  The energy spectrum, atom-dimer scattering length, and atom-trimer scattering
length for systems of three and four ultracold atoms with $\delta$-function
interactions in one dimension are presented as a function of the relative mass
ratio of the interacting atoms. The Born-Oppenheimer approach is used to treat
three-body ("HHL") systems of one light and two heavy atoms, as well as
four-body ("HHHL") systems of one light and three heavy atoms. Zero-range
interactions of arbitrary strength are assumed between different atoms, but the
heavy atoms are assumed to be noninteracting among themselves. Both fermionic
and bosonic heavy atoms are considered.
