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Speaker |
Rotondo, Michael |
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Co-autors |
Vladimir Popov, Remo Ruffini and She-Sheng Xue |
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Talk Title |
On the gravitational and electrodynamical stability of massive nuclear density cores |
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Abstract |
We present a unified treatment of nuclear density cores recovering the classic results for neutral atoms with heavy nuclei having a mass number $A\approx 10^2$--$10^6$ and extrapolating these results to massive nuclear density cores with $A\approx(m_{\rm Planck}/m_n)^3 \sim 10^{57}$. The treatment consists of solving the relativistic Thomas-Fermi equation describing a degenerate system of $N_n$ neutrons, $N_p$ protons and $N_e$ electrons in beta equilibrium with $N_p=N_e$. The $N_p$ protons are distributed at a constant density within a spherical core of radius $R_c$. A new island of stability is found for $A>A_R = 0.039\left(\frac{N_p}{A}\right)^{1/2}\left( \frac{m_{\rm Planck}}{m_n}\right)^3$. The Coulomb repulsion, screened by relativistic electrons, is balanced by the gravitational self-interaction of the core. In analogy to heavy nuclei they present, near their surface, an overcritical electric field. The relation between $A$ and $N_p$ is given for an arbitrary value of the mass number, and the phenomenological relations for $A< 1.5\cdot 10^{2}$ are obtained as a limiting case. |
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