Classical line shapes based on analytical solutions of bimolecular trajectories in collision induced emission. II. Reactive collisions

The classical theory of collision induced emission (CIE) from pairs of dissimilar rare gas atoms was developed in Paper I [D. Reguera and G. Birnbaum, J. Chem. Phys. 125, 184304 (2006)] from a knowledge of the straight line collision trajectory and the assumption that the magnitude of the dipole could be represented by an exponential function of the inter-nuclear distance. This theory is extended here to deal with other functional forms of the induced dipole as revealed by ab initio calculations. Accurate analytical expression for the CIE can be obtained by least square fitting of the ab initio values of the dipole as a function of inter-atomic separation using a sum of exponentials and then proceeding as in Paper I. However, we also show how the multi-exponential fit can be replaced by a simpler fit using only two analytic functions. Our analysis is applied to the polar molecules HF and HBr. Unlike the rare gas atoms considered previously, these atomic pairs form stable bound diatomic molecules. We show that, interestingly, the spectra of these reactive molecules are characterized by the presence of multiple peaks. We also discuss the CIE arising from half collisions in excited electronic states, which in principle could be probed in photo-dissociation experiments.

Evanescent field of vectorial highly non-paraxial beams

In terms of the Fourier spectrum, a simple but general analytical expression is given for the evanescent field associated to a certain kind of non-paraxial exact solutions of the Maxwell equations. This expression enables one to compare the relative weight of the evanescent wave with regard to the propagating field. In addition, in those cases in which the evanescent term is significant, the magnitude of the field components across the transverse profile (including the evanescent features) can be determined. These results are applied to some illustrative examples.

Highly eccentric hip-hop solutions of the 2N

We show the existence of families of hip-hop solutions in the equal-mass 2N-body problem which are close to highly eccentric planar elliptic homographic motions of 2N bodies plus small perpendicular non-harmonic oscillations. By introducing a parameter ϵ, the homographic motion and the small amplitude oscillations can be uncoupled into a purely Keplerian homographic motion of fixed period and a vertical oscillation described by a Hill type equation. Small changes in the eccentricity induce large variations in the period of the perpendicular oscillation and give rise, via a Bolzano argument, to resonant periodic solutions of the uncoupled system in a rotating frame. For small ϵ ≠ 0, the topological transversality persists and Brouwer's fixed point theorem shows the existence of this kind of solutions in the full system