DISPERSION-THEORETIC IMPULSE APPROXIMATION FOR POTENTIAL SCATTERING

Journal Article · Mon Jan 14 23:00:00 EST 1963 · Physical Review (U.S.) Superseded in part by Phys.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.129.968· OSTI ID:4757346

Rosenberg, L

In the impulse approximation for the scattering of a particle by a bound system, the amplitude is a sum of integrals over two-body scattering amplitudes, off the energy shell, folded into bound-state wave functions. In the usual formulation, the nonphysical two-body amplitudes are replaced by physical amplitudes with no firm justification for this procedure. The dispersion- theoretic formulation presented here, for elastic scattering, removes this difficulty; for low values of t, the momentum transfer squared, the discontinuity across the cut in the t plane can be expressed in terms of the absorptive part of the physical two-body amplitude and the asymptotic form of the bound-state wave function. Working with a nonrelativistic model, it is shown that the Cutkosky method for finding absorptive parts of Feynman amplitudes applies here as well. The analyticity of the amplitude is a conjecture, based on a proof that the second and third Born approximations satisfy a Mandelstam representation. The method of this proof is an adaptation of techniques recently developed by Eden and others in the relativistic case. (auth)

• Research Organization: Univ. of Pennsylvaniz, Philadelphia
• NSA Number: NSA-17-007512
• OSTI ID: 4757346
• Journal Information: Physical Review (U.S.) Superseded in part by Phys.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 D, Journal Name: Physical Review (U.S.) Superseded in part by Phys.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: 129; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ABSORPTION
BINDING ENERGY
BORN APPROXIMATION
BOUND STATE
DIFFERENTIAL EQUATIONS
DISPERSION RELATIONS
ELASTIC SCATTERING
ELEMENTARY PARTICLES
ENERGY
FEYNMAN DIAGRAM
FEYNMAN METHOD
FIELD THEORY
INTEGRALS
MANDELSTAM REPRESENTATION
MATHEMATICS
MOMENTUM
PERTURBATION THEORY
PHYSICS
PULSES
QUANTUM MECHANICS
RELATIVITY THEORY
SCATTERING
SCATTERING AMPLITUDE