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The integral relations formalism introduced in \cite{bar09,rom11}, anddesigned to describe 1+$N$ reactions, is extended here to collision energiesabove the threshold for the target breakup. These two relations are completelygeneral, and in this work they are used together with the adiabatic expansionmethod for the description of 1+2 reactions. The neutron-deuteron breakup, forwhich 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 thebreakup threshold and the possibility of using soft-core two-body potentialsplus a short-range three-body force will be investigated. Comparisons toprevious calculations for the three-body recombination and collisiondissociation rates will be shown.

Integral relations and the adiabatic expansion method for 1+2 reactions above the breakup threshold: Helium trimers with soft-core potentials