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We consider a few-boson system confined to one dimension with a singledistinguishable particle of lesser mass. All particle interactions are modeledwith $\delta$-functions, but due to the mass imbalance the problem isnonintegrable. Universal few-body binding energies, atom-dimer and atom-trimerscattering lengths are all calculated in terms of two parameters, namely themass ratio: $m_{\text{L}}/m_{\text{H}}$, and ratio$g_{\text{HH}}/g_{\text{HL}}$ of the $\delta$-function couplings. Wespecifically identify the values of these ratios for which the atom-dimer oratom-trimer scattering lengths vanish or diverge. We identify regions in thisparameter space in which various few-body inelastic process becomeenergetically allowed. In the Tonks-Girardeau limit ($g_{\text{HH}}\rightarrow\infty$), our results are relevant to experiments involving trapped fermionswith an impurity atom.

Few-Boson Processes in the Presence of an Attractive Impurity under One-Dimensional Confinement