0000000001105441
AUTHOR
G. V. Avakov
showing 2 related works from this author
About Compactness of Faddeev Integral Equations for Three Charged Particles
1999
Momentum space three-body integral equations of the Faddeev type can not be used for Coulomb-like potentials, for energies above the breakup threshold. The reason is the occurrence of singularities in their kernels which destroy the compactness properties known to exist for purely short-range interactions. Using the rigorously equivalent formulation in terms of an effective-two- body theory, we prove that the nondiagonal kernels occurring therein possess on and off the energy shell only integrable singularities, provided all three particles have charges of the same sign (ie., only repulsive Coulomb interactions). In contrast, if some of the charges have opposite signs the nondiagonal kernel…
Momentum space integral equations for three charged particles: Nondiagonal kernels
2000
Standard solution methods are known to be applicable to Faddeev-type momentum space integral equations for three-body transition amplitudes, not only for purely short-range interactions but also, after suitable modifications, for potentials possessing Coulomb tails provided the total energy is below the three-body threshold. For energies above that threshold, however, long-range Coulomb forces have been suspected to give rise to such severe singularities in the kernels, even of the modified equations, that their compactness properties are lost. Using the rigorously equivalent formulation in terms of an effective-two-body theory we prove that, for all energies, the nondiagonal kernels occurr…