ANALYTIC PROPERTIES OF THE AMPLITUDE FOR THE SCATTERING OF A PARTICLE BY A CENTRAL POTENTIAL

Journal Article · Sat Aug 01 04:00:00 EDT 1959 · Annals of Physics (New York) (U.S.)

DOI:https://doi.org/10.1016/0003-4916(59)90053-3· OSTI ID:4232319

Klein, A; Zemach, C

A new proof is given that the scattering amplitude, considered as a function of energy, for fixed momentum transfer, has those analytic properties in the energy variable which imply a dispersion relation. The proof is based on the known behavior of the Green's function, as the resolvent of a self-adjoint transformation, and on the study of the Born series. The class of potentials considered is the same as in previous stadies. It is shown that for potentials of arbitrary strength the Born series converges uniformly to its first term for sufficiently high energies, real or complex. The analytic properties of the scattering amplitude as a functlon of momentum transfer for fixed real energy are- also investigated and used to establish the domain of convergence of partial wave and related expansions. In particular the use of such expansions to define the amplitude in the unphysical region which occurs in the dispersion relation is fully justified for the same domain of momentam transfer for which the relation itself is valid, i.e.: DELTA < 2 alpha , where DELTA is the momentum transfer and alpha /sup -1/ the range of the potential. All proofs apply equally to the Sehroedinger and to the Klein-Gordon equations. ( auth)

• Research Organization: Univ. of Pennsylvania, Philadelphia; Univ. of California, Berkeley
• NSA Number: NSA-13-021634
• OSTI ID: 4232319
• Journal Information: Annals of Physics (New York) (U.S.), Journal Name: Annals of Physics (New York) (U.S.) Vol. Vol: 7; ISSN APNYA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

BEHAVIOR
BORN APPROXIMATION
CONFIGURATION
DISPERSION RELATIONS
ELEMENTARY PARTICLES
ENERGY
FIELD THEORY
GREEN FUNCTION
KLEIN-GORDON EQUATION
MATHEMATICS
MOMENTUM
MOTION
PARTICLES
PERTURBATION THEORY
PHYSICS AND MATHEMATICS
QUANTUM MECHANICS
RELATIVITY THEORY
SCATTERING
SCATTERING AMPLITUDE
SCHROEDINGER EQUATION