Astron. Astrophys. 350, 497-512 (1999)

Appendix A: nuclear equation of state

The momentum and density dependent interaction is given by [the upper (lower) sign corresponds to nucleons with equal (unequal) isospin] (Myers & Swiatecki 1990):

The quantities , , and [ with , see (A4)] denote the baryon number density, Fermi momentum, and the kinetic single-particle energy of symmetric nuclear matter at saturation ( denotes the isospin), respectively. The choice leads to a better description of asymmetric nuclear systems, and the behaviour of the optical potentials is improved by the term , where .

The parameter set is given by the most recent adjustment of Myers & Swiatecki (1996, 1998): , , , , , and , which leads to the following properties of symmetric nuclear matter at saturation density ( fm^-3): energy per baryon MeV, incompressibility MeV, symmetry energy MeV and effective nucleon mass .

The potentials radial dependence, g, is chosen to be of Yukawa type. The function is normalized to unity:

This leads to the following single particle energy u (Strobel et al. 1999):

with the one-particle potential :

[ and denote different isospin and the following abbreviations were used: , , , , , , and ] and the baryon number density:

In the Eqs. (A3), (A4), and (A5) denotes the Fermi-Dirac distribution function (see Fig. A1 as an example) of a baryon with isospin ():

where denotes the one-particle energy:

Hint: in Eq. (A6) is not the chemical potential in normal sense, because of the density dependent part in the interaction, for an explanation see Myers & Swiatecki (1990), Appendix A. The chemical potentials of neutrons and protons, , can be derived over the thermodynamic derivatives:

in which f is the free energy per baryon and the rest-mass of neutrons or protons.

Fig. A1. Fermi-Dirac distribution function for the neutrons of the EOS at fm-3. MeV, MeV, , MeV and MeV at the Fermi surface.

© European Southern Observatory (ESO) 1999

Online publication: October 4, 1999
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