Continuum wavefunction, wavepacket

We show how one can image the amplitude and phase of bound, quasibound and continuum wavefunctions, using time-resolved and frequency-resolved fluorescence. The case of unpolarized rotating molecules is considered. Explicit formulae for the extraction of the angular and radial dependence of the excited-state wavepackets are developed. The procedure is demonstrated in Na2 for excited-state wavepackets created by ultra-short pulse excitations. 

The time-dependent formalism would be rather limited if it yielded only the total cross section. However, that is not the case all partial photodissociation cross sections a(Ef,n) can be also extracted from the time-dependent wavepacket. We assume that for large times the wavepacket has completely left the interaction zone and moves entirely in the asymptotic region where the interaction potential Vi(R,r) is zero. Then, the asymptotic conditions (2.59) for the stationary continuum wavefunctions can be inserted into (4.3) yielding... 

To understand the development or the absence of reflection structures one must imagine — in two dimensions — how the continuum wavefunction for a particular energy E overlaps the various ground-state wave-functions and how the overlap changes with E. This is not an easy task Figure 9.9 shows two examples of continuum wavefunctions for H2O. Alternatively, one must imagine how the time-dependent wavepacket, starting from an excited vibrational state, evolves on the upper-state PES and what kind of structures the autocorrelation function develops as the wavepacket slides down the potential slope. 

Figure 3.11 Potential energy curves for the ls

In a time-dependent picture, resonances can be viewed as localized wavepackets composed of a superposition of continuum wavefunctions, which qualitatively resemble bound states for a period of time. The unimolecular reactant in a resonance state moves within the potential energy well for a considerable period of time, leaving it only when a fairly long time interval i has elapsed x may be called the lifetime of the almost stationary resonance state. 

B state, and 1.8-2.5 A for the C state. In these ranges, electronic transition takes place as though it makes a copy of vibrational wavefunction in the common regions between the relevant electronic states. This is a reflection of the Condon principle. We note that there is counter-intuitive decrease of population in the potential well of the X state when omitting ionization, especially in the panels for Pulse 2 and Pulse 6, indicating there is some deexcitation from the excited electronic states via Rabi-oscillation like coupling with the ion continuum. Thus, complicated transfer, overlapping, and dispersion of the vibrational wavepackets proceed in each electronic state in a stepwise manner. Very fine information in the attosecond time scale is thus folded in the complicated structures and phases of the set of vibrational wavepackets [305]. 

---