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New effective $\Lambda N$ interactions are proposed for the density dependentrelativistic mean field model. The multidimensionally constrained relativisticmean field model is used to calculate ground state properties of eleven known$\Lambda$ hypernuclei with $A\ge 12$ and the corresponding core nuclei. Basedon effective $NN$ interactions DD-ME2 and PKDD, the ratios $R_\sigma$ and$R_\omega$ of scalar and vector coupling constants between $\Lambda N$ and $NN$interactions are determined by fitting calculated $\Lambda$ separation energiesto experimental values. We propose six new effective interactions for $\Lambda$hypernuclei: DD-ME2-Y1, DD-ME2-Y2, DD-ME2-Y3, PKDD-Y1, PKDD-Y2 and PKDD-Y3 withthree ways of grouping and including these eleven hypernuclei in the fitting.It is found that the two ratios $R_\sigma$ and $R_\omega$ are correlated welland there holds a good linear relation between them. The statistical errors ofthe ratio parameters in these effective interactions are analyzed. These neweffective interactions are used to study the equation of state of hypernuclearmatter and neutron star properties with hyperons.

New effective interactions for hypernuclei in density dependent relativistic mean field model