Nuclear matter saturation density: From finite nuclei to infinite matter

Abstract

The accuracy of Hartree-Fock (HF) calculations of the average density$\bar \rho$ in the core of atomic nuclei is studied by a comparison with selected experimental data. It is shown that the scattering of extrapolated HF values for the saturation densityρ _∞ obtained with various effective forces is largely due to a bad fit of many HF forces to experimental data. However, even after correcting the current parametrisations, an uncertainty remains for the value ofρ _∞, due to a correlation between the trends of$\bar \rho$(A) and the compression modulusK, which is reflected in the extrapolation toA=∞.

Using a generalised Skyrme functional, we show that this correlation is a particular case of a more general relation between$\bar \rho$(A) and the distribution of the binding energy between the inner and outer parts of the nuclear surface. Indications are given on possible improvements of the HF force by the inclusion of density- and momentum-dependent terms, supporting a value of ρ∞≈0.158 fm⁻³ as well as in improved agreement between HF and droplet core densities.

The relation of HF results with macroscopic models is discussed in Sect. 5, showing the rôle played by exponential contributions, but also suggesting that dilation/compression effects exist, which are not taken into account in the usual energy density and droplet models.