Rayleigh scattering cross-section

Let us compare the PM (ft = 1, 2, 3, 4) respectively associated with the incident and scattered radiations [see (6.1.11) and (6.3.52)]. From this comparison, we shall deduce the Rayleigh scattering cross-sections. For the incident radiation, 

For the scattering of a radiation by a polarizable element, we have at point r 

The parameters PM(r) associated with the scattered radiation may fluctuate in time for instance, as a result of a random rotation motion of the polarizable element. In general, the experimentalist observes the time average of the parameters P. Then, he has to extract from this average, the contribution of the orientation fluctuations, which he considers either as a nuisance or as a studydeserving effect. We shall perform the calculation by using the formula [see (6.1.13) and (6.3.58)] 

However, let us first study instantaneous scattering. We shall examine the average (6.3.59) in the next section. Let us evaluate the parameters P in terms of the parameters °P(J. To do this, we use a relation deduced from (6.3.52) 

The matrices constitute a complete basis for two-by-two matrices. On the other hand, 

---

DISCUSSION By using a mixture of hydrogen and methane as the fuel, a case 2 (see above) experiment has been contrived, i.e., the effective Rayleigh scattering cross section of the fuel, air, and products are nearly ( < 2%) equal. It was then possible to make the first application of laser Rayleigh thermometry to non-premixed flames. 

The Rayleigh scattering cross section for a dilute assembly of N scattering particles per unit volume is N times the cross section per particle. Note that there seems little in common between the formulas for Thomson and Rayleigh scattering. 

General properties of the Rayleigh scattering cross-sections lsl property... 

The total coherent (Rayleigh) scattering cross-section per atom ctr can be calculated from... 

Rayleigh scattering cross-section for a single atom... 

---