Continuous medium model of atomic nuclei

In this model, the nucleus is considered as a continuous medium with variable nucleon densities, rho/sub p/ and rho/sub n/ . The energy of the system is expressed by the formula: E[rho/sub n/,rho/sub p/] = ∫][-a1 +a2 (rho-rho0)2/rho20 +a3 ( rho/sub n/-rho/sub p/)2/rho20]] rho0 +[a4-a5 ( rho-rho0)2/rho20 -a6 ( rho/sub n/-rho/sub p/)2/rho20]Vertical Bara grad rho0 Vertical BardvVertical Bardv +e2/2 ∫ ∫ rho/sub p/(1) rho/sub p/(2)/Vertical Barr1 -r2Vertical Bar dv1dv2(1-0.7636z/sup -2/3/), where rho0 = (t/4πa3)[1+exp(r-R)/a]-1 is a reference density which is assumed to be the average density of an ideal nucleus with N = Z and without Coulomb interactions. The binding energy and the density distributions of a nucleus were determined from the condition deltaE = 0. The parameters were determined by fitting the nuclear masses and the general behavior of nuclear charge distributions. Their preliminary values are: a = 0.528 fm, t = 0.3, a1 = 16.1027 MeV, a3 = 26.583 MeV, a4 = 15.19 MeV, a6 = 14.62 MeV, a2 = (1/2)a3, a5 = (1/2)a6. With this set of parameters, together with Myers and Swiatecki's formula for shell corrections and pairing energies, the experimental nuclear masses can be reproduced within 5 MeV and the nuclear root mean square radius within a few percents. These constants probably could further be improved by fitting other nuclear properties. With this new mass formula, the empirical mass difference between mirror nuclei can be reproduced to within 4% (for A> or =20). This is a substantial improvement over the liquid drop model. A theory of nuclear giant multipole resonance was developed by this model. Preliminary calculation on the giant dipole resonance yields rather promising results