Effects of nonintegrability on stabilization of Feshbach molecules in atom waveguides

Deactivation of broad quasi-one-dimensional dibosonic molecules is analyzed. Within integrable Lieb-Liniger-McGuire (LLMG) model an exact expression does not demonstrate suppression of the deactivation at low collision energies. Solution of Faddeev equations demonstrates that when a Feshbach resonance lifts the symmetry of the LLMG model the deactivation becomes suppressed. This effect shows a way for formation of a stable gas of dibosonic Feshbach molecules.