Nonperturbative quantum and classical calculations of multiphoton vibrational excitation and dissociation of Morse molecules$^1$

The multiphoton vibrational excitation and dissociation of Morse molecules have been computed nonperturbatively using Hamilton's and Schr$\phi $dinger's time-dependent equations, for a range of laser pulse parameters. The time-dependent Schr$\phi $dinger equation is solved by the state-specific expansion approach [e.g.,1]. For its solution, emphasis has been given on the inclusion of the continuous spectrum, whose contribution to the multiphoton probabilities for resonance excitation to a number of excited discrete states as well as to dissociation has been examined as a function of laser intensity, frequency and pulse duration. An analysis of possible quantal-classical correspondences for this system is being carried out. We note that distinct features exist from previous classical calculations [2]. For example, the dependence on the laser frequency gives rise to an asymmetry around the red-shifted frequency corresponding to the maximum probability. [1] Th. Mercouris, I. D. Petsalakis and C. A. Nicolaides, J. Phys. B\textbf{ 27}, L519 (1994). [2] V. Constantoudis and C. A. Nicolaides, Phys. Rev. E \textbf{64}, 562112 (2001). \newline $^1$This work was supported by the program 'Pythagoras' which is co - funded by the European Social Fund (75\%) and Natl. Resources (25\%). \newline $^2$Physics Department, National Technical University, Athens, Greece.\newline $^3$Theoretical and Physical Chemistry Institute, Hellenic Research Foundation, Athens, Greece.