English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

It has been a long-standing question whether momentum space integralequations of the Faddeev type are applicable to reactions of three chargedparticles, in particular above the three-body threshold. For, the presence oflong-range Coulomb forces has been thought to give rise to such severesingularities in their kernels that the latter may lack the compactnessproperty known to exist in the case of purely short-range interactions.Employing the rigorously equivalent formulation in terms of aneffective-two-body theory we have proved in a preceding paper [Phys. Rev. C{\bf 61}, 064006 (2000)] that, for all energies, the nondiagonal kernelsoccurring in the integral equations which determine the transition amplitudesfor all binary collision processes, possess on and off the energy shell onlyintegrable singularities, provided all three particles have charges of the samesign, i.e., all Coulomb interactions are repulsive. In the present paper weprove that, for particles with charges of equal sign, the diagonal kernels, incontrast, possess one, but only one, nonintegrable singularity. The latter can,however, be isolated explicitly and dealt with in a well-defined manner. Takentogether these results imply that modified integral equations can beformulated, with kernels that become compact after a few iterations. Thisconcludes the proof that standard solution methods can be used for thecalculation of all binary (i.e., (in-)elastic and rearrangement) amplitudes bymeans of momentum space integral equations of the effective-two-body type.Comment: 36 pages, 2 figures, accepted for publication in Phys. Rev.

Momentum space integral equations for three charged particles. II. Diagonal kernels