Making a soft relativistic mean-field equation of state stiffer at high density

We study relativistic mean-field (RMF) models including nucleons interacting with scalar, vector and iso-vector mean fields and self- and cross- mean-field interaction terms. Usually, in such a models the magnitude of the scalar field increases monotonically with the nucleon density, and the nucleon effective mass decreases. We demonstrate that the latter quantity stops to decrease and the equation of state stiffens, provided the mean-field self-interaction potential rises sharply in a narrow vicinity of the values of mean fields corresponding to nucleon densities $n> n_{*}>n_0$, where $n_0$ is the nuclear saturation density. As the result the limiting neutron star mass increases. This procedure offers a simple way to stiffen the equation of state at densities above $n_{*}$ without altering it at densities $n\le n_{0}$. The developed scheme allows an application to neutron stars of the RMF models, which are well fitted to finite nuclei but do not fulfill the experimental constraint on the limiting neutron star mass. The exemplary application of the method to the well-known FSUGold model allows us to increase the limiting neutron star mass from $1.72~M_\odot$ to $M \geq 2.01~M_\odot$.