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In this paper we show how it is possible to investigate the nuclei dynamics of a D2+ molecular ion by using the high harmonic generation spectra emitted by the system when subjected to an intense laser field. In particular, the emitted spectra contains, in addition to the usual odd harmonic peaks, additional satellite peaks whose frequency spacing is equal to the vibrational frequency of the nuclei.

An iterative method to obtain a solution of the differential equation $$i\dot a = \hat H(t)a$$ , with Ĥ a 3×3 Hermitian matrix anda the unknown vector, is proposed. The procedure is particularly suitable for computer implementation and, as an example, has been applied to find the excitation probability of a three-level atom after the synchronous passage of two laser pulses each almost resonant with a pair of atomic levels.

When an electron scatters from an atom in the presence of a laser field which is resonant with an atomic transition, off-shell effects enter into the cross section. These only become significant at higher laser intensities where the atom may also be ionised by the laser. Cross-sections are obtained for electron-atom scattering in which these off-shell effects appear and in which the slow ionisation of the atom by the laser is included. Experiments are suggested in which simplifications can occur and which still retain these 'exotic' effects.

Previous results for the shift of the ionisation potential of an atom in a laser field are used to investigate the kinematics of multiphoton ionisation in either a laser beam or a laser pulse. Previous results for a laser beam show essentially no shifts of the 'above-threshold ionisation' peaks in the electron energy distribution and only small widths. Results for a laser pulse show the possibility of large shifts and widths growing as the pulse becomes shorter. Electrons which absorb a larger number of photons are predicted to show less shifted and narrower peaks.

An iterative analytic method for finding an exact solution of the differential equation $$i\dot a = \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{M} (t)a$$ , where $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{M} (t)$$ is a 2×2 hermitian matrix, is proposed. This method is used to solve the model problem of a two-state atom interacting with an oscillating field. The obtained results are compared with those obtained in the so-called rotating-wave approximation showing the limits of this approximate theory.

Total capture cross-sections into ground and excited hydrogen states by protons colliding with alkali atoms are reported. By means of simple models the capture of both valence and core electrons is considered. The whole capture process is viewed as one in which the greatest contribution to the total cross-section is given by electrons having orbital velocities approximately matching the projectile relative velocity. Hence, by increasing the projectile relative velocity, the more external electrons are switched off and the more tightly bound ones switched on. The OBK approximation is used and the alkali atom is treated in a one-electron picture. While the agreement with the experiment is good as to the general trend of the total cross-section, quantitative agreement is not satisfactory with the important exception of electron capture from lithium. As the results are found to be quite sensitive to the core electron binding energies, which are only approximately known, the source of the disagreement cannot be traced only to the inadequacy of the adopted scattering model. Before new more sophisticated calculations are started, accurate core electron binding energies must be known. In virtue of the good results for H+-Li collisions, the calculations are extended to D+-Li collision also. The treatment of the core electron capture given for proton-alkali atom collisions is expected to be qually suitable for any kind of many-electron target atoms.

Calculations of the triple differential cross section (TDCS) of the laser-assisted Compton effect in hydrogen-like atoms are reported. The theoretical model is a generalisation of the field-free exact treatment given years ago by Eisenberger and Platzman (1970), without resorting to the impulse approximation. The laser field is taken in the dipole approximation, homogeneous and single mode. The incident and the outgoing X-ray photon energy are taken to be 20 and 19.95 keV, respectively, and the X-ray photon scattering angle is taken as 5 degrees . The laser electric field is considered to be much smaller than the characteristic intra-atomic field, while the laser frequency is off-resonant with any pair of levels of the target atom. Significant changes in the shape of the TDCS are found when laser photons are exchanged. The origin of the modifications to the TDCs is discussed in detail. The considerations given here for modifications of the Compton electron angular distribution also largely hold true for other laser-assisted processes, such as, for instance, the X-ray photoeffect and electron-atom ionisation.

High-energy proton-alkali atom charge exchange is treated in the eikonal approximation within the framework of the well-known time-dependent semi-classical impact parameter method. Detailed calculations are specialized to the proton-lithium atom charge exchange for which the total cross-section is obtained in closed form.

An eikonal treatment is given for charged-particle potential scattering in the presence of a laser radiation field for the case in which the collision time is much smaller than the radiation field period. It is shown that the presence of the field adds a new phase shift to the field-free eikonal phase shift. Different expressions are derived for the transition probability to obtain i) after the proper limiting passages both the field-free eikonal and FBA results, and ii) laser field-dependent corrections to them. An alternative derivation of the transition probability is also given, based on a treatment due to Henneberger and Shatas, emphasizing that the present quasi-static approximation, along with similar treatments available in the literature, implies two distinct time scales: that of the variation of the radiation field and that of the transition of the quantum system involved in the scattering process. With respect to the first time scale, the collision event is assumed to take place instantaneously; on the contrary, the average collision time is taken to be sufficiently large to neglect the effect of the switching-on of the interaction. The proper limiting passages and substitutions are stated to obtain from a well-know low-frequency result one of the main results derived within the quasi-static approximation.

On the basis of simple considerations on the properties of the unitary transformations, it is shown that the correct use of the space translation method in laser-assisted X-ray photoeffect gives essentially the same results as the more conventional treatments.

The eikonal-approximation treatment, developed previously within the framework of the time-dependent impact parameter method for high-energy proton-alkali atom charge transfer, is applied to calculate total cross-sections of valence electron capture into the hydrogen atom ground state from the whole series of the alkali atoms. The latter are treated as one-electron model atoms hy means of very simple model potentials and wave functions. The calculated crosssections are compared with the corresponding quantities calculated in the OBK and first Born approximations. The eikonal results are found to be lower than OBK and FBA results. The similar total cross-section of charge transfer in proton-hydrogen collisions is also calculated as a test of the theory. The resulting hydrogen cross-section is slightly above the measured cross-section. For the hydrogen case a disagreement is found with the calculation by Dewangan within the same eikonal treatment.

The dynamics of a homonuclear diatomic molecule driven by a laser pulse is obtained beyond the fixed nuclei approximation. Laser parameters can be adjusted to confine the electron over one of the two nuclei for a relatively long time or not. A time-resolved analysis of the electromagnetic spectrum emitted by the molecule presents the usual odd harmonics far from confinement and even harmonics during the confinement periods. A physical interpretation of the results is given.

The COS-B satellite has observed the X-ray source Cen X-3 in the energy range 2 to 12 keV

Calculations are reported of the differential cross section of the laser-assisted X-ray photoeffect from K shells showing that drastic changes occur in the shape of the ejected-electron angular distribution when laser photons are exchanged during the ionisation. This process appears well suited to the study of laser effects and multiphoton exchanges in laser-assisted atomic collisions.