Two-state curve crossing processes involving rotational coupling in the Na 2 + molecular ion

We examine the relative utility of the Landau-Zener, phase integral, and semiclassical Magnus approximations for processes involving a real crossing of two potential curves. As an example we consider rotational coupling in Na ₂ ⁺ . Numerical calculations for the ¦3p〉→¦3s〉 quenching process and for ¦3p〉→¦3d〉 excitation agree well with recent experiments in the energy range 20 eV≦E_K≦50 eV. Simple expressions forS-matrix elements, differential and total cross sections in these approximations depend only on accurate evaluation of a few JWKB phases. For the total cross section further simplification of the Magnus results yields a useful semiempirical formula.     

Dynamical tunneling through a chaotic region

It is shown that a non-vibrating diatomic molecule (i.e. a rigid rotor) in the presence of a strong laser field changes its hindered rotational motion (which on the average is in resonance with the oscillating time dependent field) from anti-clockwise to clockwise (hindered) rotational motion. This transition is classically forbidden and is another example of a quantum mechanical tunneling phenomenon occurring due to the time-reversal symmetry of the Hamiltonian. Classically, the two stable rotational modes are separated by an extended chaotic region in phase space. The Husimi representation of the quasienergy states of the time-periodic quantum system enables us to localize wave packets inside the classical stability islands. The effect of the field and the molecular parameters on the perioid of this oscillation is obtained from the quasienergy splittings without the need to carry out long time dependent computations. An analytical analysis of the dynamical tunneling using an extended version of the (t,t) formalism recently developed (J. Chem. Phys.99, 4590 (1993)) is in remarkable agreement with the numerical results.Member of the Minerva center of non-linear physics of complex systems at the Technion     

Rotational-vibrational rainbows in impulsive electron — diatomic molecule collisions: I. state-to-state transitions

Collisional induced combined rotational-vibrational excitation of diatomic molecules is discussed in a simple quantum mechanical spectator model with applications to electron-molecule collisions at intermediate collision energies (≈ 10² eV) within the rigid rotor/harmonic oscillator approximation. Quantum mechanical transition probabilities of the rotational-vibrational excitation, which show typical vibrational and rotational rainbow patterns, are calculated and compared with the structure of classical rainbow singularities.