The nonrelativistic limit of the relativistic point coupling model

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We relate the relativistic finite range mean-field model (RMF-FR) to the point-coupling variant and compare the nonlinear density dependence. From this, the effective Hamiltonian of the nonlinear point-coupling model in the nonrelativistic limit is derived. Different from the nonrelativistic models, the nonlinearity in the relativistic models automatically yields contributions in the form of a weak density dependence not only in the central potential but also in the spin–orbit potential. The central potential affects the bulk and surface properties while the spin–orbit potential is crucial for the shell structure of finite nuclei. A modification in the Skyrme–Hartree–Fock model with a density-dependent spin–orbit potential inspired by the point-coupling model is suggested.