On the liquid drop model mass formulae and charge radii

An adjustment to 782 ground-state nuclear charge radii for nuclei with N, Z $ \ge$8 leads to $\ensuremath R_0 = 1.2257 A^{1/3}$ fm and $ \sigma$ = 0.124 fm for the charge radius. Assuming such a Coulomb energy $\ensuremath E_c = \frac{3}{5} e^2Z^2/1.2257 A^{\frac{1}{3}}$ , 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 do not the diffuseness correction ( $\ensuremath Z^2/A$ term), the charge exchange correction term ( $\ensuremath Z^{4/3}/A^{1/3}$ 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 play the main role to improve the accuracy of the mass formulae. The different fits lead to a surface energy coefficient of around 17-18MeV. A possible more precise formula for the Coulomb radius is $\ensuremath R_0 = 1.2332A^{1/3} + 2.8961/A^{2/3} - 0.18688A^{1/3}I$ fm with $ \sigma$ = 0.052 fm