B2 Smooth Composition Model

At p > 1013 g cm-3 the nucleon density profiles deviate significantly from the steplike distribution (Chapter 3). Oyamatsu (1993) calculated the local neutron and proton number density distributions within a Wigner-Seitz cell and fitted them in the form nj (r)

where njen, nOut, tj, and Rj are the fit parameters. The parameter tj controls the sharpness of the local density profile, while Rj determines the size of a nucleus. These parameters, as well as the sizes of Wigner-Seitz cells, are presented in Table 6 of Oyamatsu (1993) for several values of the mean baryon number density nb (for spherical and nonspherical nuclei). With increasing nb the profiles become smoother, approaching the limit of uniform matter; therefore, the parameters tj decrease.

Real local density distributions of neutrons and protons are not cut off at a certain distance from the center. Therefore, Rn and Rp can be treated only as convenient fit parameters. Near the bottom of the crust, the local density distribution is rather smooth, and the boundary between the free neutrons and the neutrons bound within the nuclei becomes rather uncertain. On the other hand, while describing properties of neutron star crust, one often uses such quantities as the radii of neutron and proton distributions (rn and rp) and the number of nucleons within a nucleus (A). To determine them, let us consider a nucleus as a combination of imaginary neutron and proton spheres of equivalent radii rn and rp and equivalent neutron and proton densities <n and npn. We define the equivalent radius rj as the radius of the imaginary steplike density distribution that reproduces the mean-square radii (B.4) of the real distribution. In this case rj = [(1 + 2/d)r2]1/2. For the distribution (B.7), the equivalent radii become

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