Three-body dynamics in one dimension: A test model for the 3-Nucleon system with irreducible pionic diagrams

摘要

We formulate the three-body problem in one dimension in terms of the(Faddeev-type) integral equation approach. As an application, we develop aspinless, one-dimensional (1-D) model that mimics three-nucleon dynamics in onedimension. Using simple two-body potentials that reproduce the deuteronbinding, we obtain that the three-body system binds at about 7.5 MeV. We thenconsider two types of residual pionic corrections in the dynamical equation;one related to the 2PI-exchange three-body diagram, the other to the1PI-exchange three-body diagram. We find that the first contribution canproduce an additional binding effect of about 0.9 MeV. The second term producessmaller binding effects, which are, however, dependent on the uncertainty inthe off-shell extrapolation of the two-body t-matrix. This presents interestinganalogies with what occurs in three dimensions. The paper also discusses thegeneral three-particle quantum scattering problem, for motion restricted to thefull line.