Absorption lineshape scattering

The model (9.73)—(9.75) was presented as an initial value problem We were interested in the rate at which a system in state 0) decays into the continua L and R and have used the steady-state analysis as a trick. The same approach can be more directly applied to genuine steady state processes such as energy resolved (also referred to as continuous wave ) absorption and scattering. Consider, for example, the absorption lineshape problem defined by Fig. 9.4. We may identify state 0) as the photon-dressed ground state, state 1) as a zero-photon excited state and the continua R and L with the radiative and nonradiative decay channels, respectively. The interactions Fyo and correspond to radiative (e.g. dipole) coupling elements between the zero photon excited state 11 and the ground state (or other lower molecular states) dressed by one photon. The radiative quantum yield is given by the flux ratio Yr = Jq r/(Jq r Jq l) = Tis/(Fijj -F F1/,). 

Note that in such spectroscopic or scattering processes the pumping state 0) represents a particular state of energy Eq out of a continuous manifold. In most cases this state belongs to one of the manifolds R and L. For example, in the absorption lineshape problem this photon-dressed ground state is one particular state of the radiative (R) continuum of such states. 

In the case of resonance absorption of synchrotron radiation by an Fe nucleus in a polycrystalline sample, the frequency dependence of the electric field of the forward scattered radiation, R(oj), takes a Lorentzian lineshape. In order to gain information about the time dependence of the transmitted radiation, the expression for R(oj) has to be Fourier-transformed into R(t) [6]. 

The B-term, which contributes when I > I3, describes interference between the probe and pump beams which sets up an oscillation in the populations pn(o) -a)) and pzaCm -o)) this causes coherent scattering of the pump beam at w which can interfere with the probe and affect its absorption. Thus, the lineshape contains two contributions, a Lorentzian curve of FWHM == 2f and depth another Lorentzian... 

As earlier lectures have shown, an absorption or light scattering lineshape (l(u))) is related to molecular properties via a correlation function... 

In this section we shall examine the problems posed for the interpretation of "allowed spectroscopic lineshapes by the simultaneous influence of permanent and induced moments. These problems are quite general they arise in dielectric spectroscopy, infra-red absorption and light scattering. 

---