A momentum-space formulation without partial wave decomposition for scattering of two spin-half particles

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Abstract

A new momentum-space formulation for scattering of two spin-half particles, both either identical or unidentical, is formulated. As basis states the free linear-momentum states are not expanded into the angular-momentum states, the system's spin states are described by the product of the spin states of the two particles, and the system's isospin states by the total isospin states of the two particles. We evaluate the Lippmann-Schwinger equations for the T-matrix elements in these basis states. The azimuthal behavior of the potential and of the T-matrix elements leads to a set of coupled integral equations for the T-matrix elements in two variables only, which are the magnitude of the relative momentum and the scattering angle. Some symmetry relations for the potential and the T-matrix elements reduce the number of the integral equations to be solved. A set of six spin operators to express any interaction of two spin-half particles is introduced. We show the spin-Averaged differential cross section as being calculated in terms of the solution of the set of the integral equations.

Original languageEnglish
Title of host publication4th International Conference on Theoretical and Applied Physics, ICTAP 2014
EditorsNi Nyoman Rupiasih, Wayan Gede Suharta, Hery Suyanto
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735413665
DOIs
Publication statusPublished - 11 Mar 2016
Event4th International Conference on Theoretical and Applied Physics, ICTAP 2014 - Bali, Indonesia
Duration: 16 Oct 201417 Oct 2014

Publication series

NameAIP Conference Proceedings
Volume1719
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference4th International Conference on Theoretical and Applied Physics, ICTAP 2014
Country/TerritoryIndonesia
CityBali
Period16/10/1417/10/14

Keywords

  • 3D technique
  • spin-half particles interaction
  • spin-half particles scattering

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