Shell-model calculations and realistic effective interactions

Abstract

A review is presented of the development and current status of nuclear shell-model calculations, in which the two-body effective interaction between valence nucleons is derived from the free nucleon-nucleon potential. The significant progress made in this field within the last decade is emphasized, in particular as regards the so-called Vlow-k approach to the renormalization of the bare nucleon-nucleon interaction. In the last part of the review, we first give a survey of realistic shell-model calculations from early to present days. Then, we report recent results for neutron-rich nuclei near doubly magic Sn-132, and for the whole even-mass N = 82 isotonic chain. These illustrate how shell-model effective interactions derived from modern nucleon-nucleon potentials are able to provide an accurate description of nuclear structure properties

Role of Three-Nucleon Forces in Neutron-Rich Nuclei Beyond 132Sn

“…We have employed the experimental SP energies available from the 133 Sb and 133 Sn data [25], in order to evidence the role of the cutoff on the monopole term. As for the proton 2s 1/2 orbital, the SP energy has been taken as the empirical value in [19].…”

“…As mentioned in the Introduction, we derive the shell-model effective hamiltonians within the framework of the time-dependent degenerate linked-diagram expansion [19].…”

“…This is a smooth potential which preserves exactly the on-shell properties of the original V NN and is suitable for being used directly in nuclear structure calculations [19].…”

Evolution of single-particle states beyond132Sn

“…In this Hamiltonian, the single-particle energies are taken from experiment while the two-body effective interaction is derived within the framework of perturbation theory [11,12] starting from the CD-Bonn N N potential [13] renormalized by way of the V low−k approach [14]. Some details on the calculation of this twobody interaction can be found in [7].…”

In-beam γ -ray spectroscopy of low- and medium-spin levels in Po211

“…The interaction between the valence nucleons determine, for the most part, the properties of the levels in a nucleus while the other nucleons often form an inert core. And now with the advent, during the past decade, of more realistic shell-model calculations [1] and the improved roles of genuine and effective three-body forces for heavy nuclei, the prospects of future explorations seem promising. The best available testing ground for shell-model calculations in the heavy-element region is near the doubly magic 208 Pb nucleus.…”