Abstract
In this work we investigate $1+2$ reactions within the framework of the hyperspherical adiabatic expansion method. With this aim two integral relations, derived from the Kohn variational principle, are used. A detailed derivation of these relations is shown. The expressions derived are general, not restricted to relative $s$ partial waves, and with applicability in multichannel reactions. The convergence of the $\mathcal{K}$ matrix in terms of the adiabatic potentials is investigated. Together with a simple model case used as a test for the method, we show results for the collision of a $^{4}\mathrm{He}$ atom on a $^{4}\mathrm{He}$${}_{2}$ dimer (only the elastic channel open), and for collisions involving a $^{6}\mathrm{Li}$ and two $^{4}\mathrm{He}$ atoms (two channels open).
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