  A detailed study of the anharmonicity-induced resonances caused by the
coupling of center-of-mass and relative motion is presented for a system of two
ultracold atoms in single-well potentials. As has been confirmed
experimentally, these inelastic confinement-induced resonances are of interest,
since they can lead to coherent molecule formation, losses, and heating in
ultracold atomic gases. A perturbative model is introduced to describe the
resonance positions and the coupling strengths. The validity of the model and
the behavior of the resonances for different confinement geometries are
analyzed in comparison with exact numerical ab initio calculations. While such
resonances have so far only been detected for large positive values of the
$s$-wave scattering length, it is found that they are present also for negative
$s$-wave scattering lengths, i. e. for attractive interactions. The possibility
to coherently tune the resonances by a variation of the external confinement
geometry might pave the way for coherent molecule association where magnetic
Feshbach resonances are inaccessible.
