Two-particle scattering

From scattering theory it is known that the two-particle scattering states, p,p2)+, may be constructed with the Mpller operators from the two-particle noninteracting states p,p2) by the relation... 

In conclusion, we have presented our two-band model with intraband two-particle scattering and interband pairing scattering processes to describing two-gap superconductivity in MgB2. 

Like in the case of single-particle scattering, there are other possibilities of defining optical potentials. Without going into detail we want to mention that an analogous expression to the Feshbach effective Hamiltonian (109) can be derived for two-particle scattering. The static part has now the matrix elements [H, o ,a, ] o ). For positrons as projectile... 

In Landau-FL theory a two-particle scattering matrix k3k4) is introduced... 

Let fp x,t) be the probability that a particle moving into the direction cp is at the site positioned at x and time t, and consider, first of all, only two-particle collisions. A particle may scatter into the direction cp only if it comes from a binary collision involving... 

How might the interaction between two discrete particles be described by a finite-information based physics Unlike classical mechanics, in which a collision redistributes the particles momentum, or quantum mechanics, which effectively distributes their probability amplitudes, finite physics presumably distributes the two particles information content. How can we make sense of the process A scatters J5, if B s momentum information is dispersed halfway across the galaxy [minsky82]. Minsky s answer is that the universe must do some careful bookkeeping, ... 

By measuring the scattered intensity as a function of q over multiple decades in q, information from multiple structural levels can be obtained. Two distinct scattering feamres distinguish each stmctural level, a power-law region and a knee region in a log-log plot of I q) versus q. An example of power-law scattering is shown in Figure 17.2. For particles with a smooth surface the... 

Expressions for the medium modifications of the cluster distribution functions can be derived in a quantum statistical approach to the few-body states, starting from a Hamiltonian describing the nucleon-nucleon interaction by the potential V"(12, l/2/) (1 denoting momentum, spin and isospin). We first discuss the two-particle correlations which have been considered extensively in the literature [5,7], Results for different quantities such as the spectral function, the deuteron binding energy and wave function as well as the two-nucleon scattering phase shifts in the isospin singlet and triplet channel have been evaluated for different temperatures and densities. The composition as well as the phase instability was calculated. 

Fig. 11. Scattering of two particles as viewed from the laboratory system. E is the initial ion energy and V the initial velocity. M, and Mj are masses...

Bell (1981) (see also Bell and Bickel, 1981) measured all matrix elements for fused quartz fibers of a few micrometers in diameter with a photoelastic polarization modulator similar to that of Hunt and Huffman (1973) the HeCd (441.6 nm) laser beam was normal to the fiber axes. Advantages of fibers as single-particle scattering samples are their orientation is readily fixed and they can easily be manipulated and stored. Two of the four elements for a 0.96-jtim-radius fiber are shown in Fig. 13.16 dots represent measurements and solid lines were calculated using an earlier version of the computer program in Appendix C. Bell was able to determine the fiber radius to within a few tenths of a percent by varying the radius in calculations, assuming a refractive index of 1.446 + iO.O, until an overall best fit to the measured matrix elements was obtained. 

Complete formal analysis of the recoil corrections in the framework of the relativistic two-particle equations, with derivation of all relevant kernels, perturbation theory contributions, and necessary subtraction terms may be performed along the same lines as was done for hyperfine splitting in [3]. However, these results may also be understood without a cumbersome formalism by starting with the simple scattering approximation. We will discuss recoil corrections below using this less rigorous but more physically transparent approach. 

Figure 2. Light of incident angular frequency o>0 is scattered from two particles undergoing random Brownian motion. Because the scattered light is Doppler shifted by the two particles respectively, the scattered signal contains two discrete frequencies.

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