or by assuming explicit density dependence for the meson-nucleon couplings. Of course, at the energy characteristic for nuclear binding and low-lying excited states, the heavy-meson exchange ( σ , ω , ρ ) is just a convenient representation of the effective nuclear interaction. 

Since the exchange of heavy mesons is associated with short-distance dynamics that can- not be resolved at low energies, as an alternative, the relativistic point-coupling (RMF-PC) model [10, 11] is proposed by using the zero-range point-coupling interaction instead of the meson exchange, i.e., in each channel (scalar-isoscalar, vector-isoscalar, scalar-isovector, and vector-isovector) meson exchange is replaced by the corresponding local four-point (contact) interaction between nucleons. Analogously, in the case of contact interactions, the medium effects can be taken into account by including higher-order (nonlinear coupling) interac- tion terms or by assuming a density dependence of strength parameters for the coupling interactions. 

In recent years, the RMF-PC model has attracted more and more attentions due to the following advantages. Firstly, it avoids the possible physical constrains introduced by explicit usage of the Klein-Gordon equation to describe mean meson fields, especially the fictitious σ meson. Secondly, it is possible to study the role of naturalness [12, 13] in effective theories for nuclear structure related problems. Thirdly, it provides more opportunities to investigate its relationship to the nonrelativistic approaches [14]. Finally, it is relatively easy to study the effects beyond mean-field for the nuclear low-lying collective excited states. 

In practical application of the RMF-PC model, the most widely used nonlinear cou- pling parameterizations include PC-LA [10] and PC-F1 [11]. PC-LA is determined by the ground-state observables of $^{16}$O, $^{88}$Sr, and $^{208}$Pb. Due to the explicit omission of the pairing interaction, the pairing effects are not included in the fitting procedure. Moreover, the test for naturalness in Ref. [12] shows that only six of the nine coupling constants are natural. As an improvement, PC-F1 is optimized to observables of 17 spherical nuclei including open- shell nuclei, and the pairing correlation is considered through a standard BCS approach in the fitting procedure. Furthermore, all the coupling constants of PC-F1 are turned out to be natural [11]. However, the isospin dependence of binding energy given by PC-F1 along either the isotopic or the isotonic chains deviates from the data remarkably. 

Recently, a density-dependent parametrization DD-PC1 is proposed from the equation of state (EOS) of nuclear matter and the masses of 64 axially deformed nuclei in the mass regions A ≃ 150 − 180 and A ≃ 230 − 250 [15]. Although it reproduces the binding energies, 

