Spontaneous Raman and fluorescence lineshapes

SOLVATION EFFECTS IN FOUR-WAVE MIXING AND SPONTANEOUS RAMAN AND FLUORESCENCE LINESHAPES OF POLYATOMIC MOLECULES... 

V. Correlation Functions for Spontaneous Raman and Fluorescence Lineshapes... 

V. CORRELATION FUNCTIONS FOR SPONTANEOUS RAMAN AND FLUORESCENCE LINESHAPES... 

We next turn to the spontaneous Raman and fluorescence lineshapes. In an SRF experiment, we have a single incident classical field (a ) and a single scattered mode (a>2). We shall use the Hamiltonian [Eq. (2)] with the only difference that the sum in Eq. (4) runs over j = 1,2, with El being the classical incident field and 2 being the scattered field, which will be treated quantum mechanically. In an SRF experiment, we monitor the scattered field with both time and frequency resolution. The operator representing the rate of emission of co2 photons is... 

S. Mukamel, Solvatation effects in four-wave mixing and spontaneous Raman and fluorescence lineshapes of polyatomic molecules, Adv. Chem. Phys. 70 165 (1988). 

In the previous sections, we derived general correlation function expressions for the nonlinear response function that allow us to calculate any 4WM process. The final results were recast as a product of Liouville space operators [Eqs. (49) and (53)], or in terms of the four-time correlation function of the dipole operator [Eq. (57)]. We then developed the factorization approximation [Eqs. (60) and (63)], which simplifies these expressions considerably. In this section, we shall consider the problem of spontaneous Raman and fluorescence spectroscopy. General formal expressions analogous to those obtained for 4WM will be derived. This will enable us to treat both experiments in a similar fashion and compare their information content. We shall start with the ordinary absorption lineshape. Consider our system interacting with a stationary monochromatic electromagnetic field with frequency w. The total initial density matrix is given by... 

In conclusion, in this section we presented the formal expressions for the absorption lineshape [Eq. (70)] and for spontaneous Raman and fluorescence spectroscopy. For the latter, we derived Liouville space expressions in the time and the frequency domain [Eqs. (74) and (75)], an ordinary correlation function expression [Eq. (76)], and, finally, the factorization approximation resulted in Eqs. (77) and (78). The factorization approximation is expected to hold in many cases for steady-state experiments and for time-resolved experiments with low temporal resolution. It is possible to observe a time-dependent shift of spontaneous emission lineshapes using picosecond excitation and detection [66-68]. This shift arises from the reorganization process of the solvent and also from vibrational relaxation that occurs during the t2 time interval. A proper treatment of these effects requires going beyond the... 

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