UNITARY IMPULSE APPROXIMATION

Journal Article · Mon Jul 15 04:00:00 EDT 1963 · Physical Review (U.S.) Superseded in part by Phys.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.131.874· OSTI ID:4703553

Rosenberg, L

With the aid of multiple scattering expansions, Blankenbecler's generalized unitarity relation is derived for a multichannel three-body potential scattering problem. A matrix representation of the scattering amplitudes is obtained in the form of Heitler's integral equation, with the K matrix replaced by a matrix N, so that generalized unitarity is automatically satisfied if N has no physical cut in the total energy variable. A simple, physically reasonable, choice for N leads to representations of the inelastic amplitudes that have the form of initial- (or final-) state interaction corrections to the impulse approximation. With the elastic amplitude given, no sums over three-body phase space appear. The elastic amplitude itself is obtained as the solution of an integral equation that sums all diagrams that are iterations of the basic impulse approximation diagram. It is explicitly demonstrated that the partial-wave amplitudes thus obtained must satisfy unitarity even when the impulse approximation is nonunitary. A convergent iterative solution is presented that treats the effects of longer ranged forces first and should be appropriate for high-energy diffraction scattering. Rearrangement collisions are treated in a similar way. (auth)

• Research Organization: Univ. of Pennsylvania, Philadelphia
• NSA Number: NSA-17-028193
• OSTI ID: 4703553
• Journal Information: Physical Review (U.S.) Superseded in part by Phys.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 D, Journal Name: Physical Review (U.S.) Superseded in part by Phys.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: 131; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

BINDING ENERGY
COLLISIONS
CROSS SECTIONS
DIAGRAMS
DIFFERENTIAL EQUATIONS
DIFFRACTION
ELECTRONS
ENERGY
ENERGY LEVELS
HEITLER-LONDON THEORY
IMPULSE APPROXIMATION
INTERACTIONS
K-MATRIX
MANY BODY PROBLEM
MATHEMATICS
MATRICES
NUCLEAR STRUCTURE
PHASE SPACE
PHYSICS
QUANTUM MECHANICS
SCATTERING