Nuclear matter compressibility from isoscalar giant monopole resonance

Abstract

We examine the status of the nuclear matter compressibility K"obtained from experimental data of the strength distribution of the giant monopole resonance in nuclei and employing a least-squares fit to a semiempirical expansion of the nucleus compressibility E~in A ' '. We present arguments indicating that all the coefficients of this expansion must be determined by a fit to the data. In our analysis we have used the entire data set, correcting for systematic energy differences between data sets measured in different laboratories, and applying the same criteria to all sets in extracting the uncertainties. Contrary to recent statements by Sharma and collaborators, we find that the present complete data set is not adequate to limit the range of IC" to better than about a factor of 1.7 (200 to 350 MeV).

Theoretical understanding of the nuclear incompressibility: where do we stand?

“…(4) is statistically meaningless and would indeed leave K ∞ basically undetermined (fits which lead to 100 MeV or 400 MeV may be equally acceptable). Similar conclusions were reached by S. Shlomo and D. Youngblood [6]. Therefore, we will not discuss these so-called "macroscopic approaches" to K ∞ .…”

Scaling calculation of isoscalar giant resonances in relativistic Thomas–Fermi theory

“…In Figure 1 we have drawn further RETF results for the excitation energy of the monopole mode in comparison with the experimental data listed in Ref. [49], as a function of the number of particles of the nucleus. (The RTF calculation displays basically the same trend as the RETF results.)…”

“…One should note, however, that the scaling calculation provides a prediction for the mean value or centroid of the excitation energy of the resonance. To establish a relation between the incompressibility K ∞ and the experimentally measured energies of the monopole mode the most favourable situation is met in heavy nuclei, where the strength of the GMR is less fragmented than in medium and light nuclei [42,49]. If we take into account the excitation energies of 116 Sn, 144 Sm and 208 Pb, according to Table 1 Refs.…”

Isoscalar giant resonances inCa48

“…This property of the ISGMR and the variation of the incompressibility coefficient with neutron number can also be used to extract the asymmetry coefficient K sym in the EOS of asymmetric NM [5]. In the analysis of experimental data on E 0 it is common to employ two approaches: (i) Adopting a semiclassical model to relate E 0 to an incompressibility coefficient K A of the nucleus and carry out a Leptodermous (A -1/3 ) expansion of K A , similar to a mass formula, to parameterize K A into volume, surface, symmetry and Coulomb terms [6,7]; and (ii) Carrying out microscopic calculations of the strength function S(E) of the ISGMR, within a fully self consistent mean-field based random phase approximation (RPA), with specific interactions (see the review [8]) and comparing with the experimental data. The values of K NM and K sym , are then deduced from the interaction that best reproduced the experimental data.…”

“…In early analysis of the experimental data on the ISGMR [7,9,10], the Leptodermous expansion of K A was used to determine the volume, surface, symmetry and coulomb coefficients. However, the limitations of such an analysis were pointed out in Refs.…”