We have revisited the problem of a hydrogen molecular ion in the presence of a short intense laser field. Our approach for time-propagation the initial state subject to the Schrödinger equation is similar to that presented by Kulander et al. [1]. A common simplification to the full problem is the reduction to one dimension with two degrees of freedom, one for the nuclear separation (R) and one for the electronic motion along the internuclear (z) axis, with the electric field also along this axis. The goals of the present project are: 1) to apply our method, developed for e-H collisional excitation and ionization [2], to an explicitly time-dependent problem; 2) to check different time-propagation schemes; 3) to visualize the results; 4) to extract the physics by projection techniques; and 5) to try avoiding masking potentials that reduce the norm of the wavefunction.Going beyond the Born-Oppenheimer approximation, we solve the time-dependent Schrödinger equationby time-propagating the initial statewhere G 1σg R (z) is the electronic ground state for fixed R and F The screening parameters q n = 0.03 and q e = 1.0 are used to smooth out the Coulomb singularity. The term z f(t) E 0 sin(ωt) represents the effect of the electric field with amplitude E 0 and angular frequency ω. Finally, f (t) is a smooth turn-on/turn-off function for the field.We have used intensities of 1−2×10 18 W/m 2 , turn-on/turn-off times of 2−4 periods, and ontimes up to about 20 periods. We also follow the system for several periods after the pulse is over. Typical observables to calculate are < R(t) > and < z(t) >. However, < R(t) > has limited meaning since it includes vibration, dissociation, and Coulomb explosion; the same is true for < z(t) >. Looking at the complete nuclear and electronic distributions reveals significantly more information.We therefore created movies to watch for bond-stretching and bond-healing, vibrational excitation, dissociation (electron stays with one of the protons) and ionization (electron leaves the system and protons undergo "Coulomb explosion"). Links to these movies can be found at http://bartschat.drake.edu/. We are currently working on our projection techniques to find, for example, the probability of exciting a particular vibrational and/or electronic state.

An analytic solution of the Gross-Pitaevskii equation for a rotating Bose-Einstein condensate of trapped atoms describes the onset of vorticity when the rotational speed is increased, starting with the entry of the first vortex and followed by the formation of growing symmetric Wigner molecules. It explains the staircase of angular momentum jumps and the behavior of the bosonic occupancies observed in numerical studies. The similarity of this behavior and mesoscopic superconductors is discussed.

The density matrix parametrisation of collisionally excited atomic ensembles is generalised to account for projectile and target spin polarisations. The density matrix elements, containing spin-resolved alignment and orientation parameters, can be determined by measurements of the 'generalised Stokes parameters' introduced by Andersen and Bartschat (1994) to describe scattered-projectile-polarised-photon coincidence experiments. Focusing on electron impact excitation of light alkali-type targets and mercury, the present experimental status of such experiments is reviewed, in particular with regard to the 'perfect scattering experiment' whereby all independent scattering amplitudes are determined.

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An overview is given of the present understanding of excitation in electron–atom collisions, with particular emphasis on the extent to which a "perfect scattering experiment" in the Bederson sense has been achieved. Recent experimental and theoretical results are put into a common framework, generalizing the ideas and systematics, presented in a review paper, of the case of excitation by spin-polarized electron beams. For various levels of complexity, complete sets of coherence parameters are suggested, and their relationships to generalized Stokes parameters and generalized STU parameters are pointed out.