ W/${\mathrm{cm}}^{2}$) multiphoton processes in molecules can be investigated using a simple, collinear model for ${\mathrm{H}}_{2}^{+}$. We discuss properties of this model and report preliminary calculations related to recent experimental results. We find that the excitation and ionization dynamics of the molecular ion depend strongly on the laser wavelength, pulse shape, intensity, and particularly on the initial vibrational state of the molecule. \textcopyright{} 1996 The American Physical Society.

This project has pursued the possibility of producing ultra-short pulses of coherent light using harmonic conversion of a mid-infrared light source, focused into an atomic gas medium. This was a joint effort with Louis DiMauro's experimental group at Brookhaven National Laboratory and in collaboration with Ken Schafer from Louisiana State University and Mette Gaarde from Lund University on the theoretical part. High order harmonic generation (HHG) in nobel gas media using short-pulse visible and near infrared lasers has become an established method for producing coherent, short pulse radiation at wavelengths from the ultraviolet to soft x-rays. We recently proposed that this approach could lead to extremely short pulses, potentially less than one fs, provided the unavoidable frequency chirp of the highest harmonics, could be removed by compressing the pulses with a grating pair. Sources of sub-fs pulses would provide unique opportunities to study dynamical processes on time scales short compared to those associated with nuclear motion. Truly stroboscopic pictures of chemical reaction dynamics would be possible, for example. In this research project we have chosen much smaller driving frequencies than used previously in HHG studies for two reasons. First, this will allow us to measure the pulse lengths of the compressed harmonics because they will be in the vacuum ultraviolet where coincidence measurements are possible. Second, the wavelengths of these harmonics will be idea for pump-probe experiments of quantum dynamical control studies. Our theoretical effort was concentrated in two areas. We used our time-dependent quantum numerical codes to evaluate the harmonic response of alkali atoms to the mid-IR laser excitation. Results were obtained for potassium, the initial species to be used in the experiments, then sodium and rubidium to investigate the possibility of higher conversion efficiencies. In fact, rubidium was found to be significantly better than potassium, both because it provided a stronger harmonic response and because the target gas could be maintained at about an order of magnitude higher pressure than with potassium. The second theoretical focus was the development of an adiabatic approximation for solving the equations governing the propagation of the generated harmonic fields through the laser-excited medium. A code was constructed using this approximation and the first phase matching calculations in this ultra-short pulse regime were carried out. The experimental effort was slowed by difficulties with the potassium source which were solved and photoelectron and harmonic spectra were obtained, the first ever at these wavelengths. These preliminary experiments were carried out using a ps laser source and an estimate of the bandwidth of the harmonics was obtained. The spectral width indicated that our prediction that the harmonic pulse lengths can be two orders of magnitude shorter than the driving field appears probable. Soon the experiments will switch to a 100 fs driver and the attempt to reach the sub-fs regime will then be possible. W e found that potassium, the target in the initial studies had a lower than expected conversion efficiency so that experiments were initiated using rubidium. This has proved to be better by more than three orders of magnitude. A large fraction of this improvement was due to the metal source running at a much higher pressure. A further increase will be obtained when the shorter pulse driver is installed. An additional paper on these preliminary results is now being prepared. The project was quite successful, although a bit behind schedule because of experimental problems. The theoretical predictions seem to have been corroborated by the measurements thus far. We also found some unexpected differences in the behavior of the different alkali atoms to mulitphoton excitation and ionization at these wavelengths.

High precision photoelectron energy and angular distributions in helium and neon atoms for a broad intensity range reflect the change in the continuum dynamics that occurs as the ionization process evolves into the pure tunneling regime. Elastic rescattering of the laser-driven free electron from its parent ion core leaves a distinct signature on the spectra, providing a direct quantitative test of the various theories of strong field multiphoton ionization. We show that it takes a relatively complete semi-classical rescattering model to accurately reproduce the observed photoelectron distributions. However, the calculated inelastic rescattering rate fails to reproduce the measured nonsequential double ionization yields.

A numerical method for solving the time-dependent Schrodinger equation for a one-electron atomic system in an intense, short-pulsed laser field is presented. An effective potential formalism is proposed and tested for representing the excitation of the valence electrons in rare gases. Results for ion production yields, photoelectron distributions and harmonic conversion are presented and compared to recent experimental results.

Recent experiments by Larsson et al. have confirmed the prediction of a high energy (∼9.5 eV) peak in the cross section for dissociative recombination of H+3. This peak is caused by four doubly excited resonance states of H3. Electron scattering calculations using the complex Kohn method provide resonance positions and widths as functions of the internuclear geometry. This information was used as input to a wave packet calculation for the dissociation dynamics on a fit to the resonant state potential energy surfaces. The resulting cross sections agree well with this experiment.

Supercomputer simulations predict the creation of an unexpectedly stable form of atomic matter when ordinary atoms are irradiated by very intense, high-frequency laser pulses. In the rising edge of a very intense pulse of ionizing radiation, the atom's wave function distorts adiabatically into a distribution with two well-separated peaks. As the intensity increases, the peak spacing increases so that the atomic electron spends more time far from the nucleus and the ionization rate decreases. This leads to the surprising and counter-intuitive result that the atom becomes more stable as the ionizing radiation gets stronger.

Recent calculations of ionization rates for H 2 + by an intense λ=228nm laser show a strong dependence of the rate constant on the internuclear distance R. We have performed comparable time-dependent calculations for H 2 + in fields I≤1×10 15W/cm2 for a wide range of fixed R (2–8au) and wavelengths (228–1064 nm). Indeed we obtain excellent agreement with the results of Chelkowski etal 1 at λ=228nm. At large R we find the ionization rate for all wavelengths rapidly approaches that of H(ls). However, at R≈2au and especially for the longer wavelength lasers, such as the λ=769nm Ti: sapphire laser, the large ionization potential (29eV) of the molecule allows it to easily survive intensities up to I=5×10 14W/cm2 for typical short pulses of, say, 150 fsec.

A surprising array of effects have been observed during high-intensity, short-pulse laser excitation of atoms and molecules. To model these measurements, methods have been developed to solve the time-dependent Schrödinger equation for an atom in a time varying, classical electromagnetic field. Studies on many atomic and molecular systems have been performed over a range of intensities from the regime within which perturbative techniques are valid up to field strengths well above an atomic unit (I > 3.51x1016 W/cm2). These calculations have provided predictions for ionization rates, photoelectron energy and angular distributions and photoemission rates. The effects of ac Stark shifted and intensity broadened intermediate states on the emission processes have been investigated. At high frequency and the highest intensities atoms are found to undergo a transition to a state or states which are surprisingly stable with respect to ionization. This had been predicted using a Floquet approach which did not allow for the time variation of the pulse envelope. The time-dependent calculations, however, show that an appreciable fraction of the electronic wave function can survive the rapid rise of an intense pulse and become stabilized with a greatly reduced ionization rate. Here we present a discussion of some of the most recent results.

For pt.I see ibid., vol.8, p.460 (1975). Cross sections for the transfer ionization process, He++Mg to He+Mg2++e, have been calculated using several different approximations for the wavefunction of the initial electronic state. The first was a frozen-orbital calculation using molecular orbitals associated with the neutral diatomic species HeMg. The second was a quasi-stabilization calculation involving configuration interaction among several frozen-orbital-type states. The final calculation used the hole-state model of Schwartz (1970) and of Bagus and Schaefer (1971). A critical analysis is made of these three methods and estimates provided for their conditions of applicability. Specifically, the results lead us to question whether the hole-state model is appropriate at all to this system.

The method of complex coordinates is a useful tool for studying many bound-free transitions. Recently the method has been used to calculate photoabsorption cross sections of one- and two-electron atoms. The authors have performed calculations on the photoabsorption of lithium and sodium by the complex-coordinate method using different pseudopotentials. The results from the different pseudopotentials are compared with other theoretical and experimental results.

A time‐dependent wavepacket approach is used to calculate quantum mechanical probabilities for reaction, dissociation, and inelastic transitions for the collinear H+H2 system. The interaction used is a realistic LEPS‐type surface. Results are reported for collision energies between 3 and 12 eV and for three different initial vibrational states of the H2. The probability of reaction is found to be very small at these energies. We find vibrational enhancement of dissociation and the inelastic transition probabilities from a vibrationally excited diatom have an oscillatory structure. We solve the time‐dependent Schrodinger equation using a newly developed predictor–corrector method.

Two model, collinear triatomic systems are investigated in which the intrafragment vibrational modes are decoupled from the interfragment bond distance in the dissociation channel. Resonances are found in both systems whose amplitudes are predominately outside the interaction region. The consequences of the existence of such resonances on reaction probabilities, dissociation rates, and absorption properties of states near the dissociation limit are discussed.

Recent experiments have demonstrated that the finite rate of vibrational relaxation in the formation of KrF affects the saturation characteristics of the KrF(B) state during extraction of laser light. We have assembled a collisional radiative model using calculated Einstein A coefficients for the lowest twenty KrF states and an approximate calculation of the rate of vibrational energy transfer between KrF and a buffer gas. The model describes the flow of excitation through the vibrational levels of KrF, and demonstrates the effects of vibrational relaxation on KrF(B) saturation and spectra. The results of these calculations agree qualitatively with the published experimental results. In addition, we find that, due to the relaxation kinetics of KrF, Kr2F, a major absorber, is not truly saturable.

A theoretical investigation has been conducted to the exothermic transfer ionization reaction, He++Mg to He+Mg2++e-. The mechanisms assumed is autoionization of the diatomic ion HeMg+. To compute the potential energy curves and autoionization width descriptive of this process, Hartree-Fock single-configuration electronic wave-functions have been constructed for the initial discrete state, He+-Mg, and for the final continuum state, He-Mg+2-e-. As the internuclear separation varies from 3 to 5 bohr, the lifetime for autoionization grows from 8.75*10-14 to 3.2*10-13 s. The cross section for transfer ionization has been computed according to Miller's classical trajectory theory of Penning ionization. This cross section reaches a maximum value of 12.9 a02 for a collision energy equal to 1 hartree. Because of the inadequacy of our approximate potential energy function for the initial state, the theoretical cross section the authors have computed here is believed to be unreliable for energies less than this value.

Accurate calculations of several electronically excited states of H3 which are important in dissociative recombination of H3 + are reported. These surfaces allow discussion of the dissociation products. For electron energies above 1 eV the dominant product is expected to be vibrationally excited H2 (X1 Sigma g +)+H(2s or 2p). The threshold for directly producing H- from ground state H3 + is predicted to be 5.8 eV.

We present a method for calculating Franck–Condon factors for the photodissociation of triatomic molecules. We use the R‐matrix propagation techniques developed by Light and Walker for reactive scattering processes. The method is used to study the collinear dissociation of a model CO2 system. Franck–Condon overlaps are calculated for three different initial states and probabilities for populating particular vibrational levels of the CO fragments are obtained. We present results for a range of photon energies. We find that the partial cross sections exhibit a series of resonant or Fano line shapes. The structure in the cross sections depends sensitively on the initial vibrational state, but the peak values are not significantly effected.

A collinear, symmetric reactive scattering system which exhibits a highly oscillatory reaction probability as a function of collision energy has been studied. The A+BA model consists of two coupled Morse oscillators. The peaks in the reaction probability are due to resonances which have been analyzed using local and hyperspherical mode bound state expansions. In a small range of collision energy, resonances are found some of which are local and some hyperspherical in character. Resonance energies calculated using bound state techniques are compared to those from exact quantum mechanical scattering calculations.

The predissociation of H3 Rydberg states by the two lowest electronic states of H3 is studied using time‐dependent wave packet techniques. The final vibrational state distribution function and branching ratios between two‐ and three‐body channels are calculated within a two‐dimensional approximation. The effect of initial vibrational excitation on these distributions is studied, and comparison is made to recent experiments.

We compare the results of a classical model for the laser enhancement of the H+LiF→Li+HF reaction to accurate quantum mechanical results. Structure in the reaction probability as a function of collision energy below the fieldfree threshold predicted classically by Orel and Miller is found to be less pronounced in the quantum results. A much better understanding of the various causes of the observed maxima and also of the reliability of this classical model are obtained as a result of these calculations. A fundamental inconsistency in the classical model introduced when the Langer modification is made which can lead to unphysical results is discussed and a procedure for correcting this inconsistency is presented. Improved results are obtained.

Faulkner and Richardson’s approach for evaluating multi‐dimensional Franck‐condon and Herzberg‐Teller integrals is used to calculate Franck‐condon factors for polyatomic molecules and generalized to include transitions from excited states to excited states. (AIP)

Collinar model systems are described for reactions in a Stong laser field. H+H2 reaction and Li+FH reaction are discussed. The reaction probability is calculated in both cases. (AIP)