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Amplitudes for the reaction $\pi^-p\to \Lambda K^0$ are reconstructed fromdata on the differential cross section $d\sigma/d\Omega$, the recoilpolarization $P$, and on the spin rotation parameter $\beta$. At low energies,no data on $\beta$ exist, resulting in ambiguities. An approximation using $S$and $P$ waves leads only to a fair description of the data on $d\sigma/d\Omega$and $P$; in this case, there are two sets of amplitudes. Including $D$ waves,the data on $d\sigma/d\Omega$ and $P$ are well reproduced by the fit but now,there are several distinct solutions which describe the data with identicalprecision. In the range where the spin rotation parameter $\beta$ was measured,a full and unambiguous reconstruction of the partial wave amplitudes ispossible. The energy-independent amplitudes are compared to the energydependent amplitudes which resulted from a coupled channel fit (BnGa2011-02) toa large data set including both pion and photo-induced reactions. Significantdeviations are observed. Consistency between energy dependent and energyindependent solutions by choosing the energy independent solution which isclosest to the energy dependent solution. In a second step, the {\it known}energy dependent solution for low (or high) partial waves is imposed and onlythe high (or low) partial waves are fitted leading to smaller uncertainties.

Study of ambiguities in $\pi^-p\to \Lambda K^0$ scattering amplitudes