PHYSICAL REVIEW C 83, 034311 (2011)

High-K four-quasiparticle states in 138 Gd
M. G. Procter,1 D. M. Cullen,1,* C. Scholey,2 P. T. Greenlees,2 J. Hirvonen,2 U. Jakobsson,2 P. Jones,2 R. Julin,2 S. Juutinen,2 S. Ketelhut,2 M. Leino,2 N. M. Lumley,1 P. J. R. Mason,1,† P. Nieminen,2 M. Nyman,2,‡ P. Peura,2 P. Rahkila,2 J.-M. Regis,3 P. Ruotsalainen,2 J. Sar´ n,2 Y. Shi,4 J. Sorri,2 S. Stolze,2 J. Uusitalo,2 and F. R. Xu4 e
Schuster Laboratory, University of Manchester, Manchester M13 9PL, United Kingdom 2 Department of Physics, University of Jyv¨ skyl¨ , FIN-40014 Jyv¨ skyl¨ , Finland a a a a 3 Institut f¨ r Kernphysik, Universit¨ t zu K¨ ln, D-50937 K¨ ln, Germany u a o o 4 Department of Technical Physics, Peking University, Beijing 100871, China (Received 12 November 2010; revised manuscript received 8 February 2011; published 10 March 2011) States above the known K π = 8− 6 µs isomer in 138 Gd have been populated with the 106 Cd(36 Ar,2p2n) reaction at a beam energy of 180 MeV at the University of Jyv¨ skyl¨ , Finland. The recoil-isomer tagging technique was a a utilized to correlate delayed γ -ray decays, detected in the GREAT focal plane spectrometer, with prompt decays measured in the JUROGAM II spectrometer at the target position. The lifetime of the K π = 8− isomeric state has been remeasured as 6.2(2) µs. Two high-lying strongly coupled bands have been established with K π 12− . Potential-energy surface calculations, in conjunction with g factor measurements, reveal that they are built upon four-quasiparticle structures comprising two-quasineutron plus two-quasiproton conﬁgurations. The short half-life or lack of hindrance for the decays from these four-quasiparticle band-head states is reasoned to be a consequence of increased triaxial deformation and mixing due to the high density of states relative to the lower two-quasiparticle 6-µs isomeric state. DOI: 10.1103/PhysRevC.83.034311 I. INTRODUCTION PACS number(s): 21.10.Re, 23.20.Lv, 23.35.+g, 27.60.+j
1

The study of isomeric nuclear states provides information to interpret intrinsic single-particle nuclear conﬁgurations. The presence of isomers can result from a multitude of structural effects that lead to a hindrance in the measured transition probabilities when compared with theoretical single-particle estimates [1]. Neutron-deﬁcient rare-earth nuclei have been shown to exhibit a collection of isomeric states. These are established to predominantly result from changes in nuclear deformations between different quasiparticle conﬁgurations: shape isomers, as well as the hindrances related to large variations in the total angular momentum projections of axially symmetric deformed states: K isomers. In particular, the midshell N = 74 isotones provide several examples of long-lived K isomers. Systematic studies of the isotones, 132 Ce [2,3], 134 Nd [4], 136 Sm [5,6], 138 Gd [7,8], and 140 Dy [9,10] have assigned low-lying isomeric states to two-quasineutron [514]9/2− ⊗[404]7/2+ conﬁgurations with an angular momentum projection of K π = 8− . These isomeric states are observed to decay back to the ground-state rotational bands at a rotational frequency in the region of the ﬁrst h11/2 proton alignment [11]. These band crossings result in the introduction of admixtures of nonzero K values into the ground-state sequence to the extent that in 138 Gd the 8+ member of the

On Leave at Department of Physics, University of Jyv¨ skyl¨ , a a FIN-40014 Jyv¨ skyl¨ , Finland. a a † Present address: Department of Physics, University of Surrey, Guildford GU2 5XH, United Kingdom. ‡ Present address: Department of Physics, University of Helsinki, FIN-00014 Helsinki, Finland. 0556-2813/2011/83(3)/034311(11)

*

ground-state band is calculated to consist of approximately 8% of the K = 8 conﬁguration [7]. Such band mixing is one explanation behind the trend in measured hindrances per degree of K forbiddenness observed across the N = 74 isotones, where the reduced hindrance is established to decrease with increasing mass. Another possible contribution to the isomer hindrance lies in the change in shape between the isomeric and ground-state structures and the effect of triaxial degrees of freedom. For instance, a second, fragmented decay path out of the 8− isomeric state was recently identiﬁed in 132 Ce [3]. The K π = 8− isomer was deduced to have an element of triaxial deformation and an appreciable amount of γ softness. The identiﬁcation of the underlying single-particle conﬁguration of isomeric states, such as those identiﬁed in the neutron-deﬁcient N = 74 isotones, usually requires an understanding of the γ -ray transitions that feed the isomeric state. The measurement of γ -ray intensity branching ratios I (M1)/I (E2) above an isomeric state allows a comparison to be made between experimental and theoretical g factors for all of the possible quasiparticle conﬁgurations around the Fermi surface. However, strongly coupled bands above isomeric states are often weakly populated because they are nonyrast. This can make it difﬁcult to isolate them from the vast number of decays associated with fusion-evaporation reactions. The work presented in this paper has utilized the recoil-isomer tagging technique, which has proven successful in analyzing states built upon isomeric conﬁgurations in nuclei in the rare-earth area of the nuclear chart [8,12–16]. This technique was ﬁrst used in 138 Gd to correlate prompt and delayed transitions across a 6-µs isomeric state [7,8]. The high selectivity and sensitivity of this method allowed the weakest of transitions associated with a K π = 8− isomer to be identiﬁed in the prompt spectra. In addition, higher-lying
©2011 American Physical Society

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PHYSICAL REVIEW C 83, 034311 (2011)

prompt rotational structures were observed and assumed to arise from four-quasiparticle conﬁgurations, which fed into the known K π = 8− isomeric state [8]. In the present experiment, the higher statistics collected have resulted in the extension of the K π = 8− band and have linked in the higher-lying four-quasiparticle states. The experimentally measured properties of these states, g factors, angular distributions, and aligned angular momenta, have been compared with theoretical potential-energy surface (PES) calculations to assign underlying single-particle conﬁgurations to these multiquasiparticle states. The higher-lying fourquasiparticle states do not appear to show any hindrance in the measured transition strengths. This lack of hindrance may suggest that at higher spins, the prolate, near axially symmetric shape associated with the lower-lying K π = 8− isomeric state is lost. The presence of triaxial deformation makes the assignment of multiquasiparticle states to speciﬁc conﬁgurations difﬁcult; indeed, different conﬁgurations have been assigned to what at ﬁrst glance appear to be analogous bands across the lower-mass even-even isotones [2,4,6]. The validity of K as a good quantum number with triaxially deformed shapes is important to being able to fully understand the structure of multiquasiparticle states. A theoretical framework that encompasses triaxial degrees of freedom is essential to be able to examine these structures. Alternatively, the lack of isomerism for the decay from higher-lying four-quasiparticle structures may also be the result of statistical mixing of states with the same spin and parity [17]. Since these high-spin four-quasiparticle structures lie at high excitation energies, the density of nuclear states is greater than at energies where the two-quasiparticle K π = 8− states are typically observed. This larger density of states is expected to increase the probability for decay [17].

counter (MWPC) at the entrance to two double-sided silicon strip detectors (DSSDs) [22] into which the recoiling nuclei were implanted. Conditions imposed on the time of ﬂight (TOF) between the MWPC and the DSSD and the measured energy loss in the MWPC provided a method to distinguish the beamlike from targetlike nuclei. The GREAT planar and clover germanium detectors were used to detect delayed γ rays emitted after implantation. The planar strip detector had an absolute efﬁciency of ≈30% at 100 keV [21] and was ideally suited to the detection of low-energy γ -ray transitions from isomeric states. Events were time stamped by a 100-MHz clock through the triggerless total data readout (TDR) acquisition system [23]. Data were collected for off-line sorting with the GRAIN software package [24]. The data were sorted into two-dimensional spectra (matrices) and three-dimensional spectra (cubes) for analysis with the UPAK [25] and RADWARE [26] software suites, respectively. A two-dimensional, asymmetric matrix of prompt γ -ray transitions against correlated delayed γ rays was initially constructed. The prompt decays were correlated with both a recoil implantation in the DSSD and a γ ray detected in either the focal planar or clover detectors of GREAT within 20 µs after a recoil implantation. This time condition was based upon the prior knowledge of the half-life of the isomeric state in 138 Gd, measured to be 6(1) µs [7]. The matrix was background subtracted in time, using the period 0–20 µs prior to the arrival of an event in the DSSD to remove any contamination from γ -ray transitions depopulating longer-lived isomeric states or β decays from previously implanted recoils. Angular distributions were measured for several of the new γ -ray transitions in 138 Gd identiﬁed in this work. This was achieved by sorting the recoil-isomer-tagged data into the four separate rings of the JUROGAM II spectrometer. The measured intensities at each angle θ , with respect to the beam axis, were ﬁtted with Legendre polynomials of the form W (θ ) = A0 + A2 P2 cos(θ ) + A4 P4 cos(θ ), (1)

II. EXPERIMENTAL METHODS AND DATA ANALYSIS

Excited states were populated in 138 Gd via the Cd(36 Ar,2p2n)138 Gd reaction. The K130 cyclotron at the Accelerator Laboratory of the University of Jyv¨ skyl¨ was a a used to accelerate an 36 Ar8+ beam at an energy of 180 MeV onto a 1-mg/cm2 106 Cd foil located at the center of the JUROGAM II γ -ray spectrometer [18]. The beam current averaged ∼5 particle-nA (pnA) over an approximate running time of 44 h. A total of 3×109 recoil-gated prompt events were recorded, with 1×106 prompt events correlated with 138 Gd decays at the focal plane. In this reaction, 138 Gd was populated with a relative cross section of ∼6%, with 138 Eu (∼41%),137 Sm (∼16%), 138 Sm (∼12%), and 139 Gd (∼8%) populated to a larger extent. Prompt decays were detected in the JUROGAM II γ -ray spectrometer, comprising 39 Compton-suppressed germanium detectors (15 EUROGAM Phase 1 type detectors and 24 clover detectors). The total photopeak efﬁciency of JUROGAM II was 6% at 1332 keV. Recoiling fusion-evaporation residues were separated from beamlike particles by the Recoil Ion Transport Unit (RITU) gas-ﬁlled recoil separator [19,20] and were transported to the GREAT focal-plane spectrometer [21]. The GREAT spectrometer comprised a multiwire proportional
106

adopting the formalism outlined by Yamazaki [27]. Theoretically calculated distributions were compared with the experimental data points in order to determine the value of the A2 coefﬁcient. The inclusion of the A4 coefﬁcient in the theoretical I = 1 distributions was used to reveal the presence of any quadrupole mixing through the observation of the mixing-ratio parameter δ. However, the limited number of JUROGAM II detector rings only allowed the sign of δ to be determined and not its absolute value.
III. RESULTS

A previous study of states built above the K π = 8− isomer in Gd by Cullen et al. [8] was able to establish the sequence of γ rays up to the 12− state in band 1. However, due to low statistics, assignments were based upon consideration of energy sums, intensities, and branching ratios. That work was also able to tentatively identify transitions that appeared to belong to higher-lying rotational bands in 138 Gd from comparisons with the lower-mass even-even nuclei. However, without coincidence analysis, these transitions, assigned to 138 Gd, were not able to be placed in the decay scheme.
138

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PHYSICAL REVIEW C 83, 034311 (2011)

FIG. 1. Partial level scheme of states above and below the K π = 8− isomer in 138 Gd, showing the four-quasiparticle bands identiﬁed from recoil-isomer tagging in the present work. The widths of the arrows are proportional to the intensity of the transition, with the white component of each arrow indicating the calculated internal conversion component.

The new 138 Gd level scheme deduced in this work is shown in Fig. 1. For simplicity, only the ground-state band sequence up to the 8− isomer has been included. (The full level scheme of 138 Gd can be found in Ref. [11].) The new level scheme above the K π = 8− isomeric state has been considerably extended in excitation energy and spin from the previous work [8], with the identiﬁcation of two new (higher-K) four-quasiparticle bands that have been linked into the known K π = 8− band 1. Table I contains the spectroscopic information for all of the γ rays established in this work. Following the recoil-isomer tagging method outlined in Ref. [8], a series of gated matrices were constructed for analysis. Gating on the energies of known delayed transitions depopulating the K π = 8− isomer allowed the observation of the correlated prompt decays above the isomeric state. A sum of prompt spectra gated on all ﬁve delayed ground-state band transitions (221-, 384-, 489-, 556-. and 583 keV) is shown in Fig. 2(a), and the delayed spectrum resulting from a sum of gates on the known prompt transitions (396-, 416-, 428-, 433-. and 402 keV) is shown in Fig. 2(b). The high level of statistics observed in the isomer-tagged prompt

spectra allowed the construction of a recoil-isomer-tagged prompt γ -γ coincidence matrix, where only prompt coincident γ rays associated with a delayed isomeric transition were included. Finally, in order to fully examine the structure of decays depopulating the isomeric state, a delayed γ -γ matrix was constructed from delayed transitions observed in both the planar and clover detectors combined. Figure 3 shows a set of prompt spectra obtained from setting gates in the recoil-isomer-tagged prompt-prompt γ -γ matrix. Figure 3(a) shows the spectrum resulting from a single gate on the prompt 396-keV transition feeding the K π = 8− isomer in band 1. The nonobservation of the 811-keV peak, as observed in the total projection in Fig. 2(a), conﬁrms the placement of the 811-keV transition to be parallel to the 396-keV γ ray. The higher-lying transitions observed in the previous study [8] can all be seen, including several previously unidentiﬁed transitions. The K π = 8− band 1 has been extended from the previous work by the addition of the 402- and 834-keV γ rays. These were placed at the top of the band based upon

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TABLE I. Prompt γ -ray energies, intensities, initial and ﬁnal spins, angular distribution coefﬁcients, and mixing ratio signs for transitions above the K π = 8− isomer in 138 Gd deduced in this work. The errors associated with the energies and intensities have been calculated from the spread of their distribution observed in a series of spectra gated on various delayed transitions. Eγ (keV) 172.5(2) 204.6(3) 209.6(2) 230.2(2) 253.3(2) 261.3(3) 285.1(2) 299.1(4) 342.2(2) 352.9(2) 366.1(8) 378.9(3) 389.9(7) 395.8(2) 402.2(2) 414.9(9) 416.2(3) 420.4(6) 428.1(2) 433.0(2) 458.6(7) 462.4(2) 514.6(12) 552.8(13) 626.8(8) 651.2(9) 663.0(11) 762.6(8) 780.0(10) 811.1(3) 834.0(2) 842.7(4) 860.8(4) 891.4(7) Iγ 30(1) <5 33(3) 21(2) 31(3) 32(1) 34(3) 15(3) 27(3) 10(3) 6(1) 22(4) 12(2) 100(2) 31(3) 3(2) 57(5) 10(2) 48(6) 28(4) <4 9(6) 11(3) 11(3) 26(3) 12(2) 21(3) 13(5) 9(4) 35(4) 32(5) 48(3) 41(3) <3
π Jiπ → Jf

A2 −0.21(7) −0.28(7) −0.15(8) −0.35(7) −0.55(15) −0.13(4) −0.28+0.04 −0.07 −0.15(4) −0.30(7) −0.49(7) −0.66(6) −0.71(1) −0.56(10) −0.72(10) −0.61(10)

A4 0.02(1) 0.01(1) 0.02(2) 0.02(1) 0.01(1) 0.01(1) 0.01(1) 0.00(1) 0.02(1) 0.01(1) 0.02(1) 0.03(1) 0.01(2) 0.03(1) 0.02+0.03 −0.01

signδ + − + − − + − + + − − − − − −

σL M1/E2 (M1) M1/E2 M1/E2 M1/E2 M1/E2 M1/E2 M1/E2 M1/E2 M1/E2 (M1) M1/E2 (M1) M1/E2 M1/E2 (E2) M1/E2 (M1) M1/E2 M1/E2 (M1) (E2) (E2) (E2) (E2) (E2) E2 (E2) (E2) E2 E2 E2 E2 (E2)

15− → 14− (14− ) → (13− ) (15− ) → (14− ) 16− → 15− (16− ) → (15− ) (14− ) → 13− 17− → 16− (17− ) → (16− ) 18− → 17− (18− ) → (17− ) (20− ) → (19− ) 14− → 13− (19− ) → (18− ) 9− → 8− 13− → 12− (15− ) → (13− ) 10− → 9− (19− ) → 18− 11− → 10− 12− → 11− (13− ) → 12− (16− ) → (14− ) 17− → 15− (17− ) → (15− ) 18− → 16− (18− ) → (16− ) (14− ) → 12− (19− ) → 17− 14− → 12− 10− → 8− 13− → 11− 11− → 9− 12− → 10− (13− ) → 11−

0.38(3)

−0.13(2) −0.05(2) −0.01(1) −0.02+0.01 −0.05 −0.03+0.01 −0.04

0.28(3) 0.15(3) 0.18+0.13 −0.07 0.12+0.11 −0.08

coincidence analysis as well as energy sums and intensity considerations. Angular distribution measurements conﬁrm the tentative dipole and quadrupole assignments proposed in the previous work as well as the new transitions established in this work (see Table I). Figure 4 shows the angular distribution measurements for four of the γ -ray transitions in band 1. A negative sign for the dipole-quadrupole mixing ratio δ in band 1 was deduced from the comparison of theoretical distributions [27] with the experimental data points, with the inclusion of the A4 coefﬁcient in the angular distribution ﬁt. The sign of the mixing ratio measured in this work is consistent with that assumed for states above the K π = 8− isomer in 136 Sm [6]. Figure 3(b) shows a spectrum gated on the prompt 261-keV transition that links band 2 to band 1. The 663-keV γ -ray observed in Fig. 3(a) is not present in Fig. 3(b), which suggests that it belongs to a parallel cascade. The intense I = 1 transitions assigned to this band are clearly seen at low energy; however, the weaker quadrupole crossover γ rays are difﬁcult

to distinguish from the background. They were established to be part of band 2 because they were observed in summed spectra, gated on all of the interband mixed dipole-quadrupole transitions. Angular-distribution measurements performed for the more intense transitions in band 2 (210-, 253-, 299-, and 353-keV) resulted in mixed dipole-quadrupole assignments. The potential quadrupole mixing into the I = 1 transitions was evaluated by comparing the experimental data points with theoretical distributions that included the A4 coefﬁcient. From this comparison it was possible to establish a small negative mixing ratio for each of the measured transitions. Figure 3(c) shows the prompt spectrum resulting from a single gate set on the 253-keV γ ray in band 2. The two transitions linking bands 1 and 2 via the 261- and 663-keV γ rays are both evident in this spectrum, consistent with the placement of the band. The majority of the intensity ﬂow from band 2 to band 1 is established to pass through the 663- and 261-keV γ rays. However, the presence of the (13− ) state in band 2 suggests that band 2 also feeds into band 1 at lower

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