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Notes: The coupling of a Rydberg electron to the vibrational motion is discussed in the intermediate regime in which the orbital period is long on the scale of the vibrational motion but is still considerably faster than the rotation of the core. Two dimensionless variables characterize the dynamics: the ratio of time scales and the action exchanged between the electron and the core, per one revolution. The classical dynamics are reduced to a map which provides a realistic approximation in the limit when the action exchanged is larger than (h-dash-bar). There are two distinguishable time regimes, that of prompt processes where the corresponding spectrum is so broad that individual Rydberg states cannot be resolved and a much slower process, where the electron revolves many times around the core before it ionizes. The overall spectrum is that of a Rydberg series, where the lines are broadened by (the delayed) vibrational autoionization superimposed on a broad background. The semiclassical dynamics is quantitatively more accurate in the typical situation when the action exchanged is comparable or smaller than (h-dash-bar). Explicit analytical expressions are obtained for the width for vibrational autoionization including for the case when resonances are possible. The presence of resonances is evident in Rydberg lines which are broader. For low Rydberg states the present approach recovers the Herzberg–Jungen approximation in the weak coupling limit. © 1996 American Institute of Physics.

Notes: The effect of an electrical field on the dynamics and decay kinetics of a high Rydberg electron coupled to a core is discussed with special reference to simulations using classical dynamics and to experiment. The emphasis is on the evolution of the system within the range of Rydberg states that can be detected by delayed pulsed ionization spectroscopy (which is n(approximately-greater-than)90 for both the experiment and the computations). The Hamiltonian used in the computations is that of a diatomic ionic core about which the electron revolves. The primary coupling is due to the anisotropic part of the potential which can induce energy and angular momentum exchange between the orbital motion of the electron and the rotation of the ion. The role of the field is to modulate this coupling due to the oscillation of the orbital angular momentum l of the electron. In the region of interest, this oscillation reduces the frequency with which the electron gets near to the core and thereby slows down the decay caused by the coupling to the core. In the kinetic decay curves this is seen as a stretching of the time axis. For lower Rydberg states, where the oscillation of l is slower, the precession of the orbit, due to the central but not Coulombic part of the potential of the core, prevents the oscillation of l and the decay is not slowed down. Examination of individual trajectories demonstrates that the stretching of the time axis due to the oscillatory motion of the electron angular momentum in the presence of the field is as expected on the basis of theoretical considerations.The relation of this time stretch to the concept of the dilution effect is discussed, with special reference to the coherence width of our laser and to other details of the excitation process. A limit on the principal quantum number below which the time stretch effect will be absent is demonstrated by the computations. The trajectories show both up and down processes in which the electron escapes from the detection window by either a gain or a loss of enough energy. Either process occurs in a diffusive like fashion of many smaller steps, except for a fraction of trajectories where prompt ionization occurs. The results for ensembles of trajectories are examined in terms of the decay kinetics. It is found that after a short induction period, which can be identified with the sampling time of the available phase space, the kinetics of the decay depend only on the initial energy of the electron and on the magnitude of the field, but not on the other details of the excitation process. The computed kinetics of the up and down channels are shown to represent competing decay modes. A possible intramolecular mechanism for long time stability based on the sojourn in intermediate Rydberg states is discussed. The available experimental evidence does not suffice to rule out nor to substantiate this mechanism, and additional tests are proposed. The theoretical expectations are discussed in relation to observed time resolved decay kinetics of high Rydberg states of BBC (bisbenzenechromium) and of DABCO (1,4-diazabicyclo[2.2.2]octane).The experimental setup allows for the imposition of a weak (0.1–1.5 V/cm) electrical field in the excitation region. The role of the amplitude of the time delayed field, used to detect the surviving Rydberg states by ionization, is also examined. The observed decay kinetics are as previously reported for cold aromatic molecules: Most of the decay is on the sub-μs time scale with a minor (∼10%) longer time component. The decay rate of the faster component increases with the magnitude of the field. Many features in such an experiment, including the absolute time scales, are similar to those found in the classical trajectory computations, suggesting that the Hamiltonian used correctly describes the physics of the faster decay kinetics of the high Rydberg states. © 1995 American Institute of Physics.

Notes: A three dimensional model Hamiltonian is used to mimic and interpret the results of full molecular dynamics simulations of an ion-molecule activationless recombination process in a solvent of structureless atoms. By making an adiabatic separation of variables it is shown that the gas phase capture model, suitably modified to incorporate the dynamical role of the solvent motion, can be used also in solution. Specifically, a motion along one uncoupled coordinate describes the capture process. The angular momentum for this coordinate is constant during the approach motion and thereby it provides a suitable criterion for capture. The motion of the approaching reactants is shown to be in the strong coupling adiabatic limit. In this limit there is a combination of two effects: A weak ion-molecule attractive interaction at large separations and a substantial solvation of the ion by the liquid. Thus the solvent is able to follow the motion along the reaction coordinate and to take part in the crossing of the centrifugal barrier. A second implication of the model is the efficient deactivation of the ion pair as a result of nonadiabatic V-T transitions. These transitions are confined to the ion-pair polarization well region, i.e., to the left of the adiabatic region of the centrifugal barrier. If a "solvent-separated'' ion pair is formed the recombination process is delayed and the reorganization of the solvent is required to facilitate a successful capture. To model this effect a nonlinear, space dependent, coupling term is used in the model Hamiltonian. Comparison is made throughout between the results of full molecular dynamics simulations, computational results for the model Hamiltonian, and the predications of the adiabatic separation. The role of strong solvation in activationless recombination reactions is discussed in terms of the adiabatic separation and its breakdown. The conclusions are compared, and contrasted, with the case of activated bimolecular reactions.

Notes: We discuss the spectrum of very high Rydberg states as detected via ionization in weak external electric fields. For the conditions of interest, namely, states just below the ionization continuum and weak fields, the classical barrier to dissociation is extremely far out from the core. About the saddle point the potential is very shallow. It is concluded that ionization by tunneling is far too slow. Only electrons whose energy is above the classical barrier can be detected via ionization. However, not all electrons which energetically can ionize will necessarily do so. Electrons may fail to ionize if the fraction of their energy which is in the direction perpendicular to the field is high. The computed fraction of electrons which fails to ionize does depend, in a sensitive way, on the diabatic vs adiabatic switching on of the external field. More experiments and theoretical work is needed on this point. A classical procedure based on the adiabatic invariance of the volume in phase space is developed for the computation of the fraction of electrons that can surmount the classical barrier for a given field. Analytically exact results are obtained for adiabatic switching and for the sudden limit where the rise time of the field is shorter than the period of the orbit. For the case of diabatic switching (which is appropriate for very high n values), the exact classical computations on the yield of ionization show that the onset of ionization is at an energy of 4.25 F1/2 cm−1 below the ionization potential and the 50% point it as 3.7 F1/2 cm−1 for a field F in V/cm.

Notes: The onset of a shattering regime when a supersonic cluster undergoes an ultrafast heating by its impact at a surface, proposed on the basis of an information theoretic analysis, has now been demonstrated experimentally for molecular clusters. It is emphasized that the sudden onset of shattering as a function of impact velocity is a robust result depending essentially only on the multitude of possible isomers of larger clusters. There is one underlying assumption of the information theoretic approach—namely that there is a rather rapid thermalization of the translational degrees of freedom of the impact heated cluster so that mean energy is the only energetic constraint. When this is not necessarily the case, e.g., for ionic clusters at lower energies, there will not be extensive fragmentation. © 1996 American Institute of Physics.

Notes: The problem of zero point energy in classical trajectory computations is discussed and illustrated by an example of dissociation where the zero point energy is used to provide the required energy. This is not possible in quantal dynamics. A proposed route to the alleviation of the problem, based on using classical-like trajectories which mimic the solution of the (expectation values) of Heisenberg equations of motion, is discussed. In general, one cannot simultaneously correct for all possible expectation values, so the remedy is at best partial. The variable whose expectation value and variance is to be handled correctly is examined in detail for a one-dimensional anharmonic potential, and is identified with the logarithmic derivative of the wave function in the Wentzel–Kramers–Brillouin (WKB) approximation. The multidimensional case is also discussed and it is pointed out that the zero point energy problem can be particularly severe for systems which exhibit a locally unstable classical motion. © 1996 American Institute of Physics.