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Results on $\Lambda$ hyperon production are reported for collisions of p(3.5GeV) + Nb, studied with the High Acceptance Di-Electron Spectrometer (HADES) atSIS18 at GSI Helmholtzzentrum for Heavy-Ion Research, Darmstadt. The transversemass distributions in rapidity bins are well described by Boltzmann shapes witha maximum inverse slope parameter of about $90\,$MeV at a rapidity of $y=1.0$,i.e. slightly below the center-of-mass rapidity for nucleon-nucleon collisions,$y_{cm}=1.12$. The rapidity density decreases monotonically with increasingrapidity within a rapidity window ranging from 0.3 to 1.3. The $\Lambda$phase-space distribution is compared with results of other experiments and withpredictions of two transport approaches which are available publicly. None ofthe present versions of the employed models is able to fully reproduce theexperimental distributions, i.e. in absolute yield and in shape. Presumably,this finding results from an insufficient modelling in the transport models ofthe elementary processes being relevant for $\Lambda$ production, rescatteringand absorption. The present high-statistics data allow for a genuinetwo-dimensional investigation as a function of phase space of theself-analyzing $\Lambda$ polarization in the weak decay $\Lambda\rightarrow p\pi^-$. Finite negative values of the polarization in the order of $5-20\,\%$are observed over the entire phase space studied. The absolute value of thepolarization increases almost linearly with increasing transverse momentum for$p_t>300\,$MeV/c and increases with decreasing rapidity for $y < 0.8$.

Lambda hyperon production and polarization in collisions of p(3.5 GeV) + Nb