On the nuclear curvature energy

Abstract

Abstract. The curvature energy coefficient of the nuclear mass formula ac is first calculated for the model case of a Fermi gas bounded by an external Woods-Saxon potential. The semiclassical theory of Wigner and Kirkwood is used and ac is found to be close to zero. It is, however, shown that this low value is due to the lack of selfconsistency of the potential. When available, the results of the model compare very well with quantal values and the extrapolation to the spherical cavity (billiard) checks with the value for ac known from the Balian-Bloch theory. Second, the selfconsistent case is generalised to finite range forces. No indication is found that this modifies the fact that all theoretical values for ac are larger than about 7 MeV which is an order of magnitude above the empirical value.

Variational Wigner–Kirkwood ℏ Expansion

“…[17] for relativistic mean field models, where spin-orbit fluctuations also may become important with some particular parametrizations of the relativistic interaction). Thus, Table I shows that the influence of Friedel oscillations is small [16]. On the other hand, the DFT calculations (same table) present a significant difference with the quantal result, even when they are performed to fourth order in .…”

“…The analysis of semi-infinite matter embedded in an external potential [16] shows that the Friedel oscillations are of small amplitude in the particle and kinetic energy densities, and of negligible effect on the surface and curvature energies. Thus, the semiclassical calculations are expected to give a good approximation to these energies.…”

“…For a Skyrme force [1], the constrained energy density E=e&*\ of a symmetric system can be written as 16) where the interacting energy density U is a function of the density \ and its derivative \$=d\Âdz. It is given by means of the parameters t 0 , t 1 , t 2 and t 3 that define the Ginzburg Landau functional U(\, \$):…”

“Parking-garage” structures in nuclear astrophysics and cellular biophysics

“…1. Reinhard et al [9], see also [10], use a leptodermous (thin-skinned) expansion and density functionals in order to calculate a curvature energy term for Eq. 1 that goes like a curve A 1/3 .…”

Low densities in nuclear and neutron matters and in the nuclear surface

“…Of course, this term cannot be obtained from nuclear matter calculations, and the parameter η has to be considered as a phenomenological one. This energy density functional could be understood within the Kohn-Sham (KS) theory [24] where the finite range Hartree term has been expanded in terms of distributions [25] providing the gradient term and where the bulk BHF energy density basically corresponds to the exchangecorrelation part. In a KS approach based on this functional the hamiltonian density will be…”