Pion-nucleus scattering using finite binding potentials
A nonperturbative treatment of finite binding potentials in pion-bound nucleon scattering is developed. Coupled differential equations in configuration space are derived from a model wave function broken into two parts. Coordinates from the source of binding to the pion and to the nucleon are used in the elastic channel, while pion-nucleon center-of-mass coordinates are used for the excited channels. The excited channel equations are solved in closed form using a separable nonlocal pion-nucleon interaction. When the solution is inserted into the elastic channel equation, a relativistically modified single-particle equation for the elastically scattered meson is derived, which features an optical potential with both local and nonlocal parts. This model is used in conjunction with first order multiple scattering theory to construct pion-nucleus scattering. In the present application of the model the assumed pion-nucleon interaction is taken to be s wave with threshold p-wave behavior. The region around the 33 resonance is numerically studied for both the three-body model and for pions on /sup 16/O. A consistent, inclusive treatment of many effects familiar from earlier work is obtained. Results from the three-body calculation show that the peak cross section is shifted upwards by about the binding energy of the struck nucleon. However, nonlinear effects drive the peak downwards when the three-body model is incorporated in the pion-nucleus formalism, so that several bound nucleons simultaneously scatter the meson. Effects of this kind are not expected to be sensitive to the use of an artificial l=0 ..pi..N interaction. Resonances caused by the binding potential are found to be important in both the three-body and the ..pi..-/sup 16/O calculations. This suggests significant corrections to an impulse approximation approach.
- Research Organization:
- University of Pittsburgh, Pittsburgh, Pennsylvania 15260
- OSTI ID:
- 5634250
- Journal Information:
- Phys. Rev., C; (United States), Vol. 21:1
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
OXYGEN 16 TARGET
PION REACTIONS
ELASTIC SCATTERING
ANGULAR MOMENTUM
BINDING ENERGY
ENERGY DEPENDENCE
IMPULSE APPROXIMATION
MULTIPLE SCATTERING
OPTICAL MODELS
PHASE SHIFT
PION-NUCLEON INTERACTIONS
SCHROEDINGER EQUATION
THREE-BODY PROBLEM
TOTAL CROSS SECTIONS
WOODS-SAXON POTENTIAL
CHARGED-PARTICLE REACTIONS
CROSS SECTIONS
DIFFERENTIAL EQUATIONS
ENERGY
EQUATIONS
HADRON REACTIONS
HADRON-HADRON INTERACTIONS
INTERACTIONS
MANY-BODY PROBLEM
MESON REACTIONS
MESON-BARYON INTERACTIONS
MESON-NUCLEON INTERACTIONS
NUCLEAR POTENTIAL
NUCLEAR REACTIONS
PARTICLE INTERACTIONS
POTENTIALS
SCATTERING
TARGETS
WAVE EQUATIONS
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