Nuclear matter incompressibility from a semi-empirical analysis of breathing-mode energies

Abstract

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.

Relativistic hydrodynamics for heavy-ion collisions. II. Compression of nuclear matter and the phase transition to the quark-gluon plasma

“…the EoS for TA matter in [1]). In contrast to the diagrams for the thermodynamical variables p, T, µ which enter Gibbs' phase equilibrium conditions (15), there is no obvious sign for the mixed phase (such as edges due to the phase boundaries) in the entropy density. The reason is that this quantity is a linear interpolation between s H and s Q (similar to (16,17)) in this phase.…”

“…When fitting the two parameters C 2 V , C 2 S to reproduce the experimental values for the ground state binding energy of infinite nuclear matter, B 0 = 16 MeV, and the ground state density, n 0 = 0.15891 fm −3 [13], the effective mass in the nuclear ground state is M * 0 ≃ 0.543 M which is too small (the experimental value ranges around 0.7 M [14]), and the incompressibility is K 0 ≡ 9 dp/dn| n 0 ≃ 553 MeV which is too large by about a factor of two [15]. To adjust this shortcoming of the model, it was suggested to introduce self-interaction terms, ∼ σ 3 , σ 4 , for the scalar σ meson field in the σ − ω-Lagrangian [16].…”

Leptodermous expansion of finite-nucleus incompressibility

“…It must be stressed that all the considerations of this paper suppose the validity of the scaling model, the limitations of which are discussed in refs. 7,11).…”

A density variational approach to nuclear giant resonances at zero and finite temperature

“…In the case of scaling (described by the excitation operator r'), K, = K, But in the same limit, most Skyrme forces were found [91, 1221 to have approximately K, --K, The above empirical values thus indicate that the breathing mode in nature does not follow the scaling dynamics (as is the case also in our 2-dimensional hydrodynamical model in Section 3.1 .I ) which, in turn, puts in cause the assumption that K, = K, The results of Ref. [96] are therefore not in contradiction with our findings using the conventional family of Skyrme forces. They rather represent a phenomenological parametrization of breathing mode energies which implies that, if one takes the newest experimental data very literally, the last word about the nuclear incompressibility K, has not been told yet.…”

“…An attempt was recently made [96] to fit the newest precision data [93] of GMR energies by Eq. (3.3), using experimental values of (r') and a LDM type expansion of the incompressibility K, of the form K, = K,.+ K,A "' + (higher order terms).…”