Delayed alignments in theN=Znuclei84Moand

Abstract

The yrast band of the NϭZ nucleus 84 Mo has been extended up to the 10 ϩ state. Its moment of inertia varies smoothly up to this state ͑rotational frequency 0.6 MeV͒. The new data confirm the systematic delay of the particle alignment frequency in NϭZ nuclei with respect to the neighboring NϾZ nuclei, which has been suggested as a signature of the neutron-proton pairing interaction. Projected shell model calculations performed for the heaviest NϭZ nuclei studied so far, 84 Mo and 88 Ru, predict that the confirmation of a possible enhancement of the neutron-proton residual interaction requires the observation of still higher spins in these nuclei.The study of NϭZ nuclei is expected to give the most relevant information about the properties of the neutronproton (np) pairing interaction. In NϭZ nuclei, neutrons and protons occupy the same shell-model orbitals, and thus can have the largest probability to interact with each other. It has been thought that the np pairing interaction may be the cause of the delayed rotational alignments in the even-even NϭZ nuclei in the Aϳ80 mass region, and this line of research has been actively pursued. The recently observed alignment delays in 72 Kr, 76 Sr, and 80 Zr may be such examples ͓1,2͔.Experimentally, the main difficulty in extending the study of NϭZ nuclei at higher spins is their population with extremely low cross sections in a small number of available reactions. Progress in the development of large ␥-ray arrays and associated ancillary detectors, as well as refinements of the data processing techniques, allowed recent advance in the knowledge of the heaviest NϭZ nuclei in general, and of their high spin behavior in particular. Theoretically, it has been suggested that the behavior of the moment of inertia of an NϭZ nucleus with increasing spin ͑rotation͒ would be particularly relevant in this respect. Different pairing fields (nn, pp, and np) respond differently to the Coriolis forces. The enhancement of the np interaction in NϭZ nuclei has in general an effect to sustain the pairing field under rotation. The real situation is, however, rather complicated, due to the fact that the spin alignment is also sensitively influenced by other factors such as deformation. Theoretical calculations, most of which are still schematic, have reached various conclusions on the role of different np interactions ͓3-9͔.To date, consistent delays in the crossing frequencies ͑due to alignment of the g 9/2 particles͒ in the ground state bands have been observed for the NϭZ Kr ͓1,2͔, Sr, Zr ͓2͔, and Ru ͓10͔ nuclei. The strongest effect has been observed in 72 Kr where a very delayed crossing has been located at 0.85 MeV ͓2͔. In 76 Sr there is a discernible effect which indicates a broad crossing shifted to 0.62 MeV ͑compared to Ϸ0.55 in NϾZ isotopes ͓2͔͒, while for 80 Zr ͓2͔ and 88 Ru ͓10͔ the observations indicate again a delay but the crossing has not been located yet. In this chain of NϭZ nuclei, 84 Mo is the only one which has not been studied at spins higher than 4ប.In view of the pre...

Tensor part of the Skyrme energy density functional. II. Deformation properties of magic and semi-magic nuclei

“…A rotational band built on the ground state has been observed up to a spin of 10 [62, 63, 64], although it appears to be slightly distorted at low spin. The large deformation of states in 80 Zr is also supported by the observation of strongly-coupled rotational bands built on several Nilsson states in adjacent 79 Y [65] and 81 Zr [66]. In the absence of information on the transition matrix elements at the bottom of the band in 80 Zr, however, it is not ruled out that spherical and deformed configurations might coexist in this nucleus and are strongly mixed in the ground state.…”

Overview of neutron–proton pairing

“…Based on their experiments, de Angelis et al [121], Fisher et al [127], and Mȃrginean et al [128] (and previous work cited therein) suggested a delay of the crossing between the g-band and s-band in the N = Z=36, 38,40,42, 44 nuclides as compared to the N = Z + 2 isotopes. These results initiated several theoretical studies.…”

“…Sun [128] showed that an increase of the strength of the QQ interaction (cf. Section 2.5) increases the crossing frequency too, which is expected, because a stronger QQ force enlarges the deformation.…”

“…After the year 2000, the rotational response of N ≈ Z nuclei was investigated in a number of experimental papers [127][128][129][130][131][132][133][134][135][136][137][138]. Afanasjev , Frauendorf and Ragnarsson [139,140], interpreted the rotational bands of the nuclides with A = 58 − 80 in a systematic way, where E 0 (ω, C) was calculated by means of cranked relativistic Hartree+Boguljubov (CRHB) [141].…”

Shape change induced by g 9/2 rotational alignment in 84,86Mo

“…For example, 84 Zr, 84,86 Mo are well deformed [1,2] and 88 Mo is best described as a combination of collective and single-particle excitations [3], whereas N > 46 nuclei 90,92 Mo are described by spherical shell model [4]. For more collective Z, N 44 nuclei, the evolution in collectivity, strong shape-driving effect from g 9/2 orbit and residual proton-neutron interaction act together, resulting in various interesting phenomena in this mass region, such as superdeformation in 84 Zr [1], γ-vibrations in 80,82 Sr [5,6] and delayed alignment in 84 Mo and 80 Zr [7,8]. Experimentally, with the development of γ-ray detectors, the measurement of high spin states in 84,86 Mo [7,9,10] makes it possible to test detailed theoretical calculations concerning their deformations.…”