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On the liquid drop model mass formulae and charge radii

Abstract : An adjustment to 782 ground state nuclear charge radii for nuclei with N,Z $\ge$ 8 leads to $R_0=1.2257~A^{1/3}$~fm and $\sigma =0.124$~fm for the charge radius. Assuming such a Coulomb energy $E_c=\frac {3}{5} {e^2Z^2}/{1.2257~A^{\frac {1}{3}}}$, the coefficients of different possible mass formulae derived from the liquid drop model and including the shell and pairing energies have been determined from 2027 masses verifying N,Z $\ge$ 8 and a mass uncertainty $\le $ 150 keV. These formulae take into account or not the diffuseness correction ($Z^2/A$ term), the charge exchange correction term ($Z^{4/3}/A^{1/3}$ term), the curvature energy, the Wigner terms and different powers of $I=(N-Z)/A$. The Coulomb diffuseness correction or the charge exchange correction term plays the main role to improve the accuracy of the mass formulae. The different fits lead to a surface energy coefficient of around 17-18~MeV. A possible more precise formula for the Coulomb radius is $R_0=1.2332A^{1/3}+{2.8961}/{A^{2/3}}-0.18688A^{1/3}I$~fm with $\sigma =0.052$~fm.
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G. Royer, R. Rousseau. On the liquid drop model mass formulae and charge radii. The Fifth International Conference on Exotic Nuclei and Atomic Masses ENAM'08, Sep 2008, Ryn, Poland. pp.541-545, ⟨10.1140/epja/i2008-10745-8⟩. ⟨in2p3-00436884⟩

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