Forward scattering amplitude

The optical theorem relates the integral cross section to the unaginary part of the forward scattering amplitude by... 

It is useful to consider rare gas scattering, for which a = a and ft = / . Using the optical theorem we can relate the imaginary part of the forward scattering amplitude to the total cross section.18 Explicitly, we can apply the optical theorem to the scattering amplitudes on both the left hand and right hand sides of Eq. (11.29). This procedure yields... 

These equations provide useful checks on the consistency of the experimentally measured values of aT with the calculated values of the real part of the forward scattering amplitude, or the scattering length they have been used as such by Bransden and Hutt (1975). For helium, these authors took the measured total cross sections of Coleman et al. (1976b) in the energy range 2-800 eV below 2 eV they used an extrapolation based on a least-squares fit of the functional form... 

The appearance of the forward scattering amplitude in Equation 29 enables us to give a conceptually appealing interpretation of the attenuation coefficient associated with k. Using the forward scattering theorem, which is valid for any scatterer geometry, one finds (27-30)... 

This important relationship is the optical theorem. The imaginary part of the forward scattering amplitude is proportional to the total cross section. 

The basic definition of an effective medium is that the ESU, when embedded in the effective medium, should not be detectable in an experiment using electromagnetic measurement. In other words, the extinction of the ESU should be the same as if it were replaced with a material characterized by Ceff. This criterion makes it fruitful to use a recently derived [12] optical theorem for absorbing media it relates the extinction of the spherical cell compared to that of the surrounding medium with the scattering amplitude in the direction of the impinging beam S(0) (forward scattering amplitude) by... 

The symmetries can be obtained directly from the symmetries of the two-particle Green s function. The Landau-FL parameters and are determined by the isotropic Fermi surface averages Aq = (r- (kik2 kik2 Fs of the two particle forward-scattering amplitude... 

Firstly we recall the famous relation [see, for example, Goldberger and Watson (1964)] between index of refraction and forward scattering amplitude / for a dilute material ... 

Deak L, Bottyan L, Nagy DL and Spiering H (1996) Coherent forward-scattering amplitude in transmission and grazing incidence Mossbauer spectroscopy. Physical Reviews B Condensed Matter 53 6158-6164. 

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