Finite- to zero-range relativistic mean-field interactions

We study the relation between the finite-range (meson-exchange) and zero-range (point-coupling) representations of effective nuclear interactions in the relativistic mean-field framework. Starting from the phenomenological interaction DD-ME2 with density-dependent meson-nucleon couplings, we construct a family of point-coupling effective interactions for different values of the strength parameter of the isoscalar-scalar derivative term. In the meson-exchange picture this corresponds to different values of the σ-meson mass. The parameters of the isoscalar-scalar and isovector-vector channels of the point-coupling interactions are adjusted to nuclear matter and ground-state properties of finite nuclei. By comparing results for infinite and semi-infinite nuclear matter, ground-state masses, charge radii, and collective excitations, we discuss constraints on the parameters of phenomenological point-coupling relativistic effective interaction.

Figure 1

The equation of state of symmetric nuclear matter (binding energy as function of nucleon density) for the meson-exchange interaction DD-ME2 and four different point-coupling effective interactions (cf. Table ). The insert highlights the EOS in the low-density region.

Figure 2

The density dependence of the isoscalar-scalar coupling ${\alpha }_S$ for the meson-exchange interaction DD-ME2 and the four point-coupling parameter sets (cf. Table ). The differences in the low-density region are emphasized in the insert.

Figure 3

The symmetry energy of nuclear matter as a function of nucleon density, for the meson-exchange interaction DD-ME2 and the four point-coupling parameter sets (cf. Table ). The density dependence below saturation density is shown in the insert.

Figure 4

The deviations (in percentages) between the experimental and theoretical charge radii (upper panel) and binding energies (lower panel) of 12 spherical nuclei, calculated with the meson-exchange interaction DD-ME2 and the four point-coupling parameter sets (cf. Table ).

Figure 5

The RQRPA results for the ISGMR centroid energies $(m_1/m_0)$ of ${}^{90}\mathrm{Zr}$, ${}^{116}\mathrm{Sn}$, ${}^{144}\mathrm{Sm}$, and ${}^{208}\mathrm{Pb}$, calculated with the relativistic DD-ME2 meson-exchange interaction ($K_{\mathit{nm}}=251$ MeV) and with two point-coupling effective interactions: set F ($K_{\mathit{nm}}=250$ MeV) and set G ($K_{\mathit{nm}}=230$ MeV). The theoretical results are compared with data from the TAMU [24, 25, 26] and Osaka [27, 28] compilations.