We calculate breathing-mode energies in the scaling model for several parameter sets that are under discussion in nuclear relativistic mean-field theory. The relativistic Hartree approximation is used together with a schematic approach for the surface incompressibility. Empirical data can only be reproduced reasonably with parameter sets that lead to a nuclear matter compressibility modulus not higher than 230 MeV. ͓S0556-2813͑97͒00511-6͔ PACS number͑s͒: 21.60. Jz, 21.30.Fe, 21.65.ϩf, 21.10.Re The relativistic mean-field approach ͑RMF͒ in the form of the nonlinear ϪϪ model is in full practical use for the description of nuclear properties. Despite a well founded field-theoretical background it still has some phenomenological aspects, in particular from the nonlinear terms in its Lagrangian density:The related parameters are fitted mainly to nuclear ground-state properties. Some older approved parameter sets are still under discussion ͓1-3͔ together with more recent ones ͓4,5͔, so that there is a request for convergence of the parameter sets with an overall efficiency as already reached by nonrelativistic Skyrme-Hartree-Fock ͑SHF͒ and Gogny-HF ͑GHF͒ approaches. The latter are still in vogue, e.g., as a reliable basis to extrapolate to exotic nuclei ͓6,7͔, despite their much more phenomenological basis.After some promising attempts no characteristic nuclear property seems to remain that is only describable in the framework of RMF. In principle, spin-orbit effects in nuclei could be such candidates since the spin-orbit energy density in RMF depends on gradients of the meson fields, and in SHF, differently, on the density gradient. This distinction might take effect on the spin-orbit splitting of high-lying single-particle states with the consequence of a change in the shell structure. However, recently, RMF spin-orbit potentials were shown to be reasonably well reproduced also by the Skyrme ansatz ͓8͔.The RMF approach describes the nuclear saturation mechanism realistically as a consequence of a characteristic interplay between scalar and vector meson fields. Thus, small amplitude density oscillations around the saturated ground state are a good testing field for the RMF approach. From its ansatz RMF should be superior to SHF and GHF in the description of breathing modes of nuclei, and, therefore, their RMF investigation should help to determine reliable unique RMF parameters.The present short RMF study of nuclear breathing modes starts from a previous investigation ͓9͔, which was based on the scaling model introduced by Blaizot et al. ͓10,11͔. The main deficiency of this earlier investigation came from the crude treatment of the surface incompressibility with an estimated uncertainty of around 30%. We use now a method that-although based again on a model description of the nuclear compression-does much more take into consideration the dynamics ͓12͔. In particular, it can account for the coupling of bulk and surface vibrations. It has been worked out and used in nonrelativistic dynamics of breathing modes ͓13͔. I...

K, -(300+25)MeV and an appreciable surface coefficient K,-(-750 *SO) MeV. We discuss the implication of this result for the incompressibility K,, of infinite nuclear matter.

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Abstract:We treat a general class of dynamical couplings of the surface to the bulk of a spherical nucleus during isoscalar breathing vibrations.