Reduction of a quantumn-body problem to an (n−1)-body problem

The Hamiltonian of a translationally invariant $n$-body system is reduced to that of $n-1\mathrm{}$ bodies in the field of a fixed force center by a canonical transformation. This may be interpreted as a transformation to an accelerated coordinate system with origin on one of the particles. All recoil effects are contained in effective masses and additional momentum-dependent interactions. This representation is expected to be useful in scattering and reaction calculations. Its application to the reaction ${\mathrm{D}}^{+}$ + H → D + ${\mathrm{H}}^{+}$ is discussed as an example.