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

Abstract

The status of the theoretical research on the compressional modes of finite nuclei and the incompressibility K ∞ of nuclear matter, is reviewed. It is argued that the recent experimental data on the Isoscalar Giant Monopole Resonance (ISGMR) allow extracting the value of K ∞ with an uncertainity of about ± 12 MeV. Non-relativistic (Skyrme, Gogny) and relativistic mean field models predict for K ∞ values which are significantly different from one another, namely ≈ 220-235 and ≈ 250-270 MeV respectively. It is shown that the solution of this puzzle requires a better determination of the symmetry energy at, and around, saturation. The role played by the experimental data of the Isoscalar Giant Dipole Resonance (ISGDR) is also discussed.

New Kohn-Sham density functional based on microscopic nuclear and neutron matter equations of state

“…The effect of pairing correlations is, in general, more important in the constrained calculations than in the scaled ones, especially in half-filled major shell nuclei, as is the case of 112 Table VIII. To compare with the experiment, we use as representative the constrained energyĒ 1 , which estimates the energy of the centroid in a very precise way at least in the case of the nucleus in 208 Pb [95,96] (see also [90,91]. This is a general tendency shown by mean-field models of different nature [97,98]. Several attempts to explain this behavior have been proposed in the past such as the density dependence of the incompressibility in neutron rich-matter [99] or different types of pairing interactions [48].…”

“…The fact that effective mean-field models with different values of K 0 can give similar values of E GMR in 208 Pb has actually been a general puzzle in the past (see Refs. [95,97] and references therein). The reason is the proportionality between E GMR and the square root of K 0 found by Blaizot [100] for Gogny forces.…”

Relativistic chiral Hartree-Fock description of nuclear matter with constraints from nucleon structure and confinement

“…What come out from these calculations is a globally too large value of the compressibility modulus K even there is some numerical uncertainty in its determination and even if its extraction is not free of ambiguity in the context of relativistic theories [21]. Removing the contact term (i.e., taking the Orsay prescription for the treatment of the pion and tensor rho exchanges) has the advantage to reduce the C parameter to a value closer to the lattice estimate, C ≃ 1.25, but the incompressibillity K still increases by about 15 − 20 MeV.…”

Giant resonances inTi46,48

“…The E1 strength consists of two components which have been observed from light to heavy nuclei [5,8,22,23,28]. The high-energy component is the compression mode [29], while it has been suggested that the low-energy component might be a "toroidal giant dipole mode" [30,31]. The E1 distributions were fit with two Gaussians and parameters obtained are shown in [4].…”