An accurate knowledge of the properties of the nuclear energy surface is important not only for practical reasons (to calculate nuclear masses, and to predict the properties of superheavy elements and nuclei far from the/3-stability line), but also to check and refine nuclear models. The well-known semiempirical formula for the binding energy due to Bethe and Weizsacker [1] has been subjected to a number of refinements and modifications in order to obtain better agreement with experiment [2-10]. The correction terms, introduced from theoretical considerations, fake into account the specific features of the distribution of nucleons in the nucleus (the diffuseness of the boundary, the nonuniformity of the distribution in the inner region, and the difference between the neutron and proton densities) [2-5], the effects of deformation and compressibility of the nuclei [6-10], Coulomb exchange interaction [3, 61, etc. However, because there is no rigorous theory of the nucleus the role of the various correction terms remain unclear. As far as their empirical basis is concerned, the introduction of correction terms into the equation for the binding energy, despite the addition of new parameters, does not lead to any appreciable improvement in the agreement with experiment. Nevertheless, the introduction of purely empirical corrections to the parity and the effects of the shells considerably improves the agreement with experiment [1, 3, 6, 11]. All this stimulated us to try to clarify the features of the structure of the formula for the binding energy, without previous resource to any model representations, and based exclusively on experimental data. It is well lmown that for any fixed mass number A the stability of the isobars falls, while the energy increases the further the nuclei are from the region of stability both on the neutron-excess side and on the proton-excess side. A detailed analysis of the experimental data given in [12-15], shows that within the limits of experimental error the isobar cross sections of the energy surface in the regions between the magic numbers of neutrons and protons are (for nuclei of each of the four types of parity) quadratic parabolas, so that the total energy of a nucleus with mass number A and charge Z can be represented in the form [12-14]

Empirical analysis of the formula for the binding energy of nuclei

Nuclear subshells and an exact equation for the nuclear binding energy

The Coulomb energies of nuclei are calculated on the basis of data from electromagnetic experiments. It is established that the substitution of the Coulomb energies calculated in this way into the formula for the nuclear masses results in loss in quality. On the other hand, the Coulomb energies obtained from the mass formula do not reproduce the nuclear dimensions sufficiently well. It is shown that a consistent description of the binding energies and the nuclear dimensions is possible on introducing the dependence of the mass number in the density parameters of the charge distribution.

V. M. Vymyatnin

Papers

Empirical analysis of the formula for the binding energy of nuclei

Nuclear subshells and an exact equation for the nuclear binding energy

Optimal mass formula and Coulomb energy of nuclei