Few-boson processes in the presence of an attractive impurity under one-dimensional confinement

We consider the universal few-body physics of a single light impurity atom $(L)$ interacting with a few heavier atoms $(H)$ under strict one-dimensional confinement with zero-range interactions. Due to the mass imbalance, the system is non-integrable. All universal properties are specified by the mass ratio $\beta = m_L/m_H$ and the coupling ratio $\lambda = g_{HH}/g_{HL}$, enabling the calculation of few-body ``phase diagrams'' on the $\lambda$-$\beta$ plane. Because the three-body and four-body eigenenergies determine the energy thresholds for inelastic scattering processes involving $HL$, $HHL$ and $HHHL$ collision partners, we are able to partition the $\lambda$-$\beta$ phase space into regions according to whether or not particular inelastic processes are energetically allowed.