Theory of Resonnances: Modeling Quantum Resonnances
Dynamics of Interacting Resonnances
The fast development of energy- and time-resolved experiments favours approaches which keep the variables energy and time on an equal footing. This is why the simultaneous investigation of line profiles and of the dynamics is our main objective. We employ the wave operator approach of quantum dynamics [Ph. Durand, I. Paidarová, Phys. Rev. 58 (1998) 1867] which focuses on the relevant quasi-bound states or resonances taking part in the dynamics. These quasi-bound states, localized on atoms and molecules, are described by atomic and molecular orbitals as if they were true bound states. An important characteristic of our approach is that it fully exploits the properties of analytic functions and especially analytic continuation. The applications underline the relevance of investigating simultaneously spectroscopy (line profiles) and the dynamics (transitions probabilities) by means of effective Hamiltonians which are derived from model Hamiltonians describing several resonances interacting with several continua. These effective Hamiltonians are especially relevant for describing and understanding the physics near the energy thresholds of the decaying channels. The theory is applied to the determination of line profiles in spectroscopy: Fano profiles, q-reversal effect, giant resonances...
Collision theory is reformulated in the framework of the wave operator theory of quantum dynamics which, from the beginning, focuses on the resonances. In contrast with the Moeller wave operators, our wave operators establish a one-to-one correspondence between a small number of resonances i and the same number of exact Gamow-like states projected in the space of the resonances. Instead of solving the Schroedinger equation along the real-energy axis, the resolvent becomes the basic ingredient of the theory. Since this latter is the Laplace transform of the evolution operator, the theory is able to investigate simultaneously the cross sections as well as the dynamics of the resonances.
Ph. Durand, University Pauls Sabatier, IRSAMC, Toulouse