Scattering beyond mean field

We calculate the roton [Steinhauer 2004] in atomic vapor BEC using a Jas-trow wavefunction, which allows us to calculate beyond mean-field correlations in the quantum state, giving rise to a roton peak in the structure factor at a momentum k oc a-1 (where a is the s-wave scattering length of the atoms). The relevant parameter e = J i t a (n is the density of the atoms in the BEC), is calculated over a range of values from e < 1 up to e 1. 

There have been sophisticated calculations of x these systems. In the Flory-Huggins model x is independent of molecular weight and composition. In reality, this parameter has been shown, by scattering experiments and by theoretical calculations to be a function of Af, T and 0. 3,40,49 Theoretical attempts, which are beyond the scope of the mean field predictions of the Flory-Huggins approach which applies stri ct to incompressible systems, have been made to address these questions. 3,4o 49 The theories of Bates and Muthukumar 3 and of Schweizer and Curro °> both have predictions which may be written in the following form... 

Fine colloidal particles are usually smaller than the spatial resolution of an ordinary light microscope, which means that they are invisible with regard to an afhne projection. However, when colloidal particles are laterally illuminated by very intense light against a dark background (dark field microscopy), it is possible to see the scattering patterns with an optical microscope (Fig. 2.3). Since such an instrument facilitates the indirect visualisation of fine particles beyond the optical limit, it was named ultramicroscope. 

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