On the liquid drop model mass formulae and charge radii

An adjustment to 782 ground-state nuclear charge radii for nuclei with N, Z 3 \ge8 leads to R₀ = 1.2257 A^1/3\ensuremath R_0 = 1.2257 A^{1/3} fm and s \sigma = 0.124 fm for the charge radius. Assuming such a Coulomb energy E_c = \frac35 e²Z²/1.2257 A^\frac13\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 3 \ge8 and a mass uncertainty ￡ \le150 keV. These formulae take into account or do not the diffuseness correction ( Z²/A\ensuremath Z^2/A term), the charge exchange correction term ( Z^4/3/A^1/3\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 R₀ = 1.2332A^1/3 + 2.8961/A^2/3 - 0.18688A^1/3I\ensuremath R_0 = 1.2332A^{1/3} + 2.8961/A^{2/3} - 0.18688A^{1/3}I fm with s \sigma = 0.052 fm.