On the linear term in the nuclear symmetry energy

The nuclear symmetry energy calculated in the RPA from the pairing plus symmetry force Hamiltonian with equidistant single-nucleon levels is for mass number A=48 approximately proportional to T(T+1.025), where T is the isospin quantum number. An isovector character of the pair field assumed to produce the observed odd-even mass staggering is essential for this result. The RPA contribution to the symmetry energy cannot be simulated by adding to the Hartree-Fock-Bogolyubov energy a term proportional to the isospin variance in the Bogolyubov quasiparticle vacuum, and there are significant corrections to the approximation which consist in adding half the isocranking angular velocity. The present calculation employs a smaller single-nucleon level spacing than used in a previous investigation of the model.Comment: 8 pages. Minor inaccuracies and misspellings correcte

Wigner energy, odd-even mass staggering and the time-odd mean-fields

Various properties of single-particle Hartree-Fock ground-state solutions in $N\sim Z$ nuclei are investigated. The emphasis is on a role of single-particle mean-field in odd-even mass staggering. It is shown that, unlike in traditional scenario originating from the Fermi gas or macroscopic models, the symmetry energy contribution to odd-even mass staggering is nearly cancelled by the contribution coming from the average level density. It allows to construct indicators probing both pairing as well as mean-field components to the odd-even mass staggering. The impact of the single-particle Hartree-Fock field on Wigner energy and residual $pn$ interaction in odd-odd nuclei is also discussed.Comment: Plenary talk presented at Nuclear Structure'98, Gatlinburg, Tenn., USA, August 10-15, 1998, 10 LaTeX pages, 7 postscript figures, styles: aipproc2.sty, epsfig.st

Probing effective nucleon-nucleon interaction at band termination

Low-energy nuclear structure is not sensitive enough to resolve fine details of nucleon-nucleon (NN) interaction. Insensitivity of infrared physics to the details of short-range strong interaction allows for consistent, free of ultraviolet divergences, formulation of local theory at the level of local energy density functional (LEDF) including, on the same footing, both particle-hole as well as particle-particle channels. Major difficulty is related to parameterization of the nuclear LEDF and its density dependence. It is argued that structural simplicity of terminating or isomeric states offers invaluable source of informations that can be used for fine-tuning of the NN interaction in general and the nuclear LEDF parameters in particular. Practical applications of terminating states at the level of LEDF and nuclear shell-model are discussed.Comment: Invited talk presented at the XIII Nuclear Physics Workshop, Kazimierz Dolny, Sept. 27 - Oct. 1, Poland; submitted to IJMP

Mass number dependence of the Skyrme-force-induced nuclear symmetry energy

The global mass dependence of the nuclear symmetry energy and its two basic ingredients due to the mean-level spacing and effective strength of the isovector mean-potential is studied within the Skyrme-Hartree-Fock model. In particular, our study determines the ratio of the surface-to-volume contributions to the nuclear symmetry energy to be ~1.6 and reveals that contributions due to mean-level spacing and effective strength of the isovector mean-potential are almost equal after removing momentum-dependent effects by rescaling them with isoscalar and isovector effective masses, respectively.Comment: Presented at the XII Nuclear Physics Workshop, Kazimierz Dolny, Poland, September 21-25, 200