Finite nuclei to nuclear matter: a leptodermous approach

• Published in: Physics reports 1999-10, Vol.319 (3), p.85-144
• Main Authors: Satpathy, L., Maheswari, V.S.Uma, Nayak, R.C.
• Format: Article
• Language: English
• ISSN: 0370-1573; 1873-6270
• DOI: 10.1016/S0370-1573(99)00011-3

The liquid drop model (LDM) expansions of energy and incompressibility of finite nuclei are studied in an analytical model using Skyrme-like effective interactions to examine, whether such expansions provide an unambiguous way to go from finite nuclei to nuclear matter, and thereby can yield the saturation properties of the latter, from nuclear masses. We show that the energy expansion is not unique in the sense that, its coefficients do not necessarily correspond to the ground state of nuclear matter and hence, the mass formulas based on it are not equipped to yield saturation properties. The defect is attributed to its use of liquid drop without any reference to particles as its basis, which is classical in nature. It does not possess an essential property of an interacting many-fermion system namely, the single particle property, in particular the Fermi state. It is shown that, the defect is repaired in the infinite nuclear matter model by the use of generalized Hugenholtz–Van Hove theorem of many-body theory. So this model uses infinite nuclear matter with well defined quantum mechanical attributes for its basis. The resulting expansion has the coefficients which are at the ground state of nuclear matter. Thus a well defined path from finite nuclei to nuclear matter is found out. Then using this model, the saturation density 0.1620 fm −3 and binding energy per nucleon of nuclear matter 16.108 MeV are determined from the masses of all known nuclei. The corresponding radius constant r 0 equal to 1.138 fm thus determined, agrees quite well with that obtained from electron scattering data, leading to the resolution of the so-called ‘ r 0-paradox’. Finally a well defined and stable value of 288±20 MeV for the incompressibility of nuclear matter K ∞ is extracted from the same set of masses and a nuclear equation of state is thus obtained.