Lifetime measurements of excited states in 163W and the implications for the anomalous B(E2) ratios in transitional nuclei

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Lifetime measurements of excited states in 163W and the implications for the anomalous B(E2) ratios in transitional nuclei © 2019 The Authors. Published version Lewis, M.C.; Joss, D.T.; Sayğı, B.; Page, R.D.; Cullen, D.M.; Barber, L.; Giles, M.M.; Simpson, J.; Al-Aqeel, M.A.M.; Badran, H.; Braunroth, T.; Briscoe, A.D.; Calverley, T.; Dewald, A.; Doncel, M.; Grahn, T.; Greenlees, P.T.; Henrich, C.; Herzáň, A.; Herzberg, R.-D.; Higgins, E.; Hilton, J.; Ilieva, S.; Julin, R.; Juutinen, S.; Keatings, J.; Kröll, T.; Labiche, M.; Mashtakov, K.; Nara Singh, B.S.; Parr, E.; Partanen, J.; Paul, E.S.; Rahkila, P.; Sandzelius, M.; Sarén, J.; Scholey, C.; Siciliano, M.; Spagnoletti, P.; Stolze, S.; Szwec, S.V.; Taylor, M.J.; Uusitalo, J. Lewis, M.C., Joss, D.T., Sayğı, B., Page, R.D., Cullen, D.M., Barber, L., Giles, M.M., Simpson, J., Al- Aqeel, M.A.M., Badran, H., Braunroth, T., Briscoe, A.D., Calverley, T., Dewald, A., Doncel, M., Grahn, T., Greenlees, P.T., Henrich, C., Herzáň, A., . . . Uusitalo, J. (2019). Lifetime measurements of excited states in 163W and the implications for the anomalous B(E2) ratios in transitional nuclei. Physics Letters B, 798, Article 134998-. https://doi.org/10.1016/j.physletb.2019.134998 2019 Physics Letters B 798 (2019) 134998 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Lifetime measurements of excited states in 163W and the implications for the anomalous B(E2) ratios in transitional nuclei M.C. Lewis a, D.T. Joss a,∗, B. Say˘ gı b, R.D. Page a, D.M. Cullen c, L. Barber c, M.M. Giles c, J. Simpson d, M.A.M. Al-Aqeel a,e, H. Badran f, T. Braunroth g, A.D. Briscoe a, T. Calverley a,f, A. Dewaldg, M. Doncel a, T. Grahn f, P.T. Greenlees f, C. Henrich h, A. Herzᡠna,i, R.-D. Herzberg a, E. Higgins a, J. Hilton a,f, S. Ilieva h, R. Julin f, S. Juutinen f, J. Keatings j, T. Kröll h, M. Labiche d, K. Mashtakov j, B.S. Nara Singh c,j, E. Parr a, J. Partanen f, E.S. Paul a, P. Rahkila f, M. Sandzelius f, J. Sarén f, C. Scholey f, M. Siciliano k,l, P. Spagnoletti j, S. Stolze f, S.V. Szwec f, M.J. Taylor m, J. Uusitalo f aDepartment of Physics, Oliver Lodge Laboratory, University of Liverpool, Liverpool L69 7ZE, United Kingdom bFizik Bölümü, Fen Fakültesi, Ege Üniversitesi, Bornova, ˙Izmir, 35100, Turkey cSchool of Physics & Astronomy, Schuster Building, The University of Manchester, Manchester M13 9PL, United Kingdom dUKRI-STFC Daresbury Laboratory, Daresbury, Warrington WA4 4AD, United Kingdom eImam Mohammad Ibn Saud Islamic University (IMISU), Riyadh, 11623, Saudi Arabia fDepartment of Physics, University of Jyvaskyla, Department of Physics, P.O. Box 35, FI-40014, Jyvaskyla, Finland gInstitut für Kernphysik der Universität zu Köln, Zülpicher Strasse 77, D-50937 Köln, Germany hInstitut für Kernphysik, TU Darmstadt, Schlossgartenstr. 9, 64289 Darmstadt, Germany iInstitute of Physics, Slovak Academy of Sciences, SK-84511 Bratislava, Slovakia jSchool of Engineering & Computing, University of the West of Scotland, Paisley, United Kingdom kINFN, Laboratori Nazionali di Legnaro, 35020 Legnaro (Padova), Italy lIrfu/CEA, Université de Paris-Saclay, 91191 Gif-sur-Yvette, France mDivision of Cancer Sciences, School of Medical Sciences, The University of Manchester, Manchester, M13 9PL, United Kingdom a r t i c l e i n f o a b s t r a c t Article history: Received 28 June 2019 Accepted 2 October 2019 Available online 7 October 2019 Editor: D.F. Geesaman Keywords: Mean lifetimes B(E2) reduced transition probabilities Recoil-distance Doppler-shift method Nuclear deformation Gamma-ray Spectroscopy This letter reports lifetime measurements of excited states in the odd-Nnucleus 163W using the recoildistance Doppler shift method to probe the core polarising effect of the i13/2neutron orbital on the underlying soft triaxial even-even core. The ratio B(E2:21/2+→17/2+)/B(E2:17/2+→13/2+) is consistent with the predictions of the collective rotational model. The deduced B(E2) values provide insights into the validity of collective model predictions for heavy transitional nuclei and a geometric origin for the anomalous B(E2) ratios observed in nearby even-even nuclei is proposed. ©2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 1. Introduction The emergence of collective phenomena in atomic nuclei is a central paradigm in many-body quantum physics. The residual interactions between the increasing number of valence protons and neutrons outside closed shells result in low-energy configurations with deformed shapes. The onset of deformation promotes a ge- *Corresponding author. E-mail address: da[email protected] (D.T. Joss). ometry in which one or more axes of rotation become distinct from the nuclear symmetry axis and collective rotational excitations begin to dominate the spectrum of states at low angular momenta [1]. The low-lying excited states in the heavy neutrondeficient nuclei above N=82 reflect the evolution from noncollective excitations in spherical nuclei near the closed shell to collective rotational bands in well-deformed axial rotors near the midshell. The low-lying levels vary smoothly between these two regimes through a transitional region characterised by soft triaxial shapes, https://doi.org/10.1016/j.physletb.2019.134998 0370-2693/©2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 2M.C. Lewis et al. / Physics Letters B 798 (2019) 134998 see for example [2]. A more definitive understanding of collectivity can be obtained from the measurement of B(E2) reduced transition probabilities. In heavy neutron-deficient nuclei, considerable progress has been made through measurements of excited-state lifetimes using Doppler shift methods in conjunction with selective decay correlation techniques [3]. The relationship between level excitation energies and B(E2: 2+→0+) values in the Os [4], W[5] and Pt [6]nuclei with the number of valence nucleons is readily interpreted in terms of collective models. However, ratios of reduced transition probabilities for some even-even transitional nuclides are much lower than expected from the predictions of the rotational model [4–7]. This letter reports the results of lifetime measurements of excited states in the transitional nucleus, 163W. The deduced B(E2) values constrain expectations of collective model predictions for heavy transitional nuclei and suggest a geometric origin for the anomalous B(E2) ratios observed in nearby even-even nuclei. 2. Experimental details Excited states in 163W were populated via the 106Cd(60Ni, 2pn)163W fusion-evaporation reaction in an experiment performed at the University of Jyvaskyla Accelerator Laboratory, Finland. The 60Ni beam bombarded a self-supporting isotopically enriched 106Cd target foil of thickness 1.1 mg/cm2with a Ta support of thickness 1.3 mg/cm2. The Ta foil was placed facing the beam resulting in a bombarding energy of 270 MeV and an initial reaction fragment velocity of v/c=3.1% at the front of the 106Cd target. The target was stretched and mounted in the DPUNS differential plunger device [8]along with a downstream 1.0 mg/cm2Mg degrader, which resulted in a reduction in recoil velocity of fusionevaporation residues to v/c=2.1%. The target-to-degrader distance, x, was changed to allow excited-state lifetimes to be measured using the recoil-distance Doppler-shift (RDDS) technique [3]. Gamma rays emitted at the target position were detected by the JUROGAM II γ-ray spectrometer comprising 15 Eurogam Phase 1-type [9] and 24 Eurogam clover [10] escape-suppressed hyperpure germanium detectors. The velocity-degraded fusion-evaporation residues were transported through the RITU gas-filled separator [11,12] and implanted into the double-sided silicon strip detectors (DSSDs) of the GREAT spectrometer located at the focal plane [13]. A planar double-sided germanium strip detector was mounted behind the DSSDs inside the same vacuum enclosure to detect X rays and low-energy γ rays [13]. Three clover Ge detectors were mounted perpendicular to the DSSDs outside the vacuum chamber to detect higher-energy γrays. All detector signals were timestamped to a precision of 10 nanoseconds by the total data readout data acquisition system [14]. Gamma rays detected at the target and focal-plane positions in delayed coincidence with the implanted recoils were analysed offline with the GRAIN data-analysis package [15]. 3. Results Excited states in 163W were measured in several prior experiments and bands associated with single-quasineutron f7/2, h9/2, and i13/2configurations have been observed [16–18]. A partial level scheme for 163W is displayed in Fig. 1illustrating γ-ray transitions in the νi13/2band and its decay paths to the 7/2− ground state. In the present study, the lifetimes of the yrast 17/2+ and 21/2+states in 163W were measured using the recoil-distance Doppler-shift method [3]. The experiment used 11 different target- to-degrader distances ranging from 30 to 5000 μm. The Phase 1-type detectors used in this analysis were positioned at 158◦(5 detectors) and 134◦(10 detectors) relative to the beam direction, Fig. 1. Partial level scheme showing levels and transitions in the yrast band of 163W and its decay paths to the 7/2−ground state [16,17]. The levels are labelled by their spins, parities, and excitation energies. All energies are stated in keV. The half-life of the 13/2+isomer is taken from reference [17]. which allowed the Doppler-shifted and degraded components of γ-ray transitions to be identified. Lifetimes were extracted using the Differential Decay Curve Method (DDCM) [19], of which two variations were used: a recoil-correlated γ-ray coincidence analysis and an isomer-tagged singles analysis. The recoil-correlated γ-ray coincidence analysis has the advantage of eliminating side feeding to the level of interest. For each distance measured, γrays in delayed coincidence with recoil implantations in the DSSDs were sorted into two separate asymmetric two-dimensional matrices; one consisting of γrays detected at 158◦versus coincident γrays detected either at 158◦or 134◦and the other consisting of γrays detected at 134◦versus coincident γrays detected either at 158◦or 134◦. Gamma-ray coincidences with the fully shifted component of the 555 keV 25/2+→21/2+ transition were projected onto the θ=134◦or 158◦axes of their respective matrices. Typical spectra generated using this method are shown in Fig. 2. These data were analysed using the DDCM for γ-ray coincidences [19,20]. For coincidences demanded with the fully Doppler shifted component (s) of an indirect feeding transition C(with corresponding degraded component d), a level with feeding transition Band depopulating transition Ahas a lifetime given by τ(x)={Cs,Ad}(x)−α{Cs,Bd}(x) d dx{Cs,As}(x)·1 v,(1) where quantities in braces are coincident intensities at target-to- degrader distance x, vis the average recoil velocity and α=α(x)x with α(x)={Cs,Ad}(x)+{Cs,As}(x) {Cs,Bd}(x)+{Cs,Bs}(x),(2) which corrects for differences in measured intensities in the depopulating and feeding transitions. Fig. 3shows the decay curves and lifetimes determined using normalised intensities extracted from the coincidence spectra. The mean lifetime was obtained by a weighted average of the values at each distance within the region of sensitivity. The 13/2+band head is isomeric with a half-life of 154(3) ns and is depopulated via two distinct γ-ray cascades to the ground state [17]. These isomer-delayed γrays may be detected in the GREAT planar and clover detectors at the RITU focal plane and can be used as a selective tag for γ-ray emissions at the target position. The 555 keV γ-ray transition that is used to select the νi13/2 band in 163W in the recoil-correlated γ-ray coincidence analysis is overlapped by the intense 552 keV transition originating from 164W[21], which is a strongly populated exit channel in this reaction. An isomer-decay tagged singles analysis was performed in order to confirm that this contamination in the selecting transition M.C. Lewis et al. / Physics Letters B 798 (2019) 134998 3 Table 1 Measured lifetimes and reduced transition probabilities for excited states in 163W. Eγ (keV) Iπ i→Iπ f (¯ h) Detector angle Recoil-correlated γ-ray coincidences Isomer-tagged singles Average values τ(ps) τ(ps) τ(ps) B(E2)↓(W.u.) 384.1 17/2+→13/2+158◦21.3(30) 134◦21.4(30) 134◦26.5(50) 22(2) 80(8) 506.2 21/2+→17/2+158◦2.3(6) 134◦3.8(7) 3.0(4) 154(23) Fig. 2. Recoil-correlated γγ spectra measured at θ=134◦to the beam axis for (a) the 384 keV transition depopulating and (b) the 506 keV transition feeding the 17/2+state. Coincidences were demanded with the fully Doppler-shifted component of the 555 keV transition detected at the θ=134◦or 158◦positions for all spectra shown. Fits for the fully Doppler-shifted (s) and degraded (d) components are shown by the blue dashed and red dotted lines, respectively, while the total is shown by the black solid line. does not significantly affect the measured lifetime. Recoiling 163W nuclei were selected on the condition that implantations were followed within 0.5 μs by a 102, 377 or 441 keV γray detected in the planar Ge detector or a 377 or 441 keV γray detected in the clover Ge detectors at the RITU focal plane. In a singles analysis, for a level ifed by levels hand feeding the level j, the lifetimes of excited states are given by τ(x)=− Qij(x)−bij  h ([Jhi/Jij])Qhi(x) d dx Qij(x)·1 v.(3) Here Qij(x)=Id ij(x)/(Is ij(x)+Id ij(x)) and Id ij(x) and Is ij(x) are the γ-ray intensities for the degraded and shifted components, respectively, bij is the branching ratio of level iand Jhi, Jij are the relative intensities of respective transitions [19]. In this analysis, the assumption was made that the unobserved feeding of the 17/2+levels has the same time dependence as that of the observed feeding. Fig. 3. DDCM analysis for the 17/2+(left) and 21/2+(right) levels. Top: normalised fully shifted intensity of the depopulating transition measured at θ=134◦. Middle: difference in intensity between the degraded components of the depopulating and feeding transitions. Bottom: lifetimes measured at distances within the region of sensitivity. The solid line indicates the weighted average while the dashed lines are the error bars. The weighted averages of the lifetimes measured using the coincidence and singles analyses are shown in Table 1along with the corresponding B(E2) values, which were calculated using the relation B(E2;Ii→If)=0.0816 E5 γ(1+α)τ,(4) where Iiand Ifare the spins of the initial and final levels, respectively, Eγis the γ-ray energy of the transition in MeV, αis the internal conversion coefficient for the transition [22] and τis the mean lifetime in ps of the emitting state. 4. Discussion Fig. 4(a) compares the B(E2: 17/2+→13/2+) values measured in the odd-AW isotopes with the B(E2: 2+→0+) values in the even-Aisotopes as a function of neutron number. The B(E2) values vary as a function of neutron number with lower values observed in the transitional isotopes above the N=82 closed shell and higher values in the deformed midshell region. The B(E2) values 4M.C. Lewis et al. / Physics Letters B 798 (2019) 134998 Fig. 4. (a) B(E2: 17/2+→13/2+) values for odd-N(circles) and B(E2: 2+→0+) for even-NW isotopes (filled squares). (b) Ratios of B(E2) values for W isotopes. The ratio is B(E2: 21/2+→17/2+)/B(E2: 17/2+→13/2+) for odd-Nisotopes and B(E2: 4+→2+)/B(E2: 2+→0+) for even-Nisotopes. The dashed line is the ratio predicted by the collective rotational model for even-Nisotopes. The measurements for 163W are indicated by red circles. Data are taken from refs. [23,31–41]. for the measured odd-AW isotopes follow the general trend established by the B(E2: 2+→0+) values. This pattern is consistent with the expectations of nuclear models [23]. The ratios of reduced transition probabilities in 166W and other heavy neutron-deficient nuclei have apparently anomalous values that cannot be reproduced in terms of the collective rotational model [4–7]. This is illustrated in Fig. 4(b) which compares the B(E2: 4+→2+)/B(E2: 2+→0+) with the predictions of the collective model [24]. Similarly low ratios are observed in several mass regions of the nuclear chart [25–29]. The even-AN≥94 W isotopes have ratios that are consistent with the theoretical ratio of 1.43. However, the isotope 166W is an excellent example where several excited-state lifetimes have been measured but anomalous B(E2) ratios have been extracted. The B(E2: 4+→2+)/B(E2: 2+→0+) ratio is significantly lower than the theoretical prediction at 0.33(5) [5]. It has been proposed that the W-Os-Pt nuclei undergo a phase transition between non-collective seniority and collective excitations [6]. In nuclei that have low average ground-state deformations such a transition between non-collective low-spin states and collective high-spin states can occur [30]. However, in nuclei such as 166W where the B(E2: 2+→0+) values are in excess of 100 W.u. alternative mechanisms must be considered. In this region, a common feature of even-Anuclei with apparently anomalous B(E2) ratios is that they have ratios of 4+ to 2+excitation energies close to that of a gamma-soft rotor [E(4+)/E(2+)=2.5]. Soft-triaxial nuclear deformations arise due to the spatial density distributions for protons and neutrons at the top and bottom of their shells, respectively or vice versa [42]. In the N∼92 nuclei, γ-soft shapes arise from the competing polarising effects of protons in the high-h11/2orbitals and neutrons in the low-f7/2, h9/2and i13/2orbitals, where is the projection of the single-particle angular momentum on the symmetry axis. This is reflected in the ratio of 4+to 2+excitation energies in the ground-state bands of neutron-deficient W isotopes, which have values close to the γ-soft limit of E(4+)/E(2+)=2.5. The E(4+)/E(2+) ratios for 162W[21], 164W[21] and 166W[43] are 2.25, 2.48 and 2.68, respectively. Furthermore, the signature splitting between the low-spin states of coupled bands in the neighbouring odd-Zisotones is also indicative of γ-soft triaxial shapes [44–46]. A parallel study has measured the lifetimes of low-lying states in 163Ta to confirm its quadrupole and triaxial deformations [47]. The wavefunctions of nuclear states are sensitive to the geometric shapes adopted by nuclei [48]. The B(E2) values calculated in the rotational model depend on the projections of single-particle angular momenta on the symmetry axis. The projection of the total angular momentum on the symmetry axis (K) is a good quantum number for axially deformed nuclei with a unique rotation axis but is ill-defined for soft-triaxial shapes. Therefore, the measured properties of triaxial nuclei may deviate from the predictions of collective rotational models that assume axial symmetry and hence a well-defined K-value. It follows that the resulting B(E2) ratios in odd-AW isotopes should be consistent with the collective model if the odd neutron occupies an orbital that polarises the soft-triaxial core towards an axial prolate shape. The angular momentum of the single-i13/2neutron is directed in a quasi-parallel direction to the core angular momentum and has a small component along the symmetry axis. Thus, the i13/2neutron is expected to have a strong polarising effect on the core due to its spatial orientation in an equatorial orbit. Indeed, the core-polarising influence of the i13/2neutron configurations is apparent in the three-quasiparticle structures of the light Ta isotopes, which are formed by coupling a single h11/2proton to neutron configurations in their underlying W cores [44]. In this work, lifetimes have been measured from both the 17/2+and 21/2+states in the νi13/2band of 163W. Fig. 4(b) compares the present measurements of ratios of reduced transition probabilities with those of the heavier isotopes including 167W, which is currently the only other transitional odd-Aiso- tope for which lifetime measurements have been performed [41]. Highjand low-orbitals in odd-Anuclei are highly susceptible to the Coriolis force and are effectively decoupled from the core rotation [49]. In such cases, the spectrum of excited states is characterised by rotational excitations of the even-even core coupled to angular momentum of the decoupled neutron. For this reason, the B(E2: 21/2+→17/2+)/B(E2: 17/2+→13/2+) ratios extracted for odd-Nisotopes are compared with the theoretical value of 1.43 predicted for the even-even isotopes. A ratio of B(E2: 21/2+→17/2+)/B(E2: 17/2+→13/2+) = 1.93(34) was measured for the isotope 163W, which is within 2σof the theoretical value predicted by the rotational model. The ratio extracted for 167W using the measurements of Li et al. is similarly close to the axial limit. These measurements suggest that there is no anomaly in either 167W or 163W whose core is expected to be closer to the γ-soft limit. These results indicate that rotational collective models are applicable in transitional odd-Anuclei when the occupation of a rotationally aligned high angular momentum orbital restores axial symmetry to an otherwise soft-triaxial even-even core. The anomalous B(E2) ratios observed in even-Anuclei are attributed to soft-triaxial shapes that result in poorly defined Kquantum numbers and perturbed rotational wavefunctions. M.C. Lewis et al. / Physics Letters B 798 (2019) 134998 5 5. Summary The mean lifetimes of the 17/2+and 21/2+states in the νi13/2band of 163W have been measured using the recoil-distance Doppler-Shift method in an experiment using the JUROGAM II γ-ray spectrometer in conjunction with the DPUNS differential plunger device. The ratio of extracted B(E2) reduced transition probabilities is found to be consistent with the predictions of the collective rotational model. This agreement within experimental (2σ) uncertainties suggests that the νi13/2configuration of 163W adopts an axial prolate shape. This is a marked difference from the B(E2) ratios extracted for the nearby even-even nuclei such as 166W. The anomalous B(E2) ratios in 166W and other nearby transitional nuclei are therefore attributed to their γ-soft triaxial shapes for which Kis poorly defined with consequences for nuclear wavefunctions and their dependent B(E2) values. This hypothesis could provide a useful test for the predictions of fully self-consistent mean field models that do not rely on the assumptions made in collective or geometric models. Acknowledgements This work has been supported by the UK Science and Technology Facilities Council under grants ST/P004598/1, ST/L005670/1 and ST/L005794/1; the Scientific and Technological Research Council of Turkey (TUBITAK Project No: 117F508); the EU HORIZON2020 programme “Infrastructures”, project number: 654002 (ENSAR2) and by the Academy of Finland under the Finnish Centre of Excellence Programme (Nuclear and Accelerator Based Physics Programme at JYFL). The UK/France (STFC/IN2P3) Loan Pool and GAMMAPOOL network are acknowledged for the HPGe escapesuppressed detectors of the JUROGAM II array. References [1] A. Bohr, B.R. Mottelson, Nuclear Structure Volume 2: Nuclear Deformation, W. A. Benjamin Inc., New York, USA, 1975. [2] Qiong Yang, Hua-Lei Wang, Min-Liang Liu, Fu-Rong Xu, Phys. Rev. C 94 (2016) 024310. [3] A. Dewald, O. Möller, P. Petkov, Prog. Part. Nucl. Phys. 67 (2012) 786. [4] T. Grahn, et al., Phys. Rev. C 96 (2016) 044327. [5] B. Say˘ gi, et al., Phys. Rev. C 96 (2017) 021301(R). [6] B. Cederwall, et al., Phys. Rev. Lett. 121 (2018) 022502. [7] R.B. Cakirli, R.F. Casten, J. Jolie, N. Warr, Phys. Rev. C 70 (2004) 047302. [8] M.J. Taylor, et al., Nucl. Instrum. Methods Phys. Res., Sect. A 707 (2013) 143–148. [9] C.W. Beausang, et al., Nucl. Instrum. Methods Phys. Res., Sect. A 313 (1992) 37. [10] G. Duchene, et al., Nucl. Instrum. Methods Phys. Res., Sect. A 432 (1999) 90. [11] J. Uusitalo, et al., Nucl. Instrum. Methods Phys. Res. B 204 (2003) 638. [12] J. Saren, J. Uusitalo, M. Leino, J. Sorri, Nucl. Instrum. Methods Phys. Res. A 654 (2011) 508. [13] R.D. Page, et al., Nucl. Instrum. Methods Phys. Res. B 204 (2003) 634. [14] I.H. Lazarus, et al., IEEE Trans. Nucl. Sci. 48 (2001) 567. [15] P. Rahkila, Nucl. Instrum. Methods Phys. Res., Sect. A 595 (2008) 637–642. [16] J. Thomson, et al., Phys. Rev. C 81 (2010) 014307. [17] C. Scholey, et al., Phys. Rev. C 81 (2010) 014306. [18] G.D. Dracoulis, et al., Proceedings of the International Conference of Nuclear Structure at High Angular Momentum, Ottawa, AECL Report No. vol. 2 (1992) 94 (unpublished). [19] A. Dewald, et al., Z. Phys. A 334 (1989) 163. [20] G. Böhm, A. Dewald, P. Petkov, P. von Brentano, Nucl. Instrum. Methods Phys. Res., Sect. A. 329 (1993) 248. [21] D.T. Joss, et al., Phys. Rev. C 93 (2016) 024307. [22] T. Kibédi, T.W. Burrows, M.B. Trzhaskovskaya, P.M. Davidson, C.W. Nestor Jr., Nucl. Instrum. Methods Phys. Res., Sect. A 589 (1992) 202. [23] M. Doncel, et al., Phys. Rev. C 95 (2017) 044321. [24] D.J. Rowe, J.L. Wood, Fundamentals of Nuclear Models: Foundational Models, vol. 1, World Scientific, 2009. [25] D. Hertz-Kintish, L. Zamick, S.J.Q. Robinson, Phys. Rev. C 90 (2014) 034307. [26] M.M. Giles, et al., Phys. Rev. C 99 (2019) 044317. [27] C. Louchart, et al., Phys. Rev. C 87 (2013) 0543902. [28] G. de Angelis, et al., Phys. Lett. B 535 (2002) 93–102. [29] O. Möller, et al., Phys. Rev. C 71 (2005) 064324. [30] J.J. Ressler, et al., Phys. Rev. C 69 (2004) 034317. [31] C.M. Baglin, Nucl. Data Sheets 111 (2010) 1807. [32] C.M. Baglin, E.A. McCutchan, S. Basunia, Nucl. Data Sheets 153 (2018) 1. [33] B. Singh, Nucl. Data Sheets 75 (1995) 199. [34] E. Browne, Huo Junde, Nucl. Data Sheets 87 (1999) 15. [35] J.M. Regis, et al., Nucl. Instrum. Methods Phys. Res., Sect. A 606 (2009) 466. [36] M. Rudigier, et al., Nucl. Phys. A 847 (2010) 89. [37] E.A. McCutchan, Nucl. Data Sheets 126 (2015) 151. [38] B. Singh, Nucl. Data Sheets 130 (2015) 21. [39] C.M. Baglin, Nucl. Data Sheets 111 (2010) 275. [40] C.M. Baglin, Nucl. Data Sheets 99 (2003) 1. [41] C.B. Li, et al., Phys. Rev. C 94 (2016) 044307. [42] Y.S. Chen, S. Frauendorf, G.A. Leander, Phys. Rev. C 28 (1983) 2437. [43] J. Simpson, et al., J. Phys. G 18 (1992) 1207. [44] K. Lagergren, et al., Phys. Rev. C 83 (2011) 014313. [45] M. Sandzelius, et al., Phys. Rev. C 80 (2009) 054316. [46] T.R. Davis-Merry, et al., Phys. Rev. C 91 (2015) 034319. [47] L. Barber, et al., (2019), submitted for publication. [48] G. Alaga, K. Alder, A. Bohr, B.R. Mottelson, Dan. Mat. Fys. Medd. 29 (1955) 1. [49] F.S. Stephens, Rev. Mod. Phys. 29 (1975) 43.