Properties of an analytically solvable model of multichannel scattering

Journal Article · Tue Jan 01 00:00:00 EST 1974 · Phys. Rev., A, v. 9, no. 1, pp. 301-315

DOI:https://doi.org/10.1103/PhysRevA.9.301· OSTI ID:4305348

Gerber, R B; Rosenbach, N C

A study is made of an analytically solvable model of multichannel scattering, leading to the derivation of various properties of the solutions. In this model the intrinsic potential in each channel and the interchannel coupling operators are all taken to be separable interactions. In an especially simple version of the model an assumption is also made concerning a factorization property of the coupling coefficients that pertain to these interactions. Extremely simple explicit expressions are obtained for the elastic- and the inelastic-scattering amplitudes, as well as for the Feshbach potential, the effective interaction in the elastic channel owing to the presence of all other channels. The expressions obtained are transparent to analysis, and in the simple version of the model they do not involve the evaluation of inverses or determinants of large matrices, as is the case in general for formal explicit solutions of Fredholm equations. The simple version of the model can also be extended to the case of a continuum of channels, thus being capable of describing systems with open rearrangement or dissociation channels. Within the framework of this model. a rigorous analysis is given for the case of an infinite number of channels, and conditions are obtained for convergence of the close-coupling scheme. Error bounds are obtained for an N-channel truncated calculation on an infinite-channel system. Other results obtained include: establishing the asymptotic behavior of the scattering amplitude at extremely high energies, and deriving some especially simple features, scaling properties,'' of the scattering amplitudes. (auth)

• Research Organization: Weizmann Inst. of Science, Rehovot, Israel
• Sponsoring Organization: USDOE
• NSA Number: NSA-29-028077
• OSTI ID: 4305348
• Journal Information: Phys. Rev., A, v. 9, no. 1, pp. 301-315, Other Information: Orig. Receipt Date: 30-JUN-74
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

N64500* -Physics (High Energy)-Scattering Theory
N60400 - -Physics (Atomic & Molecular)-Collision Phenomena
*COLLISIONS
*SCATTERING
BOUNDARY CONDITIONS
COUPLING
ELASTIC SCATTERING
ERRORS
FACTORIZATION
FESHBACH EQUATIONS
FREDHOLM EQUATION
INELASTIC SCATTERING
INTERACTIONS
MATHEMATICAL OPERATORS
SCALE INVARIANCE
SCATTERING AMPLITUDES FESHBACH EQUATIONS