Beyond band termination in 157 Er and the search for wobbling excitations in strongly deformed 174 Hf
High-spin terminating bands in heavy nuclei were first identified in nuclei around Er90. While examples of special terminating states have been identified in a number of erbium isotopes, almost nothing is known about the states lying beyond band termination. In the present work the high-spin structure of 157Er has been studied using the Gammasphere spectrometer. The subject of triaxial superdeformation and ‘wobbling’ modes in Lu nuclei has rightly attracted a great deal of attention. Very recently, four strongly or superdeformed (SD) sequences have been observed in 174Hf and ultimate cranker calculations predict such structures may have significant triaxial deformation. We have performed two experiments in an attempt to 0954-3899/05/101735+06$30.00 © 2005 IOP Publishing Ltd Printed in the UK S1735 S1736 M A Riley et al verify the possible triaxial nature of these bands. A lifetime measurement was performed to confirm the large (and similar) deformation of the bands. In addition, a high-statistics, thin-target experiment was run to search for linking transitions between the SD bands and possible wobbling modes. 1. Beyond band termination in 157Er High-spin terminating bands [1] in heavy nuclei were first identified in nuclei around 158 68 Er90; see [2–5] and references therein, also see [6] for a recent summary of the field. At termination, this nucleus can be considered as a spherical core ( 146 64 Gd82 ) plus 12 (4 protons and 8 neutrons) aligned valence particles which can generate a maximum spin of around 46h̄ at an excitation energy of ≈20 MeV, depending on the specific configuration. To produce higher-spin states, particle–hole excitations of the core are required and the question arises whether these excitations induce collective deformation or whether the nucleus remains oblate or near-oblate? While clear examples of the special terminating states have been identified in a number of erbium isotopes, almost nothing is known about the specific states lying above band termination in isotopes close to the textbook example of 158Er [7, 8]. In this regard, the high-spin structure of 157Er [9] has been studied using the Gammasphere spectrometer [10, 11], containing 102 Ge detectors. A 215 MeV 48Ca beam, provided by the 88-Inch Cyclotron accelerator at the Lawrence Berkeley National Laboratory, was used to bombard two stacked thin self-supporting foils of 114Cd, of total thickness 1.1 mg cm−2. A total of 1.2 × 109 events were collected when at least seven Compton-suppressed Ge detectors fired in prompt coincidence. Approximately 6.5 × 1010 quadruples (γ 4) were unfolded from the data set and replayed into a Radware-format [12] four-dimensional hypercube for coincidence analysis to establish the level scheme. The high-spin level scheme of 157Er deduced from this work is shown in figure 1 and greatly extends the previous work [5]. Bands 1 and 2 were previously established up to the band terminating states at 89/2− and 87/2−, while Band 3 have been extended from the 85/2+ state up to the new terminating state at spin 93/2+. A large number of weak high-energy γ rays feeding these terminating states has been observed in the present data. The multipolarity for a number of these transitions have been measured. In order to understand the nature of the states above band termination, calculations have been performed in the framework of the configuration-dependent, cranked Nilsson–Strutinsky formalism without pairing [6, 9] which is able to treat collective and non-collective states on the same footing. In 157Er, the three fully aligned terminating states at 87/2−, 89/2− and 93/2+ are formed by coupling the π [(h11/2)]16+ proton configuration to the three neutron configurations, ν[(i13/2)(h9/2, f7/2)]55/2−,57/2− and ν[(i13/2)(h9/2, f7/2)]61/2+ , respectively. The favoured way to make higher-spin states for I = 45–55h̄ is to excite protons from the g7/2 and d5/2 orbitals below the Z = 64 shell gap into the 5th and 6th h11/2 orbitals and into the two lowest d3/2 orbitals. A systematic investigation was carried out for ‘core-excited’ proton configurations with 1–4 particles excited across the Z = 64 gap. The lowest 25 proton configurations were then combined with the three favoured neutron configurations given above to generate 75 possible high-spin configurations in 157Er. The resulting structures are predicted to build the yrast states in 157Er up to I ≈ 55h̄. These configurations show little collectivity and terminate at a small oblate deformation ε2 ∼ −0.15. From detailed comparisons between experiment and theory, we conclude only configurations Beyond band termination in 157Er and the search for wobbling excitations in strongly deformed 174Hf S1737 Figure 1. Partial level scheme of 157Er above 30h̄ showing the many transitions feeding the special terminating states at 87/2−, 89/2− and 93/2+. with little or no collectivity are predicted to be low enough in energy to be identified with the experimental levels 1.5–2.5 MeV above the fully aligned terminating states. This is consistent with the fact that no clear discrete collective band structures have been identified in 157Er which is very different to the very high-spin behaviour of 154Dy, see [13] and references therein. 2. The search for wobbling excitations in strongly deformed 174Hf Although triaxial deformation may play a role in describing various nuclear structure phenomena, establishing experimental evidence of stable triaxiality remains a challenge. Perhaps the best evidence of triaxial deformation is the observation of a ‘wobbling’ mode since it is unique to a rotating asymmetric nucleus [1]. Indeed, wobbling excitations have been confirmed in 163Lu [14, 15] for structures based on an i13/2 proton. These bands have been labelled triaxial strongly deformed (TSD). In 174Hf four bands with large moments of inertia were identified, suggesting that they were strongly deformed (SD) [16]. Ultimate cranker (UC) calculations indicated that such structures may exist in TSD minima. Two experiments have been performed in an attempt to verify the possible triaxial nature of these bands. A lifetime measurement was performed to confirm the large (and similar) deformation of the bands. In addition, a high-statistics, thin-target experiment was run to search for linking transitions between the SD bands to provide evidence that some of the bands may be associated with wobbling excitations. The experimental details of these experiments can be found in [17]. The experimental fractional Doppler shift was extracted from a centroid shift analysis [17]. In order to determine the quadrupole moment Qt , computer simulations of the actual decay of the levels with the bands and their sidefeeding were performed with the code FITFTAU [19]. Figure 2 displays the F(τ) data for the four previously known SD bands in 174Hf along with the fits generated by FITFTAU. Large deformation has been established for all four bands with quadrupole moments ranging from Qt = 12.6 to 13.8 eb, see figures 2(a)–(d). The quoted errors are based solely on the uncertainty of determining the centroid energy of the peaks. An additional systematic error of 15–20% should be added to account for the uncertainties in the stopping powers. A new SD band in 173Hf was observed in the thin-target experiment. S1738 M A Riley et al 0.75 0.8 0.85 0.9 0.95 750 90