Numerical solution of the spinor Bethe--Salpeter equation and the Goldstein problem
The spinor Bethe--Salpeter equation describing bound states of a fermion-antifermion pair with massless-boson exchange reduces to a single (uncoupled) partial differential equation for special combinations of the fermion-boson couplings. For spinless bound states with positive or negative parity this equation is a generalization to nonvanishing bound-state masses of the equations studied by Kummer and Goldstein, respectively. In the tight-binding limit the Kummer equation has a discrete spectrum, in contrast to the Goldstein equation, while for loose binding only the generalized Goldstein equation has a nonrelativistic limit. For intermediate binding energies the equations are solved numerically. The generalized Kummer equation is shown to possess a discrete spectrum of coupling constants for all bound-state masses. For the generalized Goldstein equation a discrete spectrum of coupling constants is found only if the binding energy is smaller than a critical value.
- Research Organization:
- Institute of Theoretical Physics, University of Amsterdam, Amsterdam, The Netherlands
- OSTI ID:
- 6877334
- Journal Information:
- Ann. Phys. (N.Y.); (United States), Vol. 113:2
- Country of Publication:
- United States
- Language:
- English
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