Disassociation of a one-dimensional cold molecule via quantum scattering

Motivated by the recent experimental developments on ultracold molecules and atoms, we propose a simplest theoretical model to address the disassociation, reflection and transmission probability of a 1-dimensional cold molecule via quantum scattering. First, we give the Born approximation results in the weak interaction regime. Then, employing the Lippmann-Schwinger equation, we give the numerical solution and investigate the disassociation's dependence on the injection momentum and the interaction strengths. We find that the maximum disassociation rate has a limit as increasing the interaction strengths and injection momentum. We expect that our model can be realized in experiments in the near future.