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Laser snapshots of molecular motions  11



                                 recorded as a function of pump-probe time delay: the decrease in signal
                                 intensity with increasing pump-probe time delay monitors the loss of
                                 initial IBr* to form separated I and Br over the potential V ; and the oscil-
                                                                                 1
                                 lations superimposed upon the decay reflect the quantized nature of vibra-
                                 tional motion of the quasi-bound [I . . . Br] molecules at intermediate
                                 configurations within the bound V curve.
                                                              1
                                    A series of measurements in which the pump wavelength is varied
                                 reveal that at some energies the oscillations predominate for times beyond
                                 10ps, whilst at others the decay of population by curve-crossing wins out
                                 within 400fs or so. The time resolution of the experiment is in this
                                 example is determined by the convolution of the two laser pulse widths,
                                 here about 125fs.
                                    These attributes can be accounted for by theoretical calculations of the
                                 motion of the wavepacket over the repulsive potential, which aim to deter-
                                 mine the time-resolved ionisation signal from fundamental theory. These
                                 are performed by solving the time-dependent Schrödinger equation for the
                                 dissociation, which expresses the temporal development of the quantum
                                 wavefunction prepared by the laser pulse subject to all the forces that act
                                 on the nuclei as it progresses from starting to final states. Figure 1.4(c) dis-
                                 plays a calculated pump-probe ionisation trace that corresponds to the
                                 same initial conditions of Figure 1.4(b). A mathematical analysis of these
                                 data using the technique of Fourier transformation reveals how quantised
                                 vibrational motion of the molecule along the dissociation coordinate is
                                 transformed into kinetic energy of separation as the I and Br atoms fly
                                 apart.

                                 1.4.2 Ultrafast molecular collisions
                                 Unfortunately, femtosecond laser pulses are not so readily predisposed to
                                 study collisions between atoms and molecules by the pump-probe
                                 approach. The reason is that, typically, the time between collisions in the
                                 gas phase is on the order of nanoseconds. So, with laser pulses of sub-100fs
                                 duration, there is only about one chance in ten thousand of an ultrashort
                                 laser pulse interacting with the colliding molecules at the instant when the
                                 transfer of atoms is taking place; in other words, it is not possible to
                                 perform an accurate determination of the zero of time.
                                    An ingeneous method to circumvent this problem was first devised by
                                 Zewail and colleagues, who took advantage of the vibrational and rota-
                                 tional cooling properties and collision-free conditions of the supersonic
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