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 .
This leads to the following single particle energy u (Strobel et al. 1999):
In the Eqs. (A3), (A4), and (A5) denotes the Fermi-Dirac distribution function (see Fig. A1 as an example) of a baryon with isospin ():
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.
© European Southern Observatory (ESO) 1999
Online publication: October 4, 1999