  The interaction due to the exchange of massless neutrinos between neutrons is
a long-range force. Border effects on this multibody exchange inside a dense
core are studied and computed analytically in 1 + 1 dimensions. We demonstrate
in this work that a proper treatment of the star's border effect automatically
incorporates the condensate contribution as a consequence of the appropriate
boundary conditions for the neutrino Feynman propagator inside the star.
  The total multibody exchange contribution is infrared-safe and vanishes
exactly in 1 + 1 dimensions. The general conclusion of this work is that the
border effect does not modify the result that neutrino exchange is
infrared-safe. This toy model prepares the ground and gives the tools for the
study of the realistic 3 + 1 star.
