  The integral relations formalism introduced in \cite{bar09,rom11}, and
designed to describe 1+$N$ reactions, is extended here to collision energies
above the threshold for the target breakup. These two relations are completely
general, and in this work they are used together with the adiabatic expansion
method for the description of 1+2 reactions. The neutron-deuteron breakup, for
which benchmark calculations are available, is taken as a test of the method.
The s-wave collision between the $^4$He atom and $^4$He$_2$ dimer above the
breakup threshold and the possibility of using soft-core two-body potentials
plus a short-range three-body force will be investigated. Comparisons to
previous calculations for the three-body recombination and collision
dissociation rates will be shown.
