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A one dimensional Fermi mixture with delta--interaction is investigated inthe limit of extreme imbalance. In particular we consider the cases of only oneor two minority Fermions which interact with the Fermi-sea of the majorityFermions. We calculate dispersion relation and polaron mass for the minorityFermions as well as equal time density-density correlators. Within a clusterexpansion we derive an expression for the effective interaction potentialbetween minority Fermions. For our calculations we use a reformulation of theexact wave functions, originally obtained by Yang and Gaudin by a nested Betheansatz, in terms of determinants.

Effective interaction in an unbalanced Fermion mixture