SYSTEMATIC SOLUTION OF MULTIPARTICLE SCATTERING PROBLEMS

Journal Article · Mon Jan 13 00:00:00 EST 1964 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.133.B232· OSTI ID:4151355

Weinberg, S

S>Scattering problems for three or more particles cannot be solved by a direct use of those techniques, like the Fredholm or quasiparticle methods, that work for two particles. The trouble is that the kernel STAW- H/sub o/!/sup -1/ V of the Lippmann-Schwinger integral equation is not L/sup 2/, even for complex W. In fact, this kernel has a continuous spectrum, giving rise to cuts in the coupling-constant plane for multiparticle scattering amplitudes. It is shown how to overcome this difficulty and calculate all Green's functions and scattering amplitudes in a systematic and essentially rigorous manner. The dynamical equations are rewritten as a sequence of linear integral equations for successively larger systems, each with a kernel and inhomogeneous term that can be calculated explicitly from the solutions of the previous equations. The kernels are L/sup 2/ because they arise from connected graphs only, so each integral equation can be solved by the Fredholm quasiparticle, or other methods. The distorted wave approximation appears very naturally in this approach. One minor by-product is an explicit upper bound on the binding energy of any N- particle composite system with square-integrable potentials. A mathematical Appendix on relevant topics in functional analysis is provided. (auth)

• Research Organization: Univ. of California, Berkeley
• NSA Number: NSA-18-006034
• OSTI ID: 4151355
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 133; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

BINDING ENERGY
DIFFERENTIAL EQUATIONS
DWBA APPROXIMATION
ELEMENTARY PARTICLES
GREEN FUNCTION
INTERACTIONS
LIPPMAN-SCHWINGER EQUATION
MANY BODY PROBLEM
MATHEMATICS
NUCLEAR REACTIONS
NUCLEONS
NUMERICALS
PARTICLE MODELS
PHYSICS
QUASI PARTICLES
REACTION KINETICS
SCATTERING
SPECTRA