High-K three-quasiparticle isomers in the proton-rich nucleus Nd129

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/ High-K three-quasiparticle isomers in the proton-rich nucleus Nd129 ©2023 American Physical Society Published version Petrache, C. M.; Uusitalo, J.; Briscoe, A. D.; Sullivan, C. M.; Joss, D. T.; Tann, H.; Aktas, Ö.; Alayed, B.; Al-Aqeel, M. A. M.; Astier, A.; Badran, H.; Cederwall, B.; Delafosse, C.; Ertoprak, A.; Favier, Z.; Forsberg, U.; Gins, W.; Grahn, T.; Greenlees, P. T.; He, X. T.; Heery, J.; Hilton, J.; Kalantan, S.; Li, R.; Jodidar, P. M.; Julin, R.; Juutinen, S.; Leino, M.; Lewis, M. C.; Li, J. G.; Li, Z. P.; Luoma, M.; Lv, B. F.; McCarter, A.; Nathaniel, S.; Ojala, J.; Page, R. D.; Pakarinen, J.; Papadakis, P.; Parr, E.; Partanen, J.; Paul, E. S.; Rahkila, P.; Ruotsalainen, P.; Sandzelius, M.; Sarén, J.; Smallcombe, J.; Sorri, J.; Szwec, S.; Wang, L. J.; Wang, Y.; Waring, L.; Xu, F. R.; Zhang, J.; Zhang, Z. H.; Zheng, K. K.; Zimba, G. Petrache, C. M., Uusitalo, J., Briscoe, A. D., Sullivan, C. M., Joss, D. T., Tann, H., Aktas, Ö., Alayed, B., Al-Aqeel, M.A. M., Astier, A., Badran, H., Cederwall, B., Delafosse, C., Ertoprak, A., Favier, Z., Forsberg, U., Gins, W., Grahn, T., Greenlees, P. T., . . . Zimba, G. (2023). High-K threequasiparticle isomers in the proton-rich nucleus Nd129. Physical Review C, 108, Article 014317. https://doi.org/10.1103/PhysRevC.108.014317 2023 PHYSICAL REVIEW C 108, 014317 (2023) High-Kthree-quasiparticle isomers in the proton-rich nucleus 129Nd C. M. Petrache ,1,*J. Uusitalo,2,3A. D. Briscoe,3,2C. M. Sullivan,3D. T. Joss,3H. Tann,2,†Ö. Aktas,4B. Alayed,3 M. A. M. Al-Aqeel,3A. Astier,1H. Badran,2B. Cederwall,4C. Delafosse,2,‡A. Ertoprak,4Z. Favier,1,§U. Forsberg,2, W. Gins,2T. Grahn,2P. T. Greenlees,2X. T. He,5J. Heery,2,¶J. Hilton,2,†S. Kalantan,3R. Li,1P. M. Jodidar,1R. Julin,2 S. Juutinen,2M. Leino,2M. C. Lewis,3J. G. Li,6Z. P. Li,7M. Luoma,2B. F. Lv,6A. McCarter,3S. Nathaniel,3J. Ojala,2 R. D. Page,3J. Pakarinen,2P. Papadakis,8,** E. Parr,3,†† J. Partanen,2,‡‡ E. S. Paul,3P. Rahkila,2P. Ruotsalainen,2 M. Sandzelius,2J. Sarén,2J. Smallcombe,3J. Sorri,9,§§ S. Szwec,2, L. J. Wang,7Y. Wang,5L. Waring,3F. R. Xu,10 J. Zhang,5 Z. H. Zhang,11 K. K. Zheng,6and G. Zimba2 1Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France 2Accelerator Laboratory, Department of Physics, University of Jyväskylä, FI-40014 Jyväskylä, Finland 3Oliver Lodge Laboratory, Department of Physics, University of Liverpool, Liverpool L69 7ZE, United Kingdom 4KTH Department of Physics, Royal Institute of Technology, S-10691 Stockholm, Sweden 5College of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China 6Key Laboratory of High Precision Nuclear Spectroscopy and Center for Nuclear Matter Science, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People’s Republic of China 7School of Physical Science and Technology, Southwest University, Chongqing 400715, China 8University of Jyväskylä, Department of Physics, P.O. Box 35, FI-40014 Jyväskylä, Finland 9Sodankylä, Geophysical Observatory University of Oulu, FIN-99600 Sodankylä, Finland 10State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, China 11Mathematics and Physics Department, North China Electric Power University, Beijing 102206, China (Received 27 February 2023; revised 20 June 2023; accepted 29 June 2023; published 19 July 2023) Three three-quasiparticle isomers, one at an excitation energy of 2.3 MeV with T1/2=0.48(4) μs, and two shorter-lived with unknown half-lives at slightly lower energies have been identified in 129Nd using the MARA +JUROGAM 3 setup and the recoil tagging technique. All three isomers present decay patterns characteristic of high-Kisomers. The known 6.7 s β-decaying isomer previously assigned to the 5/2+level is now assigned to the new 7/2−ground state. A new low-spin 5/2+isomeric state with a half-life of a few tens of nanoseconds has been identified, while a previously known 2.6 s β-decay activity was assigned to the band head of the ν1/2+[411] band. The transitions depopulating the high-Kisomers to low-lying states also establish the relative energies of three low-lying one-quasiparticle bands, leading to a new spin-parity assignment of 7/2−to the ground state of 129Nd. The partial half-lives of the depopulating transitions suggest spin-parities 21/2+,19/2+, and 17/2+for the three high-Kisomers. The properties of the band built on the 21/2+isomeric state suggest a one neutron-two proton configuration. Based on the results of extensive calculations with different models, we also assign one neutron–two proton configurations to the 19/2+and 17/2+isomeric states. The assigned configurations of the 17/2+and 21/2+isomeric states involve the π9/2+[404] orbital, which is identified in three-quasiparticle bands of proton-rich A≈130 nuclei. DOI: 10.1103/PhysRevC.108.014317 *Corresponding author: [email protected] †Present address: Oliver Lodge Laboratory, Department of Physics, University of Liverpool, Liverpool L69 7ZE, United Kingdom. ‡Present address: Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France. §Present address: Irfu, CEA, Université Paris-Saclay, F-91191 Gifsur-Yvette, France. Present address: Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom; and Department of Physics, Lund University, SE-22100 Lund, Sweden. ¶Present address: Department of Physics, University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom. I. INTRODUCTION Exploring and extending the nuclear chart towards the limits of stability is one of the main endeavors in nuclear **Present address: STFC Daresbury Laboratory, Daresbury, Warrington WA4 4AD, United Kingdom. ††Present address: GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany. ‡‡Deceased. §§Present address: Radiation and Nuclear Safety Authority in Finland Jokiniemenkuja 1, 01370 Vantaa, Finland. Present address: Helsinki Institute of Physics, University of Helsinki, FIN-00014 Helsinki, Finland. 2469-9985/2023/108(1)/014317(13) 014317-1 ©2023 American Physical Society C. M. PETRACHE et al. PHYSICAL REVIEW C 108, 014317 (2023) structure. Experiments devoted to the study of extremely proton-rich nuclei by employing radioactive and stable-ion beams, as well as powerful setups composed of recoil mass spectrometers or projectile fragment separators, with highefficiency arrays for detection of γrays and charged particles at the entrance and at the focal plane of the spectrometers. A wide field of investigation remains yet unexplored with stable projectile-target combinations using newly developed instruments which have much higher sensitivity. Such studies with stable-ion beams have been recently performed with the MARA +JUROGAM 3 setup [1–3]intheA≈120 mass region, revealing extremely rich band structures in the light 119,120Ba and 118,119Cs nuclei, and phenomena unexpected in this mass region, like shape coexistence, chiral bands, or octupole correlations [4–9]. The present experiment, devoted to the study of nuclei with Z>56, reports the discovery of three high-Kisomers, one low-spin isomer, and a new spin-parity assignment to the ground state in 129Nd. From the comparison of the experimental data with configuration-constrained potential energy surfaces (CC-PES) [10], projected shell model (PSM) [11], and particle number conserving cranked shell model (PNCCSM) [12] calculations, we assign one neutron–two proton configurations to the high-spin isomers, two of them involving the π9/2+[404] orbital. These are the first reported multiquasiparticle high-Kisomers involving the π9/2[404] orbital in A≈130 nuclei, which previously were only observed in one-quasiparticle bands close to the ground state of odd-even and odd-odd nuclei like the neighboring Pr nuclei (see, e.g., [13]), and in odd-even nuclei just above the Z=50 closed shell [[14–21]. No high-Kisomers are known in the wellstudied Nd nuclei with N⩽73 [22–27], while high-Kisomers with spins 8−and 7−built on two-neutron configurations are known in N=74 and N=72 isotopes, respectively (see, e.g., [28]). The 129Nd nucleus was previously investigated using the 92Mo(40Ca,α2pn) fusion-evaporation reaction [29] and the βdecay of 129Pm [30]. Four rotational structures observed up to very high spin have been identified in Ref. [29], and configurations have been assigned based on the measured B(M1)/B(E2) ratios, aligned angular momenta, band crossings and signature splitting, and cranked shell model calculations. A 2.3 s isomer was identified by bombarding a 96Ru target with a 36Ar beam and using helium-jet fast tape transport system to measure the βdecay of 129Pm [30]. II. EXPERIMENTAL DETAILS AND RESULTS In the present work, highly excited 129Nd nuclei have been produced using the 58Ni(78Kr,α2pn) fusion-evaporation reaction. The 78Kr beam was provided by the K130 Cyclotron at the University of Jyväskylä, Finland. The target was a 750 µg/cm2thick self-supporting foil of enriched 58Ni. Two experiments have been performed. One without JUROGAM 3 to search for β-delayed proton emitters, lasting for 10 d with several beam energies between 340 MeV and 370 MeV, and a second one lasting 4 d, in which JUROGAM 3 was added and the beam energy of 364 MeV was optimized for the production of 129Nd. The in-flight double-focusing recoil mass separator MARA [1,31] was tuned for mass 133 for the low beam energies (half of the beam time), allowing the observation of mass 129 which fully overlapped with mass 133 due to an A/qambiguity. The flight time of the recoils from target to the implantation point is ≈450 ns. At the target position, the particle detector array JYUTube consisting of 96 separate scintillator detectors with SiPM (silicon photomultiplier) readouts was used for charged particle identification. In the second experiment in which the beam energy of 364 MeV was optimized for 129Nd, the MARA separator was tuned for mass 129, with the aim to search for the prompt γrays which feed the isomeric states in 129Nd using the recoil gated isomer tagging technique. Prompt γrays were detected at the target position using the JUROGAM 3 germanium-detector array consisting of 24 Euroball clover [32] and 15 Eurogam Phase I-type [33] escape-suppressed detectors, with an efficiency of ≈5% at 1.3 MeV. The clover detectors were arranged symmetrically relative to a plane perpendicular to the beam direction (12 at 75.5◦and 12 at 104.5◦), while the Phase I detectors were placed at backward angles with respect to the beam direction (five at 157.6◦and ten at 133.6◦). JYUtube was not in use. The fusion-evaporation residues were separated as a function of A/qand identified using the MARA separator. At the focal plane a position-sensitive multiwire-proportional counter (MWPC) was used to obtain A/qspectra. Part of the time a double-mass slit system was used to allow only two charge states of a given mass to be transported into the implantation detector, a 300 µm thick double-sided-silicon-strip detector (DSSD) placed 40 cm behind the MWPC. Behind the DSSD a second layer of silicon detectors (500 µm thick) is used to veto punch-through events. The time of flight (ToF) between the MWPC and DSSD is recorded. The ToF and the recoil energy deposited in the DSSD were used to distinguish between fusion recoils and scattered beam. Five clover germanium detectors surrounding the MARA focal-plane detection system were used to detect γrays emitted from long-lived isomeric states and daughters of the βdecays of the implanted recoils. All detector signals were recorded by the triggerless total data readout (TDR) data acquisition system, and time stamped by a global 100 MHz clock, which allowed the establishment of both temporal and spatial correlations between recoils and events obtained with the remaining detectors of the focal plane and of the JUROGAM 3 arrays [2,34]. The data were sorted into coincidence γγ matrices and γγγ cubes, and analyzed using the GRAIN [35] and RADWARE [36,37] packages. In the first part of the analysis new delayed transitions in coincidence with low-lying transitions already known in the one-quasiparticle bands of 129Nd were identified at the focal plane. Then in the second part, γ-, and recoil-gated prompt spectra measured in JUROGAM 3 were constructed to identify transitions above the isomers. The multipolarities and the mixing ratios of the newly identified γ-ray transitions were established based on angular correlations data. Figure 1shows a partial level scheme of 129Nd, with the previously known bands [29] drawn in black, and the new transitions drawn in red. Three high-Kisomeric states have been identified, with excitation energies of 1893, 2109, and 2284 keV, and spin-parity assignments of 17/2+,19/2+, and 21/2+, respectively, discussed in the following. The prompt-delayed γγ coincidence spectrum of Fig. 2, obtained 014317-2 HIGH-KTHREE-QUASIPARTICLE ISOMERS IN THE … PHYSICAL REVIEW C 108, 014317 (2023) FIG. 1. Partial level scheme of 129Nd showing the isomer and its decay towards the low-lying states. The new transitions are drawn in red, while transitions reported in the previous work of Zeidan et al. [29] are indicated in black. The levels with isomeric character are drawn with thick lines. Excited levels in Band 1 up to energies similar to the highest ones observed in Band 5 are included for comparison. The Nilsson configurations assigned to the bands in Ref. [29] are also indicated. The insert shows a zoom of the low-spin part of Bands 3 and 4. by gating on the 848-keV transition depopulating the 2284keV, 21/2+state and on the 551-keV transition of Band 4 detected at the MARA focal plane, shows a series of prompt transitions which have been grouped in the newly observed Band 5. Spectra of delayed transitions measured at the MARA focal plane, obtained by gating on transitions depopulating the 21/2+isomeric state and presenting transitions in the lower part of the known one-quasiparticle bands are shown in Fig. 3. A singles γ-ray spectrum, and a projection of the γγ matrix measured with the germanium detectors at the focal plane of the MARA separator are shown in Fig. 4. They give an overall view of the relative intensity of the transitions depopulating the isomers, with the 848-keV transition being the strongest. Figure 5shows two focal plane spectra obtained from the γγ matrix by gating on the 175and 391-keV transitions which depopulate the 21/2+isomer to the lower-lying 19/2+ and 17/2+isomers, respectively. The nonobservation of the transitions depopulating the 17/2+isomer in the spectrum gated by the 175-keV transition indicates the missing 216-keV connecting transition between the 19/2+and 17/2+isomers, giving thus support to the assignment of very different configurations to the two isomers. The experimental information on the transitions depopulating the three high-Kisomers is given in Table I. The half-life of the 21/2+isomeric state has been extracted from the summed time spectra between the DSSD and the germanium detectors at the focal plane of MARA, by gating on the strong and clean 848and 551-keV transitions. A value of 014317-3 C. M. PETRACHE et al. PHYSICAL REVIEW C 108, 014317 (2023) TABLE I. Energies (Eγ), spin and parity assignments (Iπ i→Iπ f), relative intensities (Tγ), and mixing ratios (δ)oftheI=1 transitions in Band 5 above the Kπ=21/2+isomer, as well as the Weisskopf hindrance factors logFWof the transitions depopulating the 21/2+isomer. Eγ(keV)aIπ i→Iπ fTγbδlog FW Band 5 250.6 (23/2+)→(21/2+) 100 0.32(7) 274.0 (25/2+)→(23/2+) 61(3) 0.43(16) 297.7 (27/2+)→(25/2+) 38(3) 0.32(6) 321.5 (29/2+)→(27/2+) 33(3) 0.38(13) 345.2 (31/2+)→(29/2+) 19(3) 368.1 (33/2+)→(31/2+) 20(3) 391.1 (35/2+)→(33/2+) 11(2) 413.5 (37/2+)→(35/2+) 14(2) 432.3 (39/2+)→(37/2+)5(2) 523.9 (25/2+)→(21/2+) 31(4) 571.7 (27/2+)→(23/2+) 32(4) 619.2 (29/2+)→(25/2+) 37(4) 666.7 (31/2+)→(27/2+) 42(4) 713.8 (33/2+)→(29/2+) 40(4) 758.7 (35/2+)→(31/2+) 39(4) 804.7 (37/2+)→(33/2+) 37(4) 844.1 (39/2+)→(35/2+) 31(4) 890.4 (41/2+)→(37/2+) 38(4) 937(2) (43/2+)→(39/2+)<10 959(2) (45/2+)→(41/2+)<10 978(2) (47/2+)→(43/2+)<10 1018(2) (49/2+)→(45/2+)<10 Decay out from the 21/2+isomer 175.3 (21/2+)→(19/2+) 15(2) 1.56(7) 391.0 (21/2+)→(17/2+) 20(2) 3.29(8) 536.7 (21/2+)→19/2+3(1) 7.70(2) 796.0 (21/2+)→17/2+6(1) 5.62(18) 847.8 (21/2+)→17/2+49(3) 4.47(5) 1049.8 (21/2+)→19/2−7(1) 10.50(9) Decay out from the 19/2+isomer 565.8 (19/2+)→21/2−24(2) 671.7 (19/2+)→17/2+19(2) 954.5 (19/2+)→15/2+22(2) 1138.4 (19/2+)→17/2−35(2) Decay out from the 17/2+isomer 659.4 (17/2+)→19/2−25(2) 739.8 (17/2+)→15/2+12(2) 822.9 (17/2+)→15/2−15(2) 924.5 (17/2+)→17/2−16(2) 1009.1 (17/2+)→13/2+10(2) 1183.5 (17/2+)→15/2−22(2) aThe uncertainty on the transition energies is 0.2 keV for transitions below 1000 keV, and 0.5 keV for transitions above 1000 keV, except when indicated differently. bRelative intensities corrected for efficiency, normalized to the intensity of the 250.6 keV transition for Band 5, and to 100% for the transitions depopulating each of the three isomers. The transition intensities were obtained from a combination of the total projection and gated spectra. T1/2=0.48(4) µs has been determined from the fit of the time spectrum with two exponential functions, the one with long half-life being necessary to account for random coincidences (see Fig. 6). Six transitions depopulating the 21/2+isomeric state have been identified: four of 537, 796, 848, and 1050 keV to Bands 1, 3 and 4, and two of 391 and 175 keV to the 17/2+and 19/2+isomeric states, respectively, which in turn decay to low-lying states of Bands 1 and 4 via ten transitions of 566, 659, 672, 740, 823, 924, 955, 1009, 1138, and 1183 keV (see Fig. 4). III. DISCUSSION A. Spin-parity and configuration assignments to the isomers One of the key issues is the assignment of spins and parities to the observed isomers. This was done by analyzing the 014317-4 HIGH-KTHREE-QUASIPARTICLE ISOMERS IN THE … PHYSICAL REVIEW C 108, 014317 (2023) 0 200 400 600 800 1000 1200 0 1 2 937 978959 432 414 391 1018 890 846 805 759 714 667 619 572 525 368 346 321 298 274 Energy [keV] 251 Counts (102) FIG. 2. Spectrum of γrays of Band 5 built on the 21/2+isomeric state measured at the target position of the JUROGAM 3 array, obtained by employing the recoil gated isomer decay tagging technique on the 848-keV transition depopulating the isomer and on the 551-keV transition of Band 4 detected by the germanium detectors at the MARA focal plane. observed decay out patterns of the isomers, including the log F W[38] values of the depopulating transitions, the singleparticle aligned angular momentum ix, kinematic moment of inertia J(1), and total angular momentum on the rotation axis Jxof the band built on the 2284-keV isomeric state (see Fig. 7). In addition, the assumption widely employed in the high-spin region of well-deformed nuclei that the spin increases with increasing excitation energy is adopted. 0 20 40 0 5 10 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 0 2 4 267 269 Nd X-rays (c) (b) 282 239 214 325 392 452 179 146 108 69 594 508 848 keV 551 (a) 360 265 479 418 524 220 198 162 130 439 796 312 537 keV Counts (10 2 ) 292 259 Energy [keV] 1050 keV FIG. 3. γγ-coincidence spectra of the delayed transitions measured at the MARA focal plane when gating on the (a) 848-keV, (b) 537-keV, and (c) 1050-keV transitions depopulating the 21/2+ isomeric state. The 267and 439-keV transitions in (b) are due to the feeding by the delayed 796-keV transition of the 17/2+level of Band 3, which subsequently decays via the 535-keV transition, contaminating thus the 537-keV gate. 10 2 10 3 10 4 10 5 10 6 0 200 400 600 800 1000 1200 10 2 10 3 10 4 10 5 10 6 175, 178 391, 392 535, 537 1050 (b) Counts (a) 848 Energy [keV] FIG. 4. (a) Singles γ-ray spectrum and (b) projection of the γγ coincidence matrix measured with the germanium detectors at the MARA focal plane, showing the ensemble of transitions depopulating the high-Kisomers and the states of Bands 1, 3, and 4 of 129Nd. The energies of the unlabeled transitions indicated with red lines are given in the text. Figure 7shows the experimental single-particle aligned angular momenta of the bands built on the 21/2+isomer in 129Nd and on the 8−isomers in the N=74 nuclei, the kinematic moment of inertia J(1), and the total angular momentum on the rotation axis Jxof the one-quasiparticle Band 1 and of the three-quasiparticle Band 5 built on the 2284-keV isomer. Based on the lowest and highest spins of the states fed by the isomers, we concluded that their spins have to be between 17/2 and 21/2. The spin-parity of the 2284-keV isomeric state can be either 17/2±,19/2±,or21/2+. The 17/2±and 19/2−assignments can be discarded because they would lead to transitions increasing spin by 1¯hfor the 17/2+assignment (17/2+→19/2+to Band 4 and 19/2+→21/2−from the 0 500 1000 1500 2000 0 200 400 600 800 1000 1200 0 500 1000 1500 ∗ 479 439 508 392 360 452 69 672 Nd X-rays (b) 550 418 239 214 198 179 162 130 146 740 659 1009 1183 566 955 Counts 175 keV 1138 (a) ∗ 848 391 keV Counts Energy [keV] FIG. 5. Focal plane spectra from γγ coincidences gated on the 175and 391-keV transitions from the 21/2+isomer, showing the depopulating transitions of the 19/2+and 17/2+isomers to states of the Bands 1, 3, and 4. Contaminating transitions are indicated with asterisks. 014317-5 C. M. PETRACHE et al. PHYSICAL REVIEW C 108, 014317 (2023) 0 100 200 300 400 500 600 700 800 1 Counts (10 3 )/10 ns Time [10 ns] 5 T 1/2 =0.48(4)μs FIG. 6. Time spectrum and its fit with two exponentials from which the half-life of the 21/2+isomeric state was determined. The spectrum is obtained with a start given by the recoils detected in the DSSD, and the stop given by the 848-keV transition depopulating the isomer and the 551-keV transition of Band 4 detected by the germanium detectors at the MARA focal plane. 2109-keV isomeric state to Band 1), or 2¯hfor the 17/2−and 19/2−assignments (15/2−→19/2+from the 1893-keV isomeric state to Band 4), which are unlikely in the de-excitation of high-spin states. The candidate configurations of the remaining 19/2+ and 21/2+possible assignments can be established from the analysis of the single-particle alignment and crossing frequency of the band built on the isomer. As one can see in Fig. 7, Band 5 above the 2284-keV isomeric state consists of two completely degenerate signature partners and has ix≈1.5¯h, indicating the presence of only high-orbitals in its configuration. The up bend at a rotational frequency of ¯hω≈0.35 MeV observed in all one-quasiparticle bands of 129Nd (see Fig. 6 of Ref. [29] and in Fig. 7) and in the bands built on the 8−isomers with two-neutron configurations of the N=74 isotones, all attributed to the alignment of a pair of h11/2protons, is absent in Band 5. With the (πh11/2)2alignment being blocked, the configuration has to involve one h11/2proton orbital, which can be either π5/2−[532] or π3/2−[541]. For Z=60 and ε2≈0.3, the Fermi surface is in the middle of the h11/2subshell where the π5/2−[532] Nilsson orbital is closest in energy, being therefore favored. To establish the orbital occupied by the second proton in the isomer configuration, we observe that J(1) of Band 5 is smaller than that of Band 1 above the up bending, where two rotationally aligned h11/2protons are present, suggesting that the second proton occupies a high- orbital, like π9/2+[404] or π5/2+[413], which by having the angular momenta perpendicular to the rotation axis have tiny contributions to J(1). The neutron has to be placed in a negative-parity orbital to get the positive parity of the isomer, which can only be ν7/2−[523]. We 0.2 0.4 0.6 h -ω (MeV) 0 4 8 12 16 Alignment ix (h - ) 128Xe K=8 130Ba K=8 132Ce K=8 134Nd K=8 129Nd K=9.5 Kπ=8bands in N=74 nuclei Kπ=21/2+ band in129Nd (a) 0 0.2 0.4 0.6 h _ω (MeV) 0 6 12 18 24 30 Jx 30 40 50 60 J(1) (h _2/MeV) Exp. Band 1 Exp. Band 5 (b) Band 1 ν7/2[523] (c) Band 1 ν7/2[523] Band 5 ν7/2[523] - π9/2[404] 5/2[532] Band 5 ν7/2[523] - π9/2[404] 5/2[532] FIG. 7. (a) Single-particle aligned angular momenta for the bands built on the 21/2+isomer in 129Nd and for the 8−isomers in the N=74 nuclei. The Harris parameters are J(0) = 14¯h2MeV−1and J(2) =38¯h4MeV−3for the N=74 isomers, and J(0) =38¯h2MeV−1and J(2) =15¯h4MeV−3for the 21/2+isomer in 129Nd; (b) experimental kinematic moments of inertia J(1); (c) projections on the cranking axis of the total angular momentum Jxfor Bands 1 and 5 of 129Nd. therefore acknowledge two candidates for the threequasiparticle configuration of the 2284-keV isomeric state, {ν7/2−[523] ⊗π(9/2+[404]5/2−[532])}21/2+and {ν7/2−[532] ⊗π(9/2+[404]3/2−[541])}19/2+. From the analysis of the logF Wvalues of the depopulating transitions one conclude that both 19/2+or 21/2+ assignments nicely fits the systematics of the E2, M1, and E1 transitions depopulating high-Kisomers [38] for all 014317-6 HIGH-KTHREE-QUASIPARTICLE ISOMERS IN THE … PHYSICAL REVIEW C 108, 014317 (2023) 0.0 0.1 0.2 0.3 0.4 X = β2cos(γ+30) (a) 0.0 0.1 0.2 0.3 0.4 Y = β2sin(γ+30) FIG. 8. Calculations for the ν7/2−[523] ⊗π(9/2+[404]5/2−[532]) configuration assigned to the 21/2+isomeric state: (a) Potential energy surface calculated with the CC-PES model; (b) Comparison between the experimental kinematic moment of inertia J(1) of Band 5 and the PNC-CSM calculations. (c) Comparison between the experimental Band 5 and the PSM calculations, using deformation parameters ε2=0.35 and ε4=0.02 which best reproduce the band-head and level energies. transitions excepting the 175and 391-keV ones. The 391keV transition has higher hindrance for both E2 and M1 characters, whereas the 175-keV transition has higher hindrance only for M1 character. The high hindrances of these two transitions would be in agreement with the systematics of the high-Kisomers only if K⩾3, which would lead to too low spins for the isomers that in turn would decay to levels with spins higher by more than 2¯hthan that of the initial states, and therefore can be discarded. To explain the logF Wvalues of the 175and 391-keV transitions we have to invoke the presence of additional hindrances, which can be induced by very different configurations or different deformations of the isomers. In order to further investigate the configuration of the 21/2+isomeric state, the mixing ratios of the I=1 and I=2 transitions depopulating a given state of spin Iof the band built on the isomer have been estimated from the transition intensities employing standard formulas valid in the approximation of an axially symmetric rotating nucleus [39,40]: δ2 1+δ2=2K2(2I−1) (I+1)(I−1+K)(I−1−K) E5 1 E5 2 T2 T1 ,(1) gK−gR Q0 =0.933E1 δ(I2−1),(2) where δis the mixing ratio, Eis the transition energy in MeV, Tis the γ-ray transition intensity, and Q0is in units of eb. The subscripts 1, 2 refer to I=1, 2 transitions, respectively. The |δ|values can be estimated from Eq. (1) by assuming a certain Kvalue, whereas the sign of δcan be obtained from the analysis of the angular correlations of the emitted γrays. From Eq. (1) one obtains |δ|≈ 0.5. If the δvalues are positive, the (gK−gR)/Q0values are also positive for a prolate shape [41]. To estimate gKwe can adopt a smaller gyromagnetic factor of gR=0.3 than the rotational approximation gR=Z/A=0.46, as suggested by that recently observed experimentally for the 8−high-Kisomer in 130Ba, for which gR=0.278(15) has been extracted instead of gR=Z/A= 0.43 [42]. We can also adopt an intrinsic quadrupole moment of Q0=5.5eb corresponding to an axially symmetric prolate shape with a deformation of β2=0.3, as suggested by the calculations. With this adopted values, one obtains a gyromagnetic factor of gK≈0.3+0.11 δ≈0.53 for I=12.5. Very similar values are obtained for higher spins. This has to be compared with calculated gKvalues for different threequasiparticle configurations, which are ≈0 for three-neutron configurations, and ≈+1 for one neutron-two proton configurations. One can therefore conclude that the configuration involving two protons is favored. This conclusion is also supported by the mixing ratios that could be extracted for the 251and 298-keV transitions of Band 5, which are positive and around 0.36+23 −9(see Table I), in fair agreement with the estimated absolute values extracted using the relations (1) and (2). For an oblate shape such a conclusion is not valid, but, as will be discussed in the following subsection, the oblate configuration can be safely discarded, because the calculated energy is too high and no minimum for an oblate shape is calculated in the potential energy surfaces. The spin-parity of the 1893-keV state is fixed as 17/2+ by the 391-keV populating transition from the 21/2+isomer and the 1009-keV depopulating transition to the 13/2+ state of Band 4 which have to be E2 otherwise one transition would be I=1 and the other one I=3 which is very unlikely. The spin-parity of the 2109-keV state is fixed as 19/2+by the 955-keV transition to the 15/2+state of Band 4, the 566-keV transition to the 21/2−state of Band 1, and the 175-keV transition from the 21/2+isomeric state. These assignments are also in agreement with the results of the calculations described in the following subsection. Very different configurations have to be chosen for the 19/2+and 17/2+isomeric states, since no transition has been observed between them. This can be realized if we adopt the ν7/2−[523] ⊗π(5/2+[413]5/2−[532]) configuration for the 17/2+isomeric state, which differs by two proton and one neutron excitations from the ν5/2+[402] ⊗ π(9/2+[404]5/2+[413]) configuration assigned to the 19/2+ isomeric state. Moreover, this configuration is similar to the ν7/2−[523] ⊗π(9/2+[404]5/2−[532]) configuration of the 21/2+isomeric state, from which it differs by one proton 014317-7 C. M. PETRACHE et al. PHYSICAL REVIEW C 108, 014317 (2023) TABLE II. Calculated energies of the assigned configurations to the three high-Kisomers. The configurations are given in terms of Nilsson quantum numbers. The shape parameters (β2,γ) resulting form the CC-PES calculations, as well as the adopted quadrupole deformations ε2 for the PNC-CSM and PSM calculations are also indicated. The approximate relation between β2and ε2is ε2≈0.95β2. IπEexp x(keV ) Configuration CC −PES (β2,γ)PNC-CSM(ε2)PSM (ε2) 21/2+2284 ν7/2−[523]π9/2+[404]5/2−[532] 2605 (0.31,−4◦) 3272 (0.31) 2247 (0.35) 19/2+2109 ν7/2−[523]π9/2+[404]3/2−[541] 3016 (0.29,−6◦) 4973 (0.29) 3195 (0.35) 19/2+2109 ν5/2+[402]π9/2+[404]5/2+[413] 3210 (0.29,−8◦) 3992 (0.29) 2786 (0.35) 17/2+1893 ν7/2−[523]π5/2+[413]5/2−[532] 3044 (0.28,0◦) 2421 (0.28) 2836 (0.35) 17/2+1893 ν5/2+[402]π9/2+[404]3/2+[411] 2702 (0.30,9◦) 4658 (0.30) 3092 (0.35) excitation, being thus in agreement with the observation of the connecting 391-keV transition. The 17/2+and 19/2+states at 1893 and 2109 keV, respectively, have decay patterns similar to those of the 2284keV 21/2+isomeric state, suggesting high-Kconfigurations and isomeric character. Their half-lives could not be directly determined in the present experiment. For estimating their half-lives, we analyzed the Weisskopf hindrance factors log F W=log τγ τWof the depopulating transitions (τγis the partial γ-ray lifetime and τWis the Weisskopf estimate), which depend on the electromagnetic character of the transition and increase nearly linearly with K[38]. It was found that they are compatible with high Kvalues ranging between 3 and 4 for half-lives of tens of nanoseconds, between 5 and 6 for half-lives of a few hundreds nanoseconds, and between 6 and 7 for half-lives of a few microseconds, giving support to their high-Knature. By imposing that the logF Wvalues of the depopulating transitions are in agreement with the systematics [38], the best agreement was obtained for half-lives between several nanoseconds and tens of nanoseconds for both isomers. The decreasing half-lives of the three high-Kisomers 21/2+,19/2+, and 17/2+can be partially related to their increasing energy relative to the yrast line. The transitions from the isomer to the previously known bands fix the absolute energies of Bands 1, 3, and 4, and at the same time confirm the relative energies of Bands 3 and 4 established in Ref. [29]. A new 406-keV E2 transition from the 9/2+state of Band 3 to the 5/2+band-head of Band 4 has been identified, which confirms the assigned relative spins and positive parity of Bands 3 and 4 [29]. The present results provide evidence that the ground state of 129Nd is 7/2−,the band-head of Band 1, not 5/2+, the band-head of Band 4, as presently adopted by ENSDF [43]. We found that the 5/2+ band-head of Band 4 decays via two delayed transitions of 69 and 108 keV to the 3/2+state of Band 3 and the newly assigned 7/2−ground state, respectively. These transitions have been observed at the focal plane of MARA in coincidence with the 848-keV transition depopulating the 21/2+isomeric state, and also in delayed coincidence with the transitions of Band 4 below the 19/2+state, the highest fed by depopulating transitions from the 21/2+isomeric state. However, they were not observed in prompt coincidence with transitions of Band 4 above the 19/2+level. This indicates that the 5/2+ band-head of Band 4 is isomeric, with a half-life of a few tens of nanoseconds. An indirect confirmation of the isomeric character of the 108-keV, 5/2+state is the nonobservation of the 69-keV transition in the previous experiment of Zeidan et al. [29], in which only prompt coincidences were measured. In the present experiment we also used a thin target, but unlike the Zeidan et al. experiment [29], we were able to observe the delayed 69and 108-keV transitions emitted at the focal plane of the MARA separator due to the feeding of Band 4 by transitions from the long-lived 21/2+isomeric state. The lowest states of Band 3 with spins 1/2+and 3/2+ have excitation energies of 17 and 39 keV, respectively. Their decays to the 7/2−ground state via low-energy E3 and M2 transitions would be extremely hindered, they most FIG. 9. Results of PSM calculations [11] for Bands 1, 2, 3, and 4 of 129Nd, adopting ε2=0.29 and ε4=0.02 taken from Ref. [45], in comparison with the data of this work and those from Ref. [29]. 014317-8