High-Energy Potential Scattering
- 1 October 1962
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 128 (1), 457-467
- https://doi.org/10.1103/physrev.128.457
Abstract
The asymptotic expansion of the phase shift in inverse powers of the momentum and the asymptotic expansion of the scattering amplitude in inverse powers of and the momentum transfer have been derived for a Dirac and Klein-Gordon particle. It is shown that at high energy (i) the higher-order phase shifts (proportional to , , where is the coupling constant) are very small and negligible in the calculation of the amplitude, (ii) the amplitude approaches the first Born approximation amplitude (linear in ) multiplied by a a phase factor. Statement (ii) holds for spherically symmetric potentials for which the first derivatives (the phase shift is expanded asymptotically up to ) exist for every real positive value of , including , and for which at least one derivative of odd order does not vanish at the origin. Statement (i) is probably correct also for potentials even at the origin [ for ]. The upper limit on the coupling constant is with the additional condition . Here is a characteristic length of the potential. The lower limit on the scattering angle is given by , where is another characteristic length of the potential and is usually of the same order of magnitude as . The problem of the model independence and other consequences of the theory are discussed.
Keywords
This publication has 17 references indexed in Scilit:
- Theory of Multiple Scattering: Second Born Approximation and Corrections to Molière's WorkPhysical Review B, 1959
- The high energy limit of the potential scatteringIl Nuovo Cimento (1869-1876), 1958
- Nuclear and Nucleon Scattering of High-Energy ElectronsAnnual Review of Nuclear Science, 1957
- High-Energy Potential ScatteringPhysical Review B, 1957
- The high energy limit of the potential scatteringIl Nuovo Cimento (1869-1876), 1957
- Relationship between the Scattering of High-Energy Dirac and Klein-Gordon ParticlesPhysical Review B, 1956
- Approximation Method for High-Energy Potential ScatteringPhysical Review B, 1956
- Electron Scattering and Nuclear StructureReviews of Modern Physics, 1956
- Potential Scattering of High-Energy Electrons in Second Born ApproximationPhysical Review B, 1956
- On the Scattering Theory of the Dirac EquationPhysical Review B, 1950