Scattering integral equations for distorted transition operators

Journal Article · Wed Nov 01 04:00:00 EST 1978 · Phys. Rev., C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.18.2017· OSTI ID:6876154

Kowalski, K L; Siciliano, E R; Thaler, R M

Methods for embedding phenomenological distorted-wave techniques for rearrangement and inelastic scattering within well-defined theories of multiparticle scattering are developed. The essential point of contact between the two approaches is in the definition and choice of distorting potential. It is shown that the concept of a channel coupling scheme allows a comparative freedom of choice for these potentials; if they are connected operators, such as optical potentials, then it is possible to obtain connected-kernel equations for the distorted transition operators. The latter are introduced in the course of exploiting the two-potential formula for the full transition operator and have the property that their matrix elements with respect to distorted waves are the physical scattering amplitudes. It is found that the distorted counterparts of the Kouri, Levin, and Tobocman and the Bencze-Redish integral equations maintain their connected-kernel and minimally coupled properties. These equations can be used to derive other integral equations with the same properties for the distorted-wave operators which consist of the product of the distorted transition operators and the wave operators corresponding to distorted waves. These simplifications are not realized for arbitrary channel coupling schemes. In order to deal with the general situation an alternative approach employing a subtraction technique which involves projections on the bound two-cluster channel states is introduced. When the distorting potentials are essentially the optical potentials in the entrance and exit channels a set of multichannel two-particle Lippmann-Schwinger integral equations for the two-cluster distorted-wave transition operators are obtained. Input into these two-particle integral equations involves the solution of a modified N-particle equation. Approximations to the latter are discussed in the particular cases of the Kouri, Levin, and Tobocman and Bencze-Redish channel coupling schemes.

• Research Organization: Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106
• OSTI ID: 6876154
• Journal Information: Phys. Rev., C; (United States), Journal Name: Phys. Rev., C; (United States) Vol. 18:5; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

653003* -- Nuclear Theory-- Nuclear Reactions & Scattering
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
AMPLITUDES
BORN APPROXIMATION
COUPLED CHANNEL THEORY
DISTORTED WAVE THEORY
DWBA
EQUATIONS
INELASTIC SCATTERING
INTEGRAL EQUATIONS
MATRIX ELEMENTS
MULTIPLE SCATTERING
OPTICAL MODELS
SCATTERING
SCATTERING AMPLITUDES