Bethe--Salpeter equation with instantaneous harmonic oscillator exchange

Journal Article · Mon Dec 01 04:00:00 EST 1980 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(80)90342-5· OSTI ID:6438474

Hostler, L C; Repko, W W

The Bethe--Salpeter equation in the form due to Cung et al. (Ann. Phys. (N.Y.) 98 (1976), 516) is investigated for the special case of instantaneous harmonic oscillator exchange. An exact reduction to a pair of coupled ordinary differential equations for the radial excitations of the /sup 3/(J +- 1)/sub J/ modes is achieved. The equations in the mass zero case are brought to a form which is quite close to Whittaker's equation. This similarity to Whittaker's equation is exploited in a computer study of the level structure as a function of the quark mass. This study covers the region from a highly relativistic spectrum depending only upon J to the nonrelativistic regime where the spectrum depends only upon L. An expression for the leptonic width of a /sup 3/S/sub 1/ state in terms of the Bethe--Salpeter wave function is derived and applied to the u-family. The effect of relativistic corrections is to reduce the predicted value of the leptonic width compared to the value calculated by assuming nonrelativistic kinematics. It is also shown that the relativistic treatment allows a /sup 3/D/sub 1/ state to couple directly to a virtual photon.

• Research Organization: Department of Physics, Wilkes College, Wilkes-Barre, Pennsylvania 18766
• OSTI ID: 6438474
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 130:2; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

645201* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- General & Scattering Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BETHE-SALPETER EQUATION
BOUND STATE
D STATES
EIGENVALUES
ENERGY LEVELS
EQUATIONS
FUNCTIONS
HARMONIC OSCILLATOR MODELS
INTERACTIONS
MATHEMATICAL MODELS
NUMERICAL SOLUTION
PARTICLE INTERACTIONS
PARTICLE PROPERTIES
PARTICLE WIDTHS
QUARK-ANTIQUARK INTERACTIONS
S STATES
WAVE FUNCTIONS