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The density dependencies of various effective interaction strengths in therelativistic mean field are studied and carefully compared for nuclear matterand neutron stars. The influences of different density dependencies arepresented and discussed on mean field potentials, saturation properties fornuclear matter, equations of state, maximum masses and corresponding radii forneutron stars. Though the interaction strengths and the potentials given byvarious interactions are quite different in nuclear matter, the differences ofsaturation properties are subtle, except for NL2 and TM2, which are mainly usedfor light nuclei, while the properties by various interactions for pure neutronmatter are quite different. To get an equation of state for neutron matterwithout any ambiguity, it is necessary to constrain the effective interactionseither by microscopic many-body calculations for the neutron matter data or thedata of nuclei with extreme isospin. For neutron stars, the interaction withlarge interaction strengths give strong potentials and largeOppenheimer-Volkoff (OV) mass limits. The density-dependent interactions DD-ME1and TW-99 favor a large neutron population due to their weak $\rho$-meson fieldat high densities. The OV mass limits calculated from different equations ofstate are 2.02 $\sim$ 2.81$ M_\odot$, and the corresponding radii are 10.78$\sim$ 13.27 km. After the inclusion of the hyperons, the corresponding valuesbecome 1.52 $\sim$ 2.06 $M_\odot$ and 10.24 $\sim$ 11.38 km.Comment: 28 pages, 10 figure

Density dependencies of interaction strengths and their influences on nuclear matter and neutron stars in relativistic mean field theory