Instabilities of relativistic mean field models and the role of nonlinear terms

The instability of nuclear matter due to particle-hole excitation modes has been studied in the framework of several relativistic mean-field (RMF) models. It is found that both the longitudinal and the transversal modes depend sensitively on the parameter sets used. The important impact of the vector and vector-scalar nonlinear terms on the stability of both modes is demonstrated. Our finding corroborates the result of previous studies, namely that certain RMF models cannot be used in high-density applications. However, we show that for certain parameter sets of RMF models this shortcoming can be alleviated by adding these nonlinear terms.

Figure 1

Longitudinal (left panels) and transversal (right panels) modes of the instability due to the particle-hole excitation with $q_0=0$ for the SNM and some selected RMF parametrizations. Different depths of the dielectric functions are shown by different colors (gray scales).

Figure 2

Longitudinal scalar ($d_S$), vector ($d_V^L$), and vector-scalar coupling propagators ($d_{\mathit{VS}}^L$) (left panels) and the corresponding contributions to the longitudinal dielectric function (right panels). Here $q=3$ fm is used.

Figure 3

Same as Fig. 2 but with $q=0.5$ fm. Different with other parameter sets that have small regular contributions, contribution of the NL3 and NL-Z parameter sets at certain density scalar propagator exhibit discontinuities (lower left) that leads to the appearance of the large positive $d_V^L{\Pi }_V$ (middle right) and negative $d_S{\Pi }_S$ (lower right) above this density.

Figure 4

Transversal propagators with $q=5$ fm (lower-left panel) and $q=0.5$ fm (upper-left panel) followed by their transversal dielectric functions (right panels).

Figure 5

Unstable longitudinal regimes I for asymmetric nuclear matter using NL3 parameter set with proton fraction equals 0.4 in the left panel and 0.22 in the right panel.