On the liquid drop model mass formulae and charge radii

An adjustment to 782 ground-state nuclear charge radii for nuclei with N, Z >= 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) = 3/5e(2) Z(2)/1.2257 A(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 >= 8 and a mass uncertainty <= 150 keV. These formulae take into account or do 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 play 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.