Finite Cross Section for Three-Particle Scattering

M. Yamazaki

In the scattering of three free incident particles, a finite cross section for the double scattering has to be defined differently from the processes other than the double scattering. That is, we want to maintain that, in order to obtain a definite quantity being connected to the experimental observation, a particular definition of the cross section has to be required for the double scattering owing to a particular time dependence of its scattering rate. Our definition differs from the ones given recently by others in a form depending on some macroscopic quantities.1), 2) In the previous paper (refered as I in the following)3), we have attained to a finite cross section by working on the basis of the wave packet formalism, while we want to give here a clear-cut derivation in a simple and familear form.

Werner Zickendraht

Werner O. Amrein, KB Sinha

Using a Hilbert space version of the Faddeev method. The authors prove finiteness and continuity as a function of the energy of the total scattering cross section for three quantum mechanical particles with two-body initial states. It is assumed that the pair potentials are locally in L q (R 3 ) for some q> 3 / 2 and decay as mod x mod -2- delta at infinity.

Rostislav V. Vedrinskii

Vladimir D Skarzhinsky, Jürgen Audretsch

We consider the Dirac equation in cylindrically symmetric magnetic fields and find its normal modes as eigenfunctions of a complete set of commuting operators. This set consists of the Dirac operator itself, the z-components of the linear and the total angular momenta, and of one of the possible spin polarization operators. The spin structure of the solution is completely fixed independently of the radial distribution of the magnetic field which influences only the radial modes. We solve explicitly the radial equations for the uniform magnetic field inside a solenoid of finite radius and consider in detail the scattering of scalar and Dirac particles in this field. For particles with low energy the scattering cross section coincides with the Aharonov - Bohm scattering cross section. We work out the first-order corrections to this result caused by the fact that the solenoid radius is finite. At high energies we obtain the classical result for the scattering cross section.