  A dispersion integral is derived that allows one to relate directly (spin
dependent) $\Lambda N$ invariant mass spectra, measured in a large-momentum
transfer reaction such as $pp\to K^+p\Lambda$ or $\gamma d\to K^+n\Lambda$, to
the scattering length for elastic $\Lambda N$ scattering. The involved
systematic uncertainties are estimated to be smaller than 0.3 fm. This estimate
is confirmed by comparing results of the proposed formalism with those of
microscopic model calculations. We also show, for the specific reaction $pp\to
K^+\Lambda p$, how polarization observables can be used to separate the two
spin states of the $\Lambda N$ system.
