Field ionization classical model

The Lorentz force F = q(v x B) causes the electron to process around the magnetic field direction B, and even if the total energy of the electron lies above the field-free ionization limit, the electron cannot escape except into the direction of B. This leads to relatively long lifetimes of such autoionizing states. The corresponding classical trajectories of the electron in such states are complicated and may even be chaotic. At present, investigations in several laboratories are attempting to determine how the chaotic behavior of the classical model is related to the term structure of the quantum states [567]. The question whether quantum chaos really exists is still matter of controversy [569-572]. 

The Rydberg atom experiments described above are well adapted to the study of the atomic observables via the very sensitive field ionization method. The observation of the field itself and its fluctuations would also be very interesting. (In the Bloch vector model, the field variables are associated to the pendulum velocity whereas the atomic ones are related to its position). It has recently been shown either by full quantum mechanical calculations or by the Bloch vector semi-classical approach that if the system is initially triggered by a small external field impinging on the cavity, the fluctuations on one phase of the field become at some time smaller than in the vacuum field. This is a case of radiation "squeezing" which would be very interesting to study on Rydberg atom maser systems. 

Calculations by Gryzinski and Kowalski (1993) for inner shell ionization by positrons also confirmed the general trend. Theirs was essentially a classical formulation based upon the binary-encounter approximation and a so-called atomic free-fall model, the latter representing the internal structure of the atom. The model allowed for the change in kinetic energy experienced by the positrons and electrons during their interactions with the screened field of the nucleus. 

Depending on the shape of the envelope function g t) and the field strengths Fi and F2, the conditions (i) and (ii) may, or may not, be simultaneously fulfilled. Ionization is expected to occur only if both (i) and (ii) are fulfilled. The overlap condition depends essentially on v. Thus, as is swept from small values to large values, overlap can be achieved, and lost again, giving rise to a broad ionization structure. A first qualitative analysis of this structure has already been achieved on the basis of (i) and (ii). The decay to the continuum is approximated by an exponential decay with decay constants determined from a classical Monte Carlo calculation. The decay is assumed to start as soon as (i) and (ii) are fulfilled. On the basis of this model Haifmans et al. (1994) obtained the ionization probabilities as a function of i>i shown as the... 

Fig. 7.8 also shows the results of a classical calculation and a quantum calculation that both confirm the prediction of the giant resonance based on the simple overlap criterion discussed above. The crosses in Fig. 7.8 are the results of classical Monte Carlo calculations. They were performed by choosing 200 different initial conditions in the classical phase space at Iq = 57. The ionization probabihty in this case was defined as the excitation probability of actions beyond the cut-off action Ic = 86. This definition is motivated by experiments that, due to stray fields and the particular experimental procedures, cannot distinguish between excitation above Ic > 86 and true ionization, i.e. excitation to the field-free hydrogen continuum. The crosses in Fig. 7.8 are close to the full line and thus confirm the model prediction. The open squares are the results of quantum calculations within the one-dimensional SSE model. The computations were performed in the simplest way, i.e. no continuum was... 

One-electron atoms subjected to a time-dependent external field provide physically realistic examples of scattering systems with chaotic classical dynamics. Recent work on atoms subjected to a sinusoidal external field or to a periodic sequence of instantaneous kicks is reviewed with the aim of exposing similarities and differences to frequently studied abstract model systems. Particular attention is paid to the fractal structure of the set of trapped unstable trajectories and to the long time behavior of survival probabilities which determine the ionization rates of the atoms. Corresponding results for unperturbed two-electron atoms are discussed. 

Virtually all non-trivial collision theories are based on the impact-parameter method and on the independent-electron model, where one active electron moves under the influence of the combined field of the nuclei and the remaining electrons frozen in their initial state. Most theories additionally rely on much more serious assumptions as, e.g., adiabatic or sudden electronic transitions, perturbative or even classical projectile/electron interactions. All these assumptions are circumvented in this work by solving the time-dependent Schrodinger equation numerically exact using the atomic-orbital coupled-channel (AO) method. This non-perturbative method provides full information of the basic single-electron mechanisms such as target excitation and ionization, electron capture and projectile excitation and ionization. Since the complex populations amplitudes are available for all important states as a function of time at any given impact parameter, practically all experimentally observable quantities may be computed. 

Kinetic and equilibrium acidities of bridgehead hydrogens in fluorinated norbornanes and bicyclo[2,2,2]octanes are accommodated by a classical field effect modelled on Kirkwood-Westheimer calculations. The stability of the donor-acceptor complexes of homoconjugated dienes e.g. norbornadiene) with tetracyanoethylene increases with increasing ionization potential of the donor hydrocarbon, and the IP values also correlate with the charge-transfer excitation energies. ... 

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