Bethe-Weizsäcker and Liquid Drop Model formulas and nuclear symmetry energy

The efficiency of different binding energy formulas derived from the Bethe-Weizsäcker formula and Liquid Drop Model including or not the curvature energy, the Wigner term and the charge exchange correction term has been determined by a least square fitting procedure to the experimental atomic masses of 2286 nuclei verifying [Formula: see text] and [Formula: see text] and the one standard deviation uncertainty on the mass lower than 170 MeV. The different fits lead to a volume coefficient [Formula: see text] of around 15.5 MeV, a surface energy coefficient [Formula: see text] of around 17-18 MeV, a relative sharp charge radius r 0 of 1.22-1.23 fm and a proton form factor correction [Formula: see text] to the Coulomb energy of around 0.9 MeV. The different adjustments lead to very different values of the coefficients of the Wigner term, the curvature energy, the constant term and exchange Coulomb term. For the isotopes verifying [Formula: see text]100 several Liquid Drop Model formulas can lead to root mean square deviations [Formula: see text] between the theoretical and experimental energies of only 0.39 MeV. An analytic formula, [Formula: see text], extracted from the liquid drop model energy, is proposed to determine the macroscopic nuclear symmetry energy, neglecting the pairing, Wigner and shell effects. For the [Formula: see text]Ca, [Formula: see text]Sn, [Formula: see text]Pb and [Formula: see text]U nuclei the coefficient [Formula: see text] of the Bethe-Weizsäcker formula takes on the values 19.5, 21.3, 22.2, and 22.4 MeV while the macroscopic symmetry energy is respectively 26, 71, 207 and 274 MeV.