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

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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):

[EQUATION]

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

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

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

[EQUATION]

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

[EQUATION]

with the one-particle potential [FORMULA]:

[EQUATION]

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

[EQUATION]

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

[EQUATION]

where [FORMULA] denotes the one-particle energy:

[EQUATION]

Hint: [FORMULA] 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, [FORMULA], can be derived over the thermodynamic derivatives:

[EQUATION]

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

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

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© European Southern Observatory (ESO) 1999

Online publication: October 4, 1999
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