Identical particle scattering

This chapter deals with qnantal and semiclassical theory of heavy-particle and electron-atom collisions. Basic and nsefnl fonnnlae for cross sections, rates and associated quantities are presented. A consistent description of the mathematics and vocabnlary of scattering is provided. Topics covered inclnde collisions, rate coefficients, qnantal transition rates and cross sections. Bom cross sections, qnantal potential scattering, collisions between identical particles, qnantal inelastic heavy-particle collisions, electron-atom inelastic collisions, semiclassical inelastic scattering and long-range interactions. 

Guinier s law exhibits two parameters, I (0) and R2, which describe structural aspects of the sample. The experimentalist should consider their determination, if the recorded SAXS data show a monotonous decay that is indicative for the scattering from uncorrelated1 particles. Particularly useful is the evaluation of Guinier s law, if almost identical particles like proteins or latices are studied in dilute solution (cf. Pilz in [101], Chap. 8). The absolute value of 1(0) is only accessible, if the scattering intensity is calibrated in absolute units (Sect. 7.10.2). 

Thus, the difference between the diagonal elements of the forward amplitude scattering matrix in the circular polarization representation has a simple physical interpretation. Although we considered identical particles for conveni-... 

We shall assume, for simplicity, that we are dealing with a very dilute solution of identical particles with random positions and orientations. Scattering data, however, can also be interpreted for po-lydisperse solutions and in cases in which there are interparticle interactions. The intensity scattered in the forward direction by a solution of particles of concentration c2 is given by (Eisenberg, 1981) ... 

The MALS-FFF analytical technique is based on the following rationale Light scattering is the method of choice when all the particles are the same size since an ensemble of identical particles produces a scattering pattern the same as a single particle but greatly enhanced. Using FFF as a fractionator to separate particles into slices each of which contains particles with a narrow distribution of sizes permits the subsequent measurement of size in each slice and hence the determination of the size distribution of the unfractionated ensemble [109]. 

Figure 5 Schematic representation of neutron Compton scattering on an entangled pair of identical particles. The state is a superposition corresponding to particles a and (3 receiving the recoil during the scattering process.

It has recently been pointed out that the indistinguishability of identical particles has also another consequence for neutron scattering. The scattering processes are spin-dependent, which is expressed by writing the scattering lengths bi (see the scattering operators above) on the form b., Bi I. sn... 

Figure 2. Suppression of identical particle collisions. Full squares measured scattering cross-section for Beliaev damping as a function of the excitation wavenumber in units of the inverse healing length. The assumptions of our analysis are tested using hydrodynamic simulations (dashed line), and found to agree with Beliaev damping theory (solid line) and the experimental data. Corrections observed in the hydrodynamic simulation take into account the full inhomogeneity and finite size of the experimental system, and validate the approximations of our analysis.

Scattering from a collection of identical particles can be also expressed in terms of the so-called particle approach to light scattering as... 

Small-Angle Neutron Scattering. The intensity of small-angle scattering, I(Q), for a concentrated colloidal dispersion of identical particles is given by (14)... 

In scattering on a pair of identical particles in H2, D2, H2O, D2O and close pairs of protons or deuterons in molecules or metal hydrides, the quantum exchange effect must be taken into account by antisymmetrization of the initial state 4 i,... 

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