Microscopic structure of low-lying0+states in deformed nuclei

Abstract

Recent high resolution (p, t) experiments have established the existence of a large number of low-lying excited 0 + levels in the deformed 158 Gd [1] and, later on, in some actinide nuclei [2] and 168 Er [3]. The number of 0 + states detected in 168 Er is particularly large, the levels below 4 MeV amounting to about 22 [4]. The distribution pattern of the two-nucleon transfer transition strengths shows that one single 0 + state is strongly populated in all nuclei, with the exception of 168 Er where the strength is fragmented into several small peaks.All theoretical studies performed so far have been confined to 158 Gd. The first was a phenomenological investigation [5], which shows that the extended (sdpf ) interacting boson model (IBM) can account for a large fraction of the detected 0 + states. The (sdpf ) IBM analysis points out the importance of the octupole degrees of freedom.In order to account for all detected states and to gain a detailed information on their properties, it is necessary to adopt microscopic approaches. The first calculation of this kind was performed in the framework of the projected shell model (PSM) [6] adopting a restricted space spanned by two and four quasiparticle states. Including the latter states was crucial for covering the whole spectrum. The calculation reproduces well all the energy levels and yields very small E2 decay strengths for the corresponding states.An extensive study of the 0 + states in 158 Gd was carried out recently [7], within the quasiparticle-phonon model (QPM) [8]. Energies, E2 and E0 transition strengths as well as two-nucleon transfer spectroscopic factors were computed and investigated. It came out that an appreciable fraction of the 0 + states in 158 Gd has large or dominant twophonon components, mostly built out of collective octupole phonons, in agreement with the IBM results [5]. The calculation has also confirmed the PSM prediction [6] of very weak quadrupole collectivity for all 0 + states. In fact, the 0 + one-phonon states came out to be linear combinations of several pairing correlated two-quasiparticle qq components. These, however, add coherently only in one state. Such a 0 + pairing collective state is strongly populated in (p, t) two-nucleon transfer reactions, in agreement with experiments.In [9] we extend the QPM study to 168 Er and some Th and U isotopes. All these nuclei were explored in the latest (p, t) experiments [2,3,4]. We intend to test if the QPM can account for the huge number of 0 + levels observed in 168 Er [4] and is able to offer a consistent picture of the properties of the 0 + states in deformed nuclei of different regions.Our study shows that it is necessary to go beyond the mean field approximation (RPA) in order to account for the large number of 0 + levels observed in 168 Er. RPA, in fact, generates only 15 0 + states be low 4 MeV. Moreover, according to our QPM calculation, several levels, specially above 3 MeV, correspond to states with appreciable, often dominant, two-phonon components. A few of these states carry to...

0+states and collective bands in228Th studied by the (p,Levon1, Graw2, Hertenberger3 et al. 2013Phys. Rev. C269700View full textAdd to dashboardCite

“…The amplitude Γ n (p, t) includes the transitions between the ground state and the one-and two-phonon components of the wave function. The numerical results of the calculations obtained according to the QPM investigation in the publication [27] are provided to us by A. V. Sushkov [29]. The QPM generates 15 0 + states below 2.5 MeV, in fair agreement with the 17 firmly assigned states.…”

“…The ability of the QPM to describe multiple 0 + states (energies, E2 and E0 strengths, two-nucleon spectroscopic factors) was demonstrated for 158 Gd [26]. An extension of the QPM to describe the 0 + states in the actinides [27] was made after our publication on the re-sults of a preliminary analysis of the experimental data [4]. These calculations are used to compare to the present detailed analysis of the experimental data for 228 Th.…”

“…These calculations are used to compare to the present detailed analysis of the experimental data for 228 Th. As for the theoretical basis of the calculations, we refer to the publications [27,28].…”

“…For higher energies admixtures of two quadrupole and two octupole phonons are present in the structure of these states, and for some of the states they became dominant. The relatively modest role of the octupole phonons in the structure of the low energy 0 + states is explained in [27] by the enforcement of the Pauli principle, leading to a spreading of the lowest two octupole phonon components among several QPM 0 + states and pushing them to higher energies. Besides the publication [27], other calculations of the same Dubna group were carried out for a microscopic description of the level structure, and transition rates between excited states in 228 Th, observed in the decay of 228 Pa [7].…”

High-resolution study of excited0+states in200Hg and202Hg

“…This research has allowed a better understanding of the changes the nuclei undergo from the transitional Gd region -over the well-deformed Yb region -to the γ-soft Pt region and further towards the 208 Pb proton-neutron shell closure. The striking high number of low-lying 0 + excitations in the Gd region [4,5] was interpreted [10] as a new signature for shape-phase transitions [11] and large numbers of 0 + states throughout the rare earth region triggered many calculations reproducing the surprisingly high 0 + density [12][13][14][15]. The latest experiments on 192 Pt, 194 Pt [8], and 198 Hg [9] showed a rather smooth decline in 0 + state density towards the proton-neutron shell closure.…”