D Richards

Structure in low frequency microwave ionisation excited hydrogen atoms

The authors present experimental results for the ionisation of excited hydrogen atoms, with initial principal quantum number n0 in the range 32<or=n0<or=48, by low frequency microwaves in the scaled frequency range 0.05( Omega (0.2. They compare these with results of a classical Monte Carlo calculation showing that there is structure in the experimental ionisation curves of quantal origin. A further comparison with a simple one-dimensional quantal theory, using an adiabatic basis, shows that the observed structure can be explained in terms of resonances between a few adiabatic states. A very simple two-state model is shown to possess all the relevant features of the system. Further analysis of this one-dimensional model shows that when the field frequency tends to zero the static field ionisation limit is approached through infinitely many such resonances, at Omega approximately=1/p, of width O(e-p), p being a large integer.

Quasi-resonances for high-frequency perturbations

The authors study the quantum dynamics of a one-dimensional hydrogen atom perturbed by a high-frequency periodic electric field. They show that a time-dependent basis comprising states which diagonalise the compensated energy Hamiltonian provides a numerically efficient description of the wavefunction by explicitly allowing for the oscillatory motion of the bound electron due to the periodic field. They use this compensated energy representation to examine the behaviour of the system and show that for moderate strength fields which are slowly switched on and off only the relative few quasi-resonant states are significantly populated; this behaviour should be experimentally observable. They also show that a basis comprising only the few, typically between ten and twenty, compensated energy quasi-resonant states provides a remarkably good and efficient basis.

A semiclassical ionization mechanism for excited hydrogen in high-frequency fields

The authors introduce a new way of approximating transitions into the continuum for those circumstances where the bound and continuum states are coupled only through the high-lying levels. The method uses classical perturbation theory to approximate the dynamics over short times: it produces transition amplitudes agreeing with Fermis golden rule in the limit of weak fields and one-photon transitions and classical dynamics in the opposite extreme where many photons are needed to reach the continuum. They apply the theory to earlier experiments measuring ionization of a highly excited hydrogen atom by the simultaneous action of microwave and static electric fields, and show that their values for the field producing 10% ionization agree reasonably well with those of the experiment.

A study of quantum dynamics in the classically chaotic regime

The authors examine the effect of the Coulomb singularity on the classical and semiclassical dynamics of the one-dimensional model for atomic hydrogen, sometimes called the surface-state-electron model, in a periodic electric field and determine a necessary condition, in terms of the field strength, frequency and the initial quantum number, for the violation of the uncertainty principle. They show that when this violation occurs the quantal transition probabilities are significantly less than the equivalent classical probabilities. This criterion is tested numerically and shown to provide a good estimate of the boundary to one of the regions in which classical dynamics fails. The authors also show that when the uncertainty principle is not violated the fluctuations of the quantal about the classical probability spectra can be related to structure in classical phase space. These fluctuations are due to different classical and quantal transport through cantori.

Ionisation of excited one-dimensional hydrogen atoms by low-frequency fields

The author develops an approximate quantal treatment of the ionisation of an excited one-dimensional hydrogen atom by a strong periodic electric field. By representing the wavefunction in terms of an adiabatic basis, ionisation can be viewed as the escape of the electron over a moving barrier; the dominant ionisation mechanism is then excitation to states near the barrier minimum. For large quantum numbers and for low-frequency fields the equations of motion solved are essentially exact during most of the field period; but for a short time, whilst the moving barrier is near its minimum, the author introduces complex energies in order to represent loss to the continuum. The net result is to obtain the relative, but not the absolute, variation of the ionisation probabilities with system parameters reasonably accurately by numerically solving a small number of coupled equations.

M-changing collisions in atom-linear molecule collisions

Reports classical trajectory calculations showing that within the sudden approximation, for a wide range of energies and potentials typical of atom or ion-linear molecule interactions, there exists, for each scattering angle, a symmetry axis to which the angular momentum transfer is approximately perpendicular. The author finds that the direction of this axis is well approximated by the bisector of the initial and final directions of the projectile, scattered by the isotropic potential component. The existence of this symmetry axis is a consequence of the short-range forces characterising these collisions and is shown to be less pronounced as the range of the force increases. When near orbiting collisions occur then this symmetry breaks down.

ROBUST SCARRED STATES

For periodically forced systems we show that the scarred state corresponding to the unstable periodic orbit of the main resonance has a lower ionisation rate than adjacent states because a representation exists in which coupling to other states is minimal. Our results explains why this scarred state has been observed in recent experiments on the microwave ionisation of excited hydrogen atoms; other previously unexplained features are also elucidated.

Resonances in low frequency ionization by periodic electric fields

The behaviour of a one-dimensional system perturbed by a low frequency, periodic electric field is examined in the limit as the field frequency, Omega , tends to zero, that is the static field limit. In particular the authors obtain estimates of the widths of each member of the infinite set of resonances between any finite value of Omega and 0. In order to obtain this estimate they derive a new analytic approximation of the two-state equation of motion. Their analysis shows why recent experiments on the ionization of excited hydrogen atoms by low frequency fields failed to observe any resonances.

Classical theory of the static Stark effect for weak fields

The classical theory is presented for an atom with one excited electron subject to Coulomb attraction and the long-range potential of a polarisable core. The electric field must not be so strong as to mix states of different principal quantum number. The theory is an essential prerequisite for the semiclassical Stark theory of highly excited non-hydrogenic atoms and ions.

Ionization mechanisms of one-dimensional oscillators in high-frequency fields

The effect of a high-frequency field on the motion of a one-dimensional anharmonic oscillator is studied. Various types of ionization mechanism are considered in both classical and quantum dynamics and it is shown that for sufficiently high-frequency fields the classical system can ionize through regular orbits. The authors construct a general area-preserving map which approximates the dynamics and obtain an explicit quantization of this approximation in terms of the Fourier components of the classical motion. This provides a very efficient approximation to the solution of the time-dependent Schrodinger equation. The authors consider the Morse oscillator in detail, showing that the classical map agrees well with the numerical solution of Hamiltons equations. Classical and quantal ionization probabilities are compared and the authors delineate circumstances where they do and do not agree.