A CONTINUOUS MEDIUM MODEL OF ATOMIC NUCLEI

Abstract：

In this model, the nucleus is consiered as a continuous medium with variable nucleon densities, ρ_p and ρ_n. The energy of the system is expressed by the formula:

where ρ_o=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 δE=0.The parameters were determined by fitting the nuclear masses and the general behavior of unclear 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 MeY, a₂=1/2 a₂, a₅=1/2 a₆. With this set of parameters, together with Myers and Swiatecki's formulae for shell corrcctions and pairing energies, the experimental nuclear masses can be reproduced wi thin 5 MeV and the nuclear mean wqare root radius within a few percent. 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 within 4% (for A≥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.