QUASIPARTICLES AND THE BORN SERIES

Journal Article · Mon Jul 01 00:00:00 EDT 1963 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.131.440· OSTI ID:4694780

Weinberg, S

Perturbation theory aiways works in nonrelativistic scattering theory, unless composite particles are present. By composite particle is meant a bound state or resonance, or one that would exist for an interaction of opposite sign; in fact, this provides a precise definition of resonances. It follows that if fictitious elementary particles are first introduced to take the place of all composite particles, then perturbation theory can aiways be used. There are several ways of accomplishing this, one of which corresponds to the N/D method. In order to prove these results it is necessary to make a detailed study of the eigenvalues of the scattering kernel, and as a by-product new proofs of the applicability of the Fredholm theorems to scattering theory, of the convergence of the Born series at high energy, of the Bargmann-Schwinger theorem on the number of bound states, of the Pais-Jost theorem on the identity of the Jost function with the Fredholm determinant, and of Levinson,s theorem are obtained. Explicit formuias for binding energies and phase shifts in potential theory are given, using first-order perturbation theory after insertion of a single quasiparticle; these formulas work well for the lowest bound state and the S-wave scattering length of the Yukawa potential, and give precisely 13.6 ev for the hydrogen atom binding energy. (auth)

• Research Organization: Univ. of California, Berkeley, CA (United States)
• NSA Number: NSA-17-026352
• OSTI ID: 4694780
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Vol. Vol: 131; Other Information: Orig. Receipt Date: 31-DEC-63
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

PHYSICS
ATOMS
BINDING ENERGY
BORN APPROXIMATION
DIFFERENTIAL EQUATIONS
EIGENVALUES
ELEMENTARY PARTICLES
ENERGY LEVELS
FIELD THEORY
FREDHOLM DETERMINANT
FREDHOLM THEOREM
HYDROGEN
INTERACTIONS
JOST FUNCTION
LEVINSON THEOREM
MATHEMATICS
N/D METHOD
NUCLEAR MODELS
PARTICLE MODELS
PERTURBATION THEORY
QUASI PARTICLES
RESONANCE
S-WAVE
SCATTERING
SCATTERING AMPLITUDE
SPECTRAL SHIFT
YUKAWA POTENTIAL