  A one dimensional Fermi mixture with delta--interaction is investigated in
the limit of extreme imbalance. In particular we consider the cases of only one
or two minority Fermions which interact with the Fermi-sea of the majority
Fermions. We calculate dispersion relation and polaron mass for the minority
Fermions as well as equal time density-density correlators. Within a cluster
expansion we derive an expression for the effective interaction potential
between minority Fermions. For our calculations we use a reformulation of the
exact wave functions, originally obtained by Yang and Gaudin by a nested Bethe
ansatz, in terms of determinants.
