# 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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Conference papers

Cited literature [13 references]

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### Citation

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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