HIGH-ENERGY POTENTIAL SCATTERING
High-energy potential scattering was investigated, assuming that the scattering was mainly forward. A method devised by Tolhoek and De Groot for obtaining approximate wave functions of charged psrticles in vonstant electric or magnetic fields either parallel or perpendicular to tbe incident direction of motion is generalized. Approximate wave functions are obtained for both Schmodinger and Dirac particles; for a Schrodinger particle in an electric field, the procedure led to Moliere's wave function. For the case of a Schrodinger particle in a scalar potential, a relation for the exact wave function , with the approximate wave function as leading term, was obtained by applying Green's theorem to the exact Green's function and the approximate wave function. The high-energy scattering amplitude was obtained for the cases of a spinless Schrodinger particle in a magnetic field, a Dirac particle in an electric field, and a form characteristic of a two-potential theory. A highenergy time-dependent formulation of scattering theory is set up for the Schrodinger equation by means of an approximate time-development operator Va. Approximate wave functions and approximate Green's functions for particles in electric and magnetic fields are derivable from the coordiaate representation of this operator. When the potential is time-independent, integral equations for the exact time-development operator, with Va as inhomogeneous term, are shown to lead to two time- independent equations for . The partial-wave analysis is discussed, with emphasis on high-energy formulas for phase shifts correspending to small or large angular momentums. An exact, but unwieldy integral expression for any phase shift is obtained in terms of the WKB approximation for the radial wave function. (auth)
- Research Organization:
- Ames Lab., Ames, Iowa
- DOE Contract Number:
- W-7405-ENG-82
- NSA Number:
- NSA-15-000997
- OSTI ID:
- 4147276
- Report Number(s):
- IS-203
- Resource Relation:
- Other Information: Orig. Receipt Date: 31-DEC-61
- Country of Publication:
- United States
- Language:
- English
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