Prog. Theor. Phys. Vol. 52 No. 1 (1974) pp. 131-146
Theory of Scattering in Three-Particle System
Department of Physics, College of General Education, Osaka University, Toyonaka
(Received December 18, 1973)
A theory of scattering in three-particle system is proposed. The Hamiltonian of the system is described in a coordinate system which is appropriate for representing the three-particle system. After a unitary transformation, the basic Hamiltonian satisfying the asymptotic condition is obtained. On the basis of this Hamiltonian, the orthogonality of the scattering states for different channels is exhibited in an exact way. The S-matrix involves explicity the contribution from the indirect interactions between two particles through the motion of the third particle. With the aid of the orthogonal character of the scattering states, a generalized optical theorem in three-particle system is derived. The integral equation for the scattering amplitude is transformed so as to be able to have a convergent series which does not involve any disconnected diagram.
DOI : 10.1143/PTP.52.131
B. A. Lippmann and J. Schwinger, Phys. Rev. 79 (1950), 489[APS].
M. Gell-Mann and M. L. Goldberger, Phys. Rev. 91 (1953), 398[APS].
- S. Sunakawa, Prog. Theor. Phys. 14 (1955), 175[PTP].
B. A. Lippmann, Phys. Rev. 102 (1956), 264[APS].
R. Aaron, R. D. Amado and B. W. Lee, Phys. Rev. 121 (1961), 319[APS].
K. R. Greider and L. R. Dodd, Phys. Rev. 146 (1966), 671[APS].
S. Weinberg, Phys. Rev. 133 (1964), 232[APS].
- S. Sunakawa, Prog. Theor. Phys. 24 (1960), 963[PTP].
- L. D. Faddeev, Sov. Phys. -JETP 12 (1961), 1014.
L. R. Dodd and K. R. Greider, Phys. Rev. 146 (1966), 675[APS].
R. D. Amado, Phys. Rev. 132 (1963), 485[APS].
R. Aaron, R. D. Amado and Y. Y. Yam, Phys. Rev. 136 (1964), B650[APS].
L. L. Foldy and W. Tobocman, Phys. Rev. 105 (1957), 1099[APS].
S. T. Epstein, Phys. Rev. 106 (1957), 598[APS].
Citing Article(s) :
Progress of Theoretical Physics Vol. 54 No. 1 (1975) pp. 79-92
Theory of Scattering in Three-Particle System and Its Application to Electron-Exciton Scattering
Kiyohisa Matsuda, Masahiko Hirooka and Sigenobu Sunakawa