Similarity of nuclear structure in theSn132andPb208

Abstract

Starting from the striking similarity of proton-neutron multiplets in 134 Sb and 210 Bi, we perform a shell-model study of nuclei with two additional protons or neutrons to find out to what extent this analogy persists. We employ effective interactions derived from the CD-Bonn nucleon-nucleon potential renormalized by use of the V low−k approach. The calculated results for 136 Sb, 212 Bi, 136 I, and 212 At are in very good agreement with the available experimental data. The similarity between 132 Sn and 208 Pb regions is discussed in connection with the effective interaction, emphasizing the role of core polarization effects.PACS numbers: 21.60. Cs, 21.30.Fe, 27.60.+j, 27.80.+w Since its advent more than fifty years ago, the shell model has been the basic framework for understanding the structure of complex nuclei in terms of individual nucleons. Within this model, nuclei around doubly closed shells play a special role. In fact, they yield direct information on the two basic ingredients of the model: singleparticle (SP) energies and matrix elements of the effective interaction. This makes them the best testing ground for realistic shell-model calculations where the effective interaction is derived from the free nucleon-nucleon (N N ) potential.For a long time our knowledge of nuclei with fewvalence particles or holes has been mostly limited to neighbors of stable or long-lived doubly magic 16 O, 40 Ca, 48 Ca, 56 Ni, and 208 Pb. However, during the last decade there has been substantial progress in the experimental study of nuclei far from the stability line, and the development of radioactive nuclear beams is currently giving strong impetus to the study of exotic nuclei around 78 Ni, 100 Sn, and 132 Sn. These new data pose challenging questions about the evolution of the shell structure, as for instance the validity of magic numbers when moving far away from stability and the existence of possible changes in the mean field as well as in the two-body interaction [1,2,3].In this context, nuclei "north-east" of 132 Sn are of special interest, since in recent experiments some peculiar properties have been observed which might be interpreted as the onset of a shell-structure modification (see introductory discussion in [4]). To investigate whether these features really depend on the exoticism of 132 Sn neighbors, we believe that a comparative study of their spectroscopic properties and those of nuclei close to stable 208 Pb is desirable.As is well known, 132 Sn and 208 Pb, which are very differently located with respect to the valley of stability, both exhibit a strong neutron-proton asymmetry and strong shell closures. The existence of a specific resemblance between 132 Sn and 208 Pb regions was pointed out long ago in Ref. [5], where it was noticed that every SP proton or neutron state in the 132 Sn region, characterized by quantum numbers (n l j), has its counterpart around 208 Pb with quantum numbers (n l + 1 j + 1). Based on this resemblance, the discrepancies between experimental and Woods-Saxon SP energies ...

β−decay of the neutron-rich isotope215Pb

“…Monopole energy shifts of single-particle levels have been observed in other mass region [33][34][35] and a similar problem related to an anomalous low-lying 5/2 + state in 135 Sb has been explained by recent shell-model calculations [36]. Similar calculations in the 208 Pb region have been initiated [37]. It will be interesting to compare our recent findings with these or other shell-model calculations.…”

Monopole-optimized effective interaction for tin isotopes

“…[38][39][40][41][42][43][44]) and heavier nuclei around shell closures [40,45,46]. The key to these calculations is a proper description of the monopole channel of the effective interaction [47], which determines the bulk properties of the effective interaction and governs the evolution of the effective singleparticle energies (the mean field) as a function of valence neutron and proton numbers [41,48].…”

Structural Stability and Level Density of Hot Rotating Doubly Magic Isotopes of Calcium

“…It is now established that the dynamic effects of nucleon-nucleon interaction result in the evolution of shell structure and hence the new magic number sequence in drip-line region. Over the last few decades, there is an ongoing argument about the nature of the 54 Ca nucleus [1][2][3]. however, these studies could not reach a common conclusion about the magicity of the 54 Ca nucleus.…”

“…The origin of magic nucleon numbers (2,8,20,28, 50, 82 and 126) had been explained by the phenomenon of complete filing of nucleus shells. The nuclei having magic numbers of nucleons in comparison with neighboring isotopes and isotones have more spherical shape, more nucleon separation energy values, specific scheme of lowest energy levels -resonance liked behavior of the first 2 + state energies E(2 + 1 ), ratios E(4 + 1 )/E(2 + 1 ), quadrupole deformation parameters δ.…”