- Access by Xinjiang University
The Radiative Collisions of Positrons and Electrons
Phys. Rev. 78, 161 – Published 15 April, 1950
DOI: https://doi.org/10.1103/PhysRev.78.161
Abstract
The general matrix elements for the collision of two electrons ( case) or a positron and an electron ( case) accompanied by the emission of a quantum of radiation are formulated. It is expected that the two cross sections will differ considerably both because of the existence of a dipole for the case, and because of the essentially different nature of the exchange phenomenon in the case arising there from the possibility of virtual pair creation or annihilation rather than the indistinguishability of the particles. Two cases are calculated in detail; the non-relativistic limit and the extreme relativistic limit in which the quantum energy is restricted to in the laboratory system. In the former case the cross section for the case is found to vanish if the momentum of the quantum is neglected, while the cross section is comparable to that for the "bremsstrahlung" process. In the latter case the cross sections of the two cases are of the same order of magnitude the cross section being greater because of the exchange terms, the exchange terms of the case being negligible in all of the cases considered.
References (14)
- C. Møller, Ann. d. Physik 126, 259 (1930)
- G. Breit, Phys. Rev. 34, 553 (1929)
- H. Bethe and E. Fermi, Zeits. f. Physik 77, 296 (1932)
- H. J. Bhabha, Proc. Roy. Soc. A154, 195 (1936)
- C. Møller, Proc. Roy. Soc. A152, 481 (1935)
- H. Bethe and W. Heitler, Proc. Roy. Soc. A146, 83 (1934)
- P. Havas, Phys. Rev. 68, 214 (1945)
- C. Møller, Proc. Roy. Soc. A152, 481 (1935)
- H. Casimir, Helv. Phys. Acta 6, 287 (1933)
- W. Heitler, Quantum Theory of Radiation (Clarendon Press, Oxford, 1944), second edition, p. 90
- W. Heitler, [10], p. 166
- A. Sommerfeld, Ann. d. Physik 11, 251 (1931)
- C. Møller, Ann. d. Physik 126, 259 (1930)
- W. Heitler, [10], p. 217