Macro-microscopic mass formulae and nuclear mass predictions

Different mass formulae derived from the liquid drop model and the pairing and shell energies of the Thomas–Fermi model have been studied and compared. They include or not the diffuseness correction to the Coulomb energy, the charge exchange correction term, the curvature energy, different forms of the Wigner term and powers of the relative neutron excess I = ( N − Z ) / A . Their coefficients have been determined by a least square fitting procedure to 2027 experimental atomic masses (G. Audi et al. (2003) [1]). The Coulomb diffuseness correction Z 2 / A term or the charge exchange correction Z 4 / 3 / A 1 / 3 term plays the main role to improve the accuracy of the mass formula. The Wigner term and the curvature energy can also be used separately but their coefficients are very unstable. The different fits lead to a surface energy coefficient of around 17–18 MeV. A large equivalent rms radius ( r 0 = 1.22 – 1.24 fm ) or a shorter central radius may be used. An rms deviation of 0.54 MeV can be reached between the experimental and theoretical masses. The remaining differences come probably mainly from the determination of the shell and pairing energies. Mass predictions of selected expressions have been compared to 161 new experimental masses and the correct agreement allows to provide extrapolations to masses of 656 selected exotic nuclei.