Oscillatory fine structure

Electronic spectra are almost always treated within the framework of the Bom-Oppenlieimer approxunation [8] which states that the total wavefiinction of a molecule can be expressed as a product of electronic, vibrational, and rotational wavefiinctions (plus, of course, the translation of the centre of mass which can always be treated separately from the internal coordinates). The physical reason for the separation is that the nuclei are much heavier than the electrons and move much more slowly, so the electron cloud nonnally follows the instantaneous position of the nuclei quite well. The integral of equation (BE 1.1) is over all internal coordinates, both electronic and nuclear. Integration over the rotational wavefiinctions gives rotational selection rules which detemiine the fine structure and band shapes of electronic transitions in gaseous molecules. Rotational selection rules will be discussed below. For molecules in condensed phases the rotational motion is suppressed and replaced by oscillatory and diflfiisional motions. 

The X-ray absorption fine structure (XAFS) acronym refers to the oscillatory structure observed in the absorption coefficient just above... 

Molecular spectra consist of numerous densely grouped lines. These are called band spectra because they appear as luminous bands. The fine structure can only be observed with high-resolution instruments. Molecular spectra of excited molecules are related to the energy states of a molecule rotating around the principal axes of inertia. Band spectra in the near-infrared are produced by energy transitions related to oscillatory vibrations of individual molecules. 

A stringent test for PSANB-ADF-NVG is the direct comparison of the wavepackets up to the quantum phase. Figure 6.19 shows the comparison of the real parts of XK R,t) and (px R, t) in the case of vibrational decay. For the collision dynamics, the similar comparison is displayed in Fig. 6.20. The agreement up to the fine oscillatory structures is quite good. We may rather conclude that the agreement is excellent for this lowest level approximation in construction of the PSANB-ADF-NVG wavefunctions. 

In both real-time spectra a fine oscillatory structure with an oscillation period Ta,620 312 fs for 620 nm and Ta,642 297 fs 642 nm, dominates the real-time evolution of the ion signal. For the shorter wavelength the first maximum of the ion signal appears after a delay time between the pump and probe pulses ofzlt4> 620 315 fs, which is nearly equal to the measured oscillation with Ta,620 312 fs, and the respective time for 642 nm is 160 fs,... 

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