Scattering in a spherical potential motion of complex plane poles and zeros
Scattering of spinless nucleons in a spherical potential is examined with the use of a computer graphics simulation VSCAT. The potential is defined stepwise and the Schroedinger equation is solved to obtain wavefunctions, scattering phases, partial-wave total cross sections and differential cross sections, which are then displayed graphically. For the particular case of a square well, partial-wave amplitudes are displayed over the complex energy plane in a 3-dimensional plot. The well depth is then varied in order to follow the motion of poles as they become resonances and then bound states. Also displayed are the partial wave zeros, which are required to satisfy Levinson's theorem for multiple bound states. We develop the requirement on well depth to produce a specified number of bound states and enumerate the energies which, at a given well depth, create equal scattering phases in adjoining partial waves delta/sub l-1/ = delta/sub l/ = delta/sub l+1/. This symmetry of scattering phases exists for both repulsive and attractive square potentials. We also briefly study a square repulsive core, which has the same triple-point symmetry as the square well. 9 figs.
- Research Organization:
- Virginia Polytechnic Inst. and State Univ., Blacksburg (USA). Dept. of Physics
- DOE Contract Number:
- AS05-76ER04928
- OSTI ID:
- 5801841
- Report Number(s):
- DOE/ER/04928-T1; ON: DE88002176
- Resource Relation:
- Other Information: Portions of this document are illegible in microfiche products
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
NUCLEONS
POTENTIAL SCATTERING
COMPUTERIZED SIMULATION
COMPUTER GRAPHICS
DIFFERENTIAL CROSS SECTIONS
NUCLEAR POTENTIAL
PARTIAL WAVES
SCATTERING AMPLITUDES
SCHROEDINGER EQUATION
SQUARE-WELL POTENTIAL
TOTAL CROSS SECTIONS
WAVE FUNCTIONS
AMPLITUDES
BARYONS
CROSS SECTIONS
DIFFERENTIAL EQUATIONS
ELASTIC SCATTERING
ELEMENTARY PARTICLES
EQUATIONS
FERMIONS
FUNCTIONS
HADRONS
PARTIAL DIFFERENTIAL EQUATIONS
POTENTIALS
SCATTERING
SIMULATION
WAVE EQUATIONS
653003* - Nuclear Theory- Nuclear Reactions & Scattering
657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics