A relation among the effective nucleon mass, the incompressibility and the effective $\sigma$-meson mass in nuclear matter

A relation among the effective nucleon mass $M^{\ast }$, the incompressibility $K$ and the effective $\sigma$-meson mass $m_{\mathrm{s}}^{\ast }$ in nuclear matter is studied by using the relativistic nuclear model. We found that there is a strong correlation between $M^{\ast }$ and $m_{\mathrm{s}}^{\ast }$, while there is only a weak correlation between $K$ and $m_{\mathrm{s}}^{\ast }$. At the normal density, $m_{\mathrm{s}}^{\ast }$ is smaller than the one at zero density, if $M^{\ast }$ is smaller than 0.8 times of the nucleon mass at zero density. It is also found that the off-shell effective mass ${\mu }_{\mathrm{s}}^{\ast }$ is related directly to $K$ and $M^{\ast }$ at the normal density.