COMPLEX ANGULAR MOMENTUM IN SPINOR BETHE-SALPETER EQUATION

Journal Article · Thu Aug 15 04:00:00 EDT 1963 · Physical Review (U.S.) Superseded in part by Phys.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.131.1857· OSTI ID:4668216

Swift, A R; Lee, B W

A model of fermion-antifermion scattering, mediated by pseudoscalar neutral bosons. is described by the corresponding spinorial Bethe-Salpeter equation in the ladder approximation. The decomposition of the equation into partial waves by means of fusion amplitudes and conventional spherical harmonics is discussed in detail; various importunt symmetries of the resulting kernel and Born amplitudes are pointed out. The resulting set of coupled equations is continued into the complex angular momentum (J) plane, and it is shown that Fredholm theory is inapplicable for any J. The equations are solved in a weak coupling, low-energy limit by an iterative scheme. The resulting solutions exhibit a cut of the square-root type extending along the real axis to G/2 pi (G = coupling constunt) in the right-hand plane; other cuts and poles prevent the extension of our solutions into the left-hand J plane. The dominance of the cut is used to extract the large momentum transfer limit and obtain certain results for the high-energy limit in the cross channel. The totul cross section for fermion-antifermion annihilation is extracted by means of the optical theorem and is found to exhibit an energy dependence of the forrn t/sup (G/2 pi /)-1/)STAInt!/ sup - 3/2/ where t is the c.m. energy squared. (auth)

• Research Organization: Univ. of Pennsylvania, Philadelphia
• NSA Number: NSA-17-031661
• OSTI ID: 4668216
• Journal Information: Physical Review (U.S.) Superseded in part by Phys.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 D, Journal Name: Physical Review (U.S.) Superseded in part by Phys.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; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ANGULAR MOMENTUM
ANNIHILATION
ANTIHYPERONS
ANTIMESONS
ANTINEUTRINOS
ANTINEUTRONS
ANTINUCLEONS
ANTIPARTICLES
ANTIPROTONS
BETHE-SALPETER EQUATION
BORN APPROXIMATION
BOSONS
COUPLING
CROSS SECTIONS
ENERGY
EQUATIONS
FERMIONS
FIELD THEORY
INTERACTIONS
MATHEMATICS
MOMENTUM
MUONS
MUONS-PLUS
OPTICAL THEOREM
PERTURBATION THEORY
PHYSICS
POSITRONS
PSEUDOSCALAR
QUANTUM MECHANICS
RELATIVITY THEORY
SCATTERING
SPIN
SPINOR
VECTORS