General algebraic treatment of identical particles in scattering processes

Franz S. Rys

Galina A. Nemova

E. Corinaldesi

Ta‐You Wu

For the problem of the scattering of an electron by a hydrogen atom, the complete equivalence is shown of the treatment of Trainor and Wu based on symmetry considerations and that of Altshuler giving a direct proof of the method of Mott and Massey. A generalization of the treatment of Altshuler to scattering processes involving non-identical particles or other rearrangement collisions is made. Also, the usual treatment involving matrix elements for transitions between states belonging to two different Hamiltonians is discussed and justified. Finally, the recent treatment by Dirac of rearrangement collisions is discussed, and it is shown that a correct formulation of the method and interpretation of the result give exactly the same result as in the usual treatment.

G. Bencze, Edward F. Redish

We consider the nonrelativistic N-body scattering problem for a system of particles in which some subsets of the particles are identical. We demonstrate how the particle identity can be included in a general class of linear integral equations for scattering operators or components of scattering operators. The Yakubovskii, Yakubovskii–Narodestkii, Rosenberg, and Bencze–Redish–Sloan equations are included in this class. Algebraic methods are used which rely on the properties of the symmetry group of the system. Operators depending only on physically distinguishable labels are introduced and linear integral equations for them are derived. This procedure maximally reduces the number of coupled equations while retaining the connectivity properties of the original equations.