Abstract
The linear term proportional tojN Zj in the nuclear symmetry energy (Wigner energy) is obtained in a model that uses isovector pairing on single particle levels from a deformed potential combined with a ~ 2 interaction. The pairing correlations are calculated by numerical diagonalization of the pairing Hamiltonian acting on the six or seven levels nearest the N = Z Fermi surface. The experimental binding energies of nuclei with N Z are well reproduced. The Wigner energy emerges as a consequence of restoring isospin symmetry.
Highlights
The nuclear ground state energy, E(N, Z), as a function of the proton number (Z) and neutron number (N) or atomic mass number (A = N + Z) is very well described by the celebrated empirical mass formula: E(N, Z) = EV + ES + EC + EP + EA + EW + ES HELL. (1)The first four terms account for the volume, surface, coulomb and pairing
The “kinetic”part accounts for the Pauli principle, which requires the nucleons to occupy higher single particle levels with increasing asymmetry |N − Z|
We have studied a model based on single particle levels in a deformed potential, isospin conserving isovector monopole pairing, and a schematic "symmetry interaction" proportional to T 2
Summary
Modern mean field approaches reproduce the ground state energies very well, except the Wigner energy, which has to be added as an ad-hoc phenomenological term This means that the physics behind the Wigner energy is not taken into account by present mean field theories. In a series of papers, Jänecke and coworkers [10] (and earlier work cited therein) demonstrated that the global N−, Z− dependence of the binding energies, including the Wigner term and the inversion of the T = 0 and T = 1 states in odd-odd N = Z nuclei with A > 40, can be well understood in terms of the competition between the familiar pair gap ∆ and a symmetry energy term of the form T (T + 1). In the present work we put this qualitative interpretation on a microscopic foundation, which will allow us to make predictions how the Wigner energy depends on deformation (inclusive fission), on angular momentum and on temperature
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