Evolution from γ-soft to stable triaxiality in 136Nd as a prerequisite of chirality

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/ Evolution from γ-soft to stable triaxiality in 136Nd as a prerequisite of chirality © the Authors, 2018. Published by the American Physical Society. Published version Lv, B. F.; Petrache, C. M.; Astier, A.; Dupont, E.; Lopez-Martens, A.; Greenlees, Paul; Badran, Hussam; Calverley, Tom; Cox, Daniel; Grahn, Tuomas; Hilton, Joshua; Julin, Rauno; Juutinen, Sakari; Konki, Joonas; Leino, Matti; Pakarinen, Janne; Papadakis, Philippos; Partanen, Jari; Rahkila, Panu; Sandzelius, Mikael; Sarén, Jan; Scholey, Catherine; Sorri, Juha; Stolze, Sanna; Uusitalo, Juha; Herzán, A.; Cederwall, B.; Ertoprak, A.; Liu, H.; Guo, S.; Liu, M. L.; Qiang, Y. H.; Wang, J. G.; Zhou, X. H.; Kuti, I.; Timár, J.; Tucholski, A.; Srebrny, J.; Andreoiu, C. Lv, B. F., Petrache, C. M., Astier, A., Dupont, E., Lopez-Martens, A., Greenlees, P., Badran, H., Calverley, T., Cox, D., Grahn, T., Hilton, J., Julin, R., Juutinen, S., Konki, J., Leino, M., Pakarinen, J., Papadakis, P., Partanen, J., Rahkila, P., . . . Andreoiu, C. (2018). Evolution from γ-soft to stable triaxiality in 136Nd as a prerequisite of chirality. Physical Review C, 98(4), Article 044304. https://doi.org/10.1103/physrevc.98.044304 2018 PHYSICAL REVIEW C 98, 044304 (2018) Evolution from γ-soft to stable triaxiality in 136Nd as a prerequisite of chirality B. F. Lv,1,2C. M. Petrache,1,*A. Astier,1E. Dupont,1A. Lopez-Martens,1P. T. Greenlees,3H. Badran,3T. Calverley,3,4 D. M. Cox,3,5T. Grahn,3J. Hilton,3,4R. Julin,3S. Juutinen,3J. Konki,3,6M. Leino,3J. Pakarinen,3P. Papadakis,3,7J. Partanen,3 P. Rahkila,3M. Sandzelius,3J. Saren,3C. Scholey,3J. Sorri,3,8S. Stolze,3J. Uusitalo,3A. Herzán,9B. Cederwall,10 A. Ertoprak,10 H. Liu,10 S. Guo,2M. L. Liu,2Y. H. Qiang,2,11,12 J. G. Wang,2X. H. Zhou,2I. Kuti,13 J. Timár,13 A. Tucholski,14 J. Srebrny,14 and C. Andreoiu15 1Centre de Sciences Nucléaires et Sciences de la Matière, CNRS/IN2P3, Université Paris-Saclay, Bâtiment 104-108, 91405 Orsay, France 2Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China 3University of Jyväskylä, Department of Physics, FIN-40014 Jyväskylä, Finland 4Department of Physics, University of Liverpool, The Oliver Lodge Laboratory, Liverpool L69 7ZE, United Kingdom 5Department of Mathematical Physics, Lund Institu of Technology, S-22362 Lund, Sweden 6CERN, CH-1211 Geneva 23, Switzerland 7Oliver Lodge Laboratory, University of Liverpool, Liverpool L69 7ZE, United Kingdom 8Sodankylä Geophysical Observatory, University of Oulu, FIN-90014 Oulu, Finland 9Institute of Physics, Slovak Academy of Sciences, SK-84511 Bratislava, Slovakia 10KTH Department of Physics, S-10691 Stockholm, Sweden 11School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000, China 12Graduate University of Chinese Academy of Sciences, Beijing 000049, China 13Hungarian Academy of Sciences, Institute of Nuclear Research, 4001 Debrecen, Hungary 14University of Warsaw, Heavy Ion Laboratory, Pasteura 5a, 02-093 Warsaw, Poland 15Department of Chemistry, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada (Received 15 August 2018; published 5 October 2018) The level structure of 136Nd has been investigated using the 100Mo(40Ar,4n) reaction and the JUROGAM II+RITU+GREAT setup. The level scheme has been extended significantly. Many new bands have been identified both at low and high spin, among which are five nearly degenerate bands interpreted as chiral partners. Excitation energies, spins, and parities of the previously known bands are revised and firmly established, and some previously known bands have been revised. Configurations are assigned to the observed bands based on cranked Nilsson-Strutinsky calculations. The band structure of 136Nd is now clarified and the various types of single-particle and collective excitations are well understood. DOI: 10.1103/PhysRevC.98.044304 I. INTRODUCTION The A≈130 mass region is among the most important areas of the nuclear landscape in which one can investigate the presence of triaxiality in deformed nuclei. Axial asymmetry was suggested for the ground states of nuclei in the region centered around Z=62,N=76 [1]. A regular increase of the level energies of the observed low-lying γbands is considered a sign of rigid triaxiality, while a staggering of the level energies is considered a sign of soft triaxial shapes. Chirality, based on the relative spatial orientation of the nuclear deformation, the active single-particle orbits, and the collective rotational axis, is considered a fingerprint of triaxiality. It *Corresponding author: [email protected] Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. was introduced to nuclear physics twenty year ago [2] and has been successfully employed to describe the observed nearly degenerate bands as rotation around an axis out of the three principal planes of the triaxial ellipsoidal shape. Nearly half of the chiral bands were observed in this region [3], widely supporting the existence of stable triaxial deformation. The studies of chirality in nuclei, both theoretical and experimental, suggested the coexistence of triaxial bands with different deformation parameters and revealed the associated phenomenon of multiple chiral doublets (MχD) [4–7]. The MχD phenomenon was first observed in 133Ce [8]. Chiral partner bands are also expected to exist in even-even nuclei, but to achieve a stable chiral geometry, at least two pairs of nucleons should be broken, with at least one proton occupying a high-jquasiparticle orbital and one neutron occupying a high-jquasihole orbital. Comparing with neighboring oddodd and odd-Anuclei, higher excitation energies are therefore needed to populate chiral bands in even-even nuclei, and high efficiency arrays are needed, since much lower intensities are expected due to the competition from various configurations comprising at least four unpaired nucleons. The first 2469-9985/2018/98(4)/044304(22) 044304-1 Published by the American Physical Society B. F. LV et al. PHYSICAL REVIEW C 98, 044304 (2018) observation of chiral bands in even-even nuclei was reported very recently in 136Nd [9] and discussed using the multi-j shell particle-rotor model in Ref. [10]. Another type of collective motion uniquely associated with a triaxial nucleus, the wobbling mode, was also recently reported in 135Pr [11]. However, the interpretation of the claimed wobbling band as transverse wobbling [12]wasrecently questioned in Ref. [13] and therefore remains unclear. At medium spin, the nuclear shape can change under the polarizing effect of unpaired nucleons resulting from broken pairs. In certain cases the triaxial shape becomes more rigid, being based on a deeper minimum of the potential energy surface, induced by the protons occupying low-orbitals in the lower part of the h11/2subshell, or by neutrons excited from orbitals below N=82 to low-(h9/2,f 7/2) orbitals lying above N=82 (see, e.g., [14,15] and references therein). In nuclei with several holes in the N=82 shell closure, a multitude of triaxial bands have been observed in several Ce and Nd nuclei, giving strong support for the existence of stable triaxial shape up to very high spins in this mass region [14–24]. In addition to triaxial shapes, nuclei of this mass region can acquire other coexisting shapes at high spin, such as spherical, axially deformed, highly deformed, and even superdeformed. This is the case for 140Nd, in which states based on a spherical shape have been observed up to spins as high as 27¯hcoexisting with triaxial shapes [25], and in which axial superdeformed and highly deformed shapes coexist at very high spin. In this nucleus, the bridge between the regions of highly deformed bands present in A≈130 nuclei and the superdeformed bands present in A≈150 nuclei is realized [26]. Highly deformed bands have been observed at medium to very high spin in several Nd nuclei [14,20–24,27– 49]. Superdeformed bands have been observed in Ce nuclei [38,50–63]. In several nuclei the shape can become oblate at medium spins, when neutrons from the upper part of the h11/2subshell are active [64–69]. Of particular interest is a new collective rotational band observed in 137Nd, which develops up to spin I=75/2¯hand Ex≈4.6 MeV above yrast, being the first evidence of an oblate deformed nucleus rotating up to very high spin [70]. This region of the nuclear chart is therefore an ideal testing ground to investigate the competition between various deformations and their evolution with spins, as well as the competition between single-particle and collective modes of excitation. To achieve such studies, which tend towards complete spectroscopy, high efficiency experimental setups and high statistics are necessary. The present work is devoted to refining the spectroscopy of 136Nd, which is the nearest even-even neighbor of the first chiral candidate 134Pr [2] and the first reported wobbler 135Pr outside of the A≈160 region [11]. Located near the center of the triaxial region, this nucleus has been investigated in several previous experiments [43–45,71–80] and in theoretical works published in Refs. [81–85]. However, most of the experimental results were reported more than twenty years ago, and only a limited level scheme had been established prior to this work. In this article, we report new experimental results on the extremely abundant structures in 136Nd populated via the 100Mo(40Ar,4n)136Nd reaction. The high-quality data allow us to extend the level scheme of 136Nd significantly. Partial results of this work on the newly observed chiral bands were reported in Ref. [9]. Sections II and III contain the description of the experiment and the data analysis. The structure of various bands is discussed in Sec. IV within the cranked Nilsson- Strutinski (CNS) framework as described in Refs. [86–89]. II. EXPERIMENTAL DETAILS High-spin states in 136Nd were populated using the 100Mo(40Ar,4n) reaction at a beam energy of 152 MeV, provided by the K130 Cyclotron at the University of Jyväskylä, Finland. We used as target a self-supporting enriched 100Mo foil of 0.5mg/cm2thickness. The 135Nd and 136Nd nuclei were the most strongly populated in the reaction, with cross sections of around 100 mb each. The JUROGAM II array [90], consisting of 24 clover and 15 coaxial tapered detectors placed at the target position, was used to detect prompt γrays. The clover detectors were placed on two rings at 75.5◦(12 clovers) and 104.5◦(12 clovers), symmetric with respect to 90◦. The tapered detectors were also placed on two rings at 133.6◦(10 detectors) and 157.6◦ (5 detectors). The high-efficiency gas-filled recoil separator RITU [91] was coupled to the JUROGAM II array. After a flight time of about 650 ns in the RITU separator, the reaction residues were implanted in the GREAT focal plane detector array [92]. The GREAT detector array was composed of several detectors: A multiwire proportional counter (MWPC) measured the position of the recoils and delivered the time reference for the delayed γ-γcoincidences and for the time of flight of the recoils between the MWPC and a doublesided silicon strip detector (DSSD). The DSSD was also used to measure the decays of the implanted recoils. Behind the DSSD, a planar Ge strip detector was mounted to measure x rays and low-energy γrays. For the measurement of highenergy γ-rays, three clover detectors were placed around the focal plane reaction chamber. A total of 5.1×1010 prompt γ-ray coincidence events with fold ⩾3 were collected without any recoil gate. All the data were recorded by the triggerless Total Data Readout (TDR) data acquisition [93] and the events were time-stamped using a 100 MHz clock. The data were sorted using the GRAIN analysis package [94]. Fully symmetrized, three-dimensional (Eγ-Eγ-Eγ) and four-dimensional (Eγ-Eγ-Eγ-Eγ) matrices were analyzed using the RADWARE [95,96] analysis package. The multipolarities of the γrays were extracted using the directional correlation from oriented states (DCO) ratios (RDCO) and two-point angular correlation (anisotropy) ratios Rac [97,98]. The values of Rac were extracted from γ-γmatrices, which were formed by sorting prompt coincidence events with combinations of 133.6◦and 157.6◦versus all angles and of 75.5◦ and 104.5◦versus all angles, by setting the same energy gates on the all-angles projection spectrum in both matrices, and projecting on the other axis. Then, the Rac ratio was calculated using the extracted intensities of the γrays of interest (Iγ) 044304-2 EVOLUTION FROM γ-SOFT TO STABLE … PHYSICAL REVIEW C 98, 044304 (2018) TABLE I. Experimental information including the γ-ray energies, energies of the initial levels Ei, intensities Iγ, anisotropies RDCO and/or Rac, multipolarities, and the spin-parity assignments to the observed states in 136Nd. The transitions listed with increasing energy are grouped in bands. The deduced values for RDCO with a stretched quadrupole gate are ≈1 for stretched quadrupole and ≈0.46 for dipole transitions, while the ratio is close to 1 for a dipole and 2.1 for a quadrupole transition when the gate is set on a dipole transition. The Rac values for stretched dipole and quadrupole transitions are ≈0.8and≈1.4. γ-ray energyaEi(keV) IntensitybRDCOcRacdMultipolarity Jπ i→Jπ f GSB 373.7 373.7 100.0 1.01(5)eE22 +→0+ 602.5 976.2 91(5) 1.06(11)eE24 +→2+ 770.2 1746.4 80(7) 0.97(9)eE26 +→4+ 886.3 2632.7 56(4) 1.01(15)eE28 +→6+ 920.1 3552.8 14(2) 0.99(16)eE210 +→8+ γband 182.7 2227.8 0.25(2) 0.73(21) M16 +→5+ 191.9 2227.8 0.12(2) E16 +→5− 368.7 1230.9 0.8(2) 1.10(25) M1/E23 +→2+ 488.5 862.2 1.7(3) 1.43(31) E22 +→2+ 490.3 3768.0 0.32(4) 0.71(9)eM1/E210 +→10+ 551.7 4319.7 2.7(2) 1.13(14)eE212 +→10+ 565.5 1541.7 1.3(4) 1.07(45) M1/E24 +→4+ 600.4 3768.0 0.7(2) 1.1(4)eE210 +→8+ 679.5 1541.7 1.8(3) 1.05(25)eE24 +→2+ 686.1 2227.8 0.71(6) 1.3(2) E26 +→4+ 711.8 5031.5 4.0(3) 1.08(17)eE214 +→12+ 725.7 5757.2 2.1(2) E216 +→14+ 735.2 5757.2 2.7(2) 1.1(2)eE216 +→14+ 766.9 4319.7 7.7(7) 1.0(2)eE212 +→10+ 811.0 2352.7 1.3(2) 1.38(23) E26 +→4+ 814.2 2045.1 6.5(6) 1.31(20) E25 +→3+ 814.9 3167.6 0.92(8) 1.05(15)eE28 +→6+ 844.8 6602.0 1.8(2) 0.98(25)eE218 +→16+ 857.2 1230.9 6.1(6) 1.16(15) M1/E23 +→2+ 862.2 862.2 1.5(3) 1.1(3)eE22 +→0+ 907.1 6602.0 0.12(1) E218 +→16+ 1017.7 7619.7 0.83(5) 1.02(18)eE220 +→18+ 1135.3 3768.0 1.9(3) 0.98(25)eE210 +→8+ 1162.7 6602.0 0.21(2) E218 +→16+ 1251.6 2227.8 0.31(3) 1.41(26) E26 +→4+ 1410.7 6602.0 0.12(3) E218 +→16+ 1410.8 5757.2 0.11(2) E216 +→14+ 1428.6 7619.7 0.15(2) E220 +→18+ Band N1 163.6 2757.3 0.05(1) M1/E28 −→7− 183.1 2940.4 0.65(8) 0.86(15) M19 −→8− 255.6 2483.4 0.65(5) 0.73(13) E16 −→6+ 273.9 2757.3 4.1(4) 1.02(15)eE28 −→6− 302.8 3243.2 0.9(1) 0.42(8)eM110 −→9− 307.7 2940.4 1.1(3) 0.45(15)eE19 −→8+ 317.7 2757.3 4.7(4) 0.54(7)eM18 −→7− 358.1 3601.3 0.72(8) 1.21(15) M1/E211 −→10− 403.7 2439.6 6.4(3) 0.99(8)eE27 −→5− 410.0 6903.2 0.18(4) E219 −→17− 410.7 4425.7 0.16(4) 0.42(11)eM113 −→12− 411.8 2757.3 0.7(1) 1.45(35) E28 −→6− 413.7 4015.0 0.10(2) M1/E212 −→11− 438.3 2483.4 1.24(7) 0.86(6) E16 −→5+ 447.5 2483.4 1.6(2) 0.84(12) M16 −→5− 044304-3 B. F. LV et al. PHYSICAL REVIEW C 98, 044304 (2018) TABLE I. (Continued.) γ-ray energyaEi(keV) IntensitybRDCOcRacdMultipolarity Jπ i→Jπ f 485.9 3243.2 3.6(4) 1.31(15) E210 −→8− 501.3 2940.4 20(1) 1.06(8)eE29 −→7− 660.9 3601.3 8(1) 1.0(1)eE211 −→9− 693.2 2439.6 21(2) 0.61(13)eE17 −→6+ 737.0 2483.4 2.3(3) 1.07(20) E16 −→6+ 743.8 6844.0 0.15(1) E218 −→16− 771.8 4015.0 3.3(3) 1.4(2) E212 −→10− 824.4 4425.7 2.7(3) 1.03(15)eE213 −→11− 832.0 7676.0 0.09(2) E2(20 −)→18− 989.4 5415.1 2.2(2) 1.06(14)eE215 −→13− 1005.9 5020.9 2.5(3) 0.97(15)eE214 −→12− 1059.7 2035.9 9.3(8) 0.64(11)eE15 −→4+ 1076.9 6492.0 0.47(4) 1.04(22)eE217 −→15− 1079.3 6100.2 0.31(2) 1.32(30) E216 −→14− Band N2 154.1 2593.7 0.21(2) 0.7(2) M17 −→7− 248.2 2593.7 2.6(2) 0.68(12) M17 −→6− 300.4 2345.5 4.7(3) 0.81(7) E16 −→5+ 316.2 2909.9 0.41(2) 0.87(17)fM1/E28 −→7− 337.0 3246.9 0.71(2) 0.63(7)fM1/E29 −→8− 365.9 2593.7 0.73(3) 0.71(13) E17 −→6+ 465.3 3712.2 0.29(2) 0.61(5)fM1/E210 −→9− 564.4 2909.9 1.1(1) 1.40(18) E28 −→6− 653.2 3246.9 3.7(2) 1.40(8) E29 −→7− 802.3 3712.2 0.63(3) 1.97(11)fE210 −→8− 847.3 2593.7 0.94(5) 0.86(6) E17 −→6+ 869.1 4116.0 3.0(2) 2.13(23)fE211 −→9− 904.2 4616.4 0.41(8) 2.17(45)fE212 −→10− 988.9 5104.9 1.47(6) 2.21(14)fE213 −→11− 1068.0 5684.4 0.22(1) 2.0(3)fE214 −→12− Band L1 123.7 3295.7 0.5(1) 0.47(12)eE110 +→9− 355.3 3295.7 9.7(3) 0.58(8)eE110 +→9− 389.9 3685.6 34(2) 1.01(20)eE212 +→10+ 414.7 3172.0 0.63(5) 0.45(12)eM19 −→8− 660.8 4346.4 23(2) 1.1(1)eE214 +→12+ 663.0 3295.7 30(3) 1.12(24)eE210 +→8+ 732.4 3172.0 0.55(2) 1.08(13)eE29 −→7− 844.9 5191.3 12.2(7) 1.10(16)eE216 +→14+ 883.1 7354.9 0.41(5) 1.5(2) E220 +→18+ 999.8 6191.1 5.7(4) 1.07(15)eE218 +→16+ 1163.8 7354.9 1.13(9) 1.47(24) E220 +→18+ 1268.7 8623.6 0.65(4) 1.53(21) E222 +→20+ 1378.2 10001.8 0.10(1) E2(24 +)→22+ 1492.3 11494.1 0.05(1) E2(26 +)→(24+) Band L2 663.4 5694.9 1.9(2) 1.12(16)eE216 +→14+ 672.9 5694.9 3.3(2) 1.04(20)eE216 +→14+ 702.3 5022.0 6.1(3) 1.13(17)eE214 +→12+ 789.5 6546.7 0.31(2) 1.46(29) E218 +→16+ 851.8 6546.7 1.5(3) 1.03(30)eE218 +→16+ 976.7 6546.7 <0.01 E218 +→16+ 1044.7 7591.4 0.43(2) 1.44(25) E220 +→18+ Band L3 487.3 4454.0 0.10(5) E213 +→11+ 678.5 5131.6 0.63(7) 1.33(23) E215 +→13+ 044304-4 EVOLUTION FROM γ-SOFT TO STABLE … PHYSICAL REVIEW C 98, 044304 (2018) TABLE I. (Continued.) γ-ray energyaEi(keV) IntensitybRDCOcRacdMultipolarity Jπ i→Jπ f 739.9 6931.0 0.52(4) 0.63(12) M119 +→18+ 750.7 5942.0 1.75(6) 0.46(6)eM117 +→16+ 768.4 4454.0 1.8(3) 1.54(50) M1/E213 +→12+ 785.2 5131.6 1.9(1) 0.58(12)eM1/E215 +→14+ 810.4 5942.0 1.35(8) 0.98(9)eE217 +→15+ 989.0 6931.0 1.5(1) 1.01(15)eE219 +→17+ 1168.8 8099.8 0.34(3) 1.37(24) E221 +→19+ Band L4 401.6 4855.6 0.35(2) 1.05(23) M1/E214 +→13+ 438.4 5570.0 0.42(3) 0.77(14) M116 +→15+ 518.6 4855.6 0.41(2) E214 +→12+ 714.4 5570.0 1.43(7) 0.97(13)eE216 +→14+ 784.2 4337.0 0.38(2) 1.33(25) E212 +→10+ 901.8 6471.8 3.1(2) 1.05(18)eE218 +→16+ 1001.3 7473.1 0.57(4) 1.1(2)eE220 +→18+ 1041.3 4337.0 0.7(2) 1.12(27)eE212 +→10+ 1088.4 8560.0 0.21(2) 1.49(29) E222 +→20+ 1170.0 4855.6 1.23(6) 1.11(19)eE214 +→12+ 1223.6 5570.0 2.5(2) 0.97(13)eE216 +→14+ 1276.7 8249.8 0.17(2) 1.5(2) E222 +→20+ 1280.4 6471.8 0.58(5) 1.10(20)eE218 +→16+ Band L5 275.1 7141.5 0.11(1) 0.47(9)eE119 −→19+ 467.4 7141.5 0.03(1) M1/E219 −→18− 518.1 8049.5 <0.01 M1/E221 −→20− 781.4 7141.5 1.5(1) 1.03(19)eE219 −→17− 908.0 8049.5 1.35(11) 0.94(12)eE221 −→19− 945.0 6360.1 1.15(9) 1.07(24)eE217 −→15− 950.4 7141.5 1.11(7) 0.53(10)eE119 −→18+ 984.9 9048.4 0.30(2) 1.37(21) E223 −→21− 998.9 9048.4 0.40(4) 1.0(2)eE223 −→21− 1168.8 6360.1 0.53(5) 0.49(8)eE117 −→16+ Band L6 390.1 7531.4 0.10(5) M1/E220 −→19− 635.2 6674.1 1.3(1) 1.03(15)eE218 −→16− 847.6 6038.9 0.31(1) 0.47(12)eE116 −→16+ 857.3 7531.4 1.23(14) 0.98(22)eE220 −→18− 860.0 8536.0 0.05(1) E222 −→20− 1004.6 8536.0 1.1(1) 1.01(18)eE222 −→20− 1018.0 6038.9 1.1(2) 1.03(37)eE216 −→14− Band L7 645.0 3277.7 7.5(6) 1.04(12)eE210 +→8+ 718.3 3996.0 4.6(3) 1.05(20)eE212 +→10+ 851.6 4848.6 2.9(2) 1.02(15)eE214 +→12+ 995.2 5842.8 1.63(17) 1.52(26) E216 +→14+ Band L8 342.7 6929.5 0.11(1) 0.71(22) M118 +→17+ 350.0 6929.5 0.45(4) 0.72(15)fM1/E218 +→17+ 743.5 6586.3 0.34(2) 0.64(16) M117 +→16+ 841.0 4837.0 0.48(3) 0.68(9) M113 +→12+ 859.7 6586.3 0.19(4) 1.58(45) E217 +→15+ 879.0 5726.6 0.58(2) 1.21(25) M1/E215 +→14+ 889.6 5726.6 0.19(2) 1.5(3) E215 +→13+ Band L9 438.7 7732.3 0.13(5) M1/E220 +→19+ 044304-5 B. F. LV et al. PHYSICAL REVIEW C 98, 044304 (2018) TABLE I. (Continued.) γ-ray energyaEi(keV) IntensitybRDCOcRacdMultipolarity Jπ i→Jπ f 743.9 8794.3 0.05(1) M1/E222 +→21+ 912.1 6754.9 0.74(3) 1.49(23) E218 +→16+ 977.4 7732.3 0.20(1) 1.43(25) E220 +→18+ 1062.3 8794.3 0.10(1) 1.44(22) E222 +→20+ Band D1 219.9 4665.9 0.82(6) 0.95(9)fM112 +→11+ 254.1 4920.0 1.72(15) 0.48(11)eM113 +→12+ 293.8 5213.8 1.42(8) 0.71(7)eM114 +→13+ 328.9 4665.9 0.30(3) 1.24(29)fM1/E212 +→12+ 345.3 5559.1 1.1(1) 0.66(9)fM1/E215 +→14+ 411.1 5970.2 0.75(4) 0.98(10)fM116 +→15+ 453.8 6424.0 0.37(9) 0.81(25)fM1/E217 +→16+ 479.3 4446.0 0.13(2) 0.83(17) M111 +→11+ 485.0 6909.0 0.23(3) 0.94(20)fM1/E218 +→17+ 583.0 4920.0 0.11(1) M1/E213 +→12+ 594.1 7503.1 0.14(2) 1.09(19) M1/E219 +→18+ 613.0 8116.1 0.05(2) M1/E220 +→19+ 618.7 7503.1 0.10(1) M1/E219 +→18+ 639.1 5559.1 0.04(2) E215 +→13+ 671.0 3966.7 0.8(1) 1.21(18)fM1/E211 +→10+ 699.2 4665.9 0.49(3) 1.1(3)fM1/E212 +→11+ 756.4 5970.2 0.06(3) E216 +→14+ 844.7 4446.0 0.09(1) (E1) 11+→11− 864.9 6424.0 0.25(10) E217 +→15+ 905.0 4920.0 0.15(2) (E1) 13+→12− 980.3 4665.9 0.16(3) 1.60(45)fM1/E212 +→12+ 1064.6 4665.9 0.26(4) 1.16(36)fE112 +→11− 1150.3 4446.0 0.62(6) 0.81(8) M111 +→10+ 1202.8 4446.0 0.05(1) (E1) 11+→10− 1234.4 4920.0 0.12(3) M1/E213 +→12+ Band D-chiral 431.7 6485.4 0.15(5) 0.93(50) M1/E217 +→16+ 503.9 6989.3 <0.01 M1/E218 +→17+ 515.2 6485.4 0.11(3) 0.73(28) M117 +→16+ 716.4 5636.4 0.03(2) E215 +→13+ 839.9 6053.7 0.22(4) 1.4(3) E216 +→14+ 1019.1 6989.3 0.10(3) 1.43(32) E218 +→16+ 1045.2 7469.2 0.12(2) 1.31(29) E219 +→17+ Band D2 117.9 6347.9 0.25(10) 0.72(37)fM1/E216 +→15+ 231.1 6579.0 0.89(6) 0.78(7) M117 +→16+ 298.1 6884.4 0.11(1) 0.86(15) M118 +→17+ 305.4 6884.4 1.41(15) 1.06(20) M1/E218 +→17+ 318.3 8050.6 0.21(2) 1.10(14) M1/E221 +→20+ 364.6 7293.6 0.50(4) 1.17(18)fM119 +→18+ 376.4 7670.0 1.9(3) 1.54(60)fM1/E220 +→19+ 380.6 8050.6 1.4(2) 0.85(12) M121 +→20+ 384.6 7293.6 0.12(2) 1.02(17)fM119 +→18+ 409.2 7293.6 1.72(9) 0.84(8)fM1/E219 +→18+ 416.3 8466.9 1.15(3) 0.98(9)fM122 +→21+ 460.4 6884.4 0.21(1) 1.16(13) M1/E218 +→17+ 481.2 8948.1 0.89(4) 0.88(9)fM1/E223 +→22+ 543.3 9491.4 0.52(1) 1.15(15)fM124 +→23+ 600.0 10091.4 0.37(10) M1/E225 +→24+ 671.8 10763.2 0.27(4) 0.85(22)fM1/E226 +→25+ 736.2 6579.0 0.55(4) 1.13(18) M1/E217 +→16+ 044304-6 EVOLUTION FROM γ-SOFT TO STABLE … PHYSICAL REVIEW C 98, 044304 (2018) TABLE I. (Continued.) γ-ray energyaEi(keV) IntensitybRDCOcRacdMultipolarity Jπ i→Jπ f 785.6 7670.0 0.08(2) E220 +→18+ 852.4 6579.0 0.5(2) 1.3(4) E217 +→15+ 914.2 6884.4 0.15(2) E218 +→16+ 942.0 4938.0 0.35(5) 0.8(2) M113 +→12+ 1292.0 6230.0 0.17(3) 1.41(42) E215 +→13+ 1393.0 6230.0 0.10(2) E215 +→13+ 1382.4 6230.0 0.14(2) 1.0(3) M1/E215 +→14+ Band D2-chiral 408.7 9248.7 0.10(3) 1.25(40) M1/E223 +→22+ (426.0) 8840.0 <0.01 M1/E222 +→21+ 447.2 9695.9 <0.02 M1/E224 +→23+ 453.1 10659.2 0.04(1) M1/E226 +→25+ 510.2 10206.1 0.05(2) M1/E225 +→24+ 599.4 11258.6 0.05(2) M1/E227 +→26+ 1120.4 8414.0 0.14(3) 1.31(42) E221 +→19+ 1167.2 11258.6 0.10(3) 1.42(60) E227 +→25+ 1167.8 10659.2 0.03(2) E226 +→24+ 1170.0 8840.0 0.18(4) 1.4(3) E222 +→20+ 1198.1 9248.7 0.15(3) 1.37(50) E223 +→21+ 1229.0 9695.9 0.10(3) 1.40(45) E224 +→22+ 1258.0 10206.1 0.05(1) E225 +→23+ Band D3 134.2 5732.2 0.13(1) 0.76(13) M115 −→14− 183.1 5532.1 1.64(7) 0.75(8) M114 −→13− 200.1 5732.2 1.53(15) 1.02(15)fM1/E215 −→14− 248.7 5980.9 1.33(10) 1.05(17)fM116 −→15− 292.0 5349.0 1.71(5) 0.79(5) M113 −→12− 333.4 5980.9 0.07(1) M1/E216 −→15− 345.4 6326.3 1.7(2) 0.74(11) M117 −→16− 355.1 5532.1 0.3(1) 1.14(43)fM114 −→13− 369.9 6326.3 0.23(1) M1/E217 −→16− 382.4 5980.9 1.03(7) 1.94(29)fE216 −→14− 383.2 5732.2 0.15(3) 1.9(4)fE215 −→13− 421.5 5598.5 0.31(1) 0.79(11) M114 −→13− 427.2 5532.1 0.05(1) M1/E214 −→13− 434.2 6760.5 1.23(9) 1.1(2)fM118 −→17− 447.3 6760.5 0.41(3) 0.8(1) M118 −→17− 448.8 8169.9 0.36(1) 1.07(17)fM121 −→20− 448.8 5980.9 0.27(12) E216 −→14− 465.7 7226.2 0.74(5) 1.19(18)fM119 −→18− 493.6 5598.5 0.42(3) 1.01(13) M1/E214 −→13− 494.9 7721.1 0.57(7) 0.92(12)fM120 −→19− 520.0 5349.0 0.35(4) 1.11(28) M1/E213 −→12− 520.2 8690.1 0.25(4) 1.28(27)fM1/E222 −→21− 542.0 9232.1 0.15(1) 1.6(3)fM1/E223 −→22− 555.1 9787.2 0.04(1) M1/E224 −→23− 557.0 5734.0 0.12(1) 1.1(1) M1/E214 −→13− 560.6 5177.0 <0.01 M1/E213 −→12− 594.1 6326.3 0.27(2) 1.3(2) E217 −→15− 732.6 5349.0 0.09(1) M1/E213 −→12− 750.1 4027.8 2.36(20) 0.74(10) E111 −→10+ 750.9 5598.5 0.58(3) 1.02(15)fM114 −→14+ 801.2 4829.0 0.41(2) 0.77(14) M112 −→11− 943.7 8169.9 0.07(2) E221 −→19− 960.6 7721.1 0.08(3) E220 −→18− 1029.2 5057.0 1.95(4) 1.08(15) M1/E212 −→11− 044304-7 B. F. LV et al. PHYSICAL REVIEW C 98, 044304 (2018) TABLE I. (Continued.) γ-ray energyaEi(keV) IntensitybRDCOcRacdMultipolarity Jπ i→Jπ f 1061.0 5177.0 1.2(3) 1.1(3) M1/E213 −→12− 1097.1 9787.2 0.02(1) E224 −→23− 1185.7 5532.1 0.26(2) 0.92(25) E114 −→14+ 1353.0 5349.0 0.4(1) 0.89(30) E113 −→12+ Band D3-chiral 945.1 7271.4 0.21(5) 1.44(55) E219 −→17− 962.1 7722.6 0.11(5) 1.5(4) E220 −→18− 988.9 8215.1 0.07(2) 1.39(32) E221 −→19− 1030.6 8751.7 0.16(3) 1.35(26) E222 −→20− Band D4 224.2 5956.4 0.07(2) M1/E216 −→15− 229.7 5647.5 1.29(10) 0.75(10)fM1/E215 −→14− 275.7 5647.5 0.54(3) 0.77(5)fM1/E215 −→14− 308.9 5956.4 2.3(2) 0.48(8)eM116 −→15− 332.3 6313.2 0.77(5) 0.84(8) M117 −→16− 338.7 5647.5 0.82(7) 0.83(11)fM1/E215 −→14− 356.8 6313.2 1.7(2) 0.93(24)fM117 −→16− 388.7 6715.0 0.61(18) M1/E218 −→17− 401.8 6715.0 1.9(2) 1.09(19)fM118 −→17− 426.6 7577.7 1.1(1) 0.97(13)fM120 −→19− 436.1 7151.1 1.82(20) 0.45(6)eM119 −→18− 445.3 8023.0 0.88(10) 0.95(27)fM121 −→20− 487.6 8510.6 0.61(6) 1.17(29)fM1/E222 −→21− 510.0 9020.6 0.30(5) 0.73(21) M123 −→22− 538.6 5956.4 0.33(6) 1.39(42) E216 −→14− 541.3 5956.4 0.24(1) 1.16(18) M1/E216 −→15− 549.8 9570.4 0.21(2) 1.13(25) M1/E224 −→23− 630.8 10201.2 0.05(2) M1/E225 −→24− 665.7 6313.2 0.23(6) 1.32(33) E217 −→15− 745.7 4347.0 0.58(3) 0.51(11)eM112 −→11− 758.6 6715.0 0.3(1) 1.94(26)fE218 −→16− 784.7 4386.0 2.9(2) 0.51(7)fM1/E212 −→11− 837.9 7151.1 0.21(4) 1.83(38)fE219 −→17− 862.7 7577.7 0.17(4) 1.98(27)fE220 −→18− 871.9 8023.0 0.15(3) 1.42(36) E221 −→19− 883.1 5308.8 0.24(3) 1.13(16)fM114 −→13− 922.8 5308.8 0.61(5) 1.9(2)fE214 −→12− 932.9 8510.6 0.15(3) 1.33(31) E222 −→20− 961.8 5308.8 0.25(2) 1.97(24)fE214 −→12− 985.8 5371.8 0.81(4) 2.01(19)fE214 −→12− 997.6 9020.6 0.15(5) E223 −→21− 1031.8 5417.8 1.4(1) 1.91(20)fE214 −→12− 1059.8 9570.4 0.12(4) 1.4(3) E224 −→22− 1070.8 5417.8 0.33(2) 1.41(21) E214 −→12− 1180.6 10201.2 0.07(2) E225 −→23− 1221.8 5647.5 0.20(2) 1.38(18) E215 −→13− Band D4-chiral 945.0 7258.2 0.10(3) 1.36(45) E219 −→17− 1022.0 7737.0 0.25(4) 1.41(27) E220 −→18− 1059.9 8211.0 0.6(3) (E2) 21−→19− 1050.3 8628.0 0.14(4) 1.26(37) E222 −→20− 1069.2 9092.2 0.10(2) 1.45(30) E223 −→21− 1172.4 9683.0 <0.01 E224 −→22− Band D5 180.2 6006.2 0.17(3) 1.51(36) M1/E216 +→15+ 231.8 6238.0 1.8(2) 0.71(12)fM1/E217 +→16+ 044304-8 EVOLUTION FROM γ-SOFT TO STABLE … PHYSICAL REVIEW C 98, 044304 (2018) 800 1000 1200 1400 1600 1800 Energy (keV) 0 1 2 3 4 5 1400 1500 1600 1700 0 1 2 3 4 5 10-3 Counts 10-2 Counts 1291 1624 1187 949 770 1514 1715 1403 1084 1027 * 760 826 890 1403 886 1514 1624 1715 ** Band T2 FIG. 7. Sum of spectra obtained by double-gating on all combinations of in-band transitions of band T2. The peaks corresponding to the contaminating transitions are indicated with asterisks. D. Search for the isomeric states Another aim of the present experiment was to search for possible long-lived isomeric states in the populated nuclei, in particular in 135Nd and 136Nd. A γ-time matrix for the focalplane clovers has been constructed, and is shown in Fig. 12. One can see delayed components of different lengths for the 729-, 884-, and 973-keV transitions below the 10+,T1/2= 410 ns isomer of 138Nd, and for the 640-, 815-, and 948-keV transitions below the 10+,T1/2=308 ns isomer of 134Ce. We also observed and confirmed the 11/2−,T1/2=2.7μs isomer of 137Pr and the 6+,T1/2=90 ns isomer of 136Pr, but we could not extract lifetimes more precise than those already known [99]. However, no long-lived isomeric states have been found in 135Nd and 136Nd in the present data. FIG. 8. (a) Sum of spectra obtained by double-gating on all combinations of the 220-, 254- and 294-keV transitions of band D1. (b) Spectrum obtained by double-gating on the 220- and 254-keV transitions of band D1. The peaks corresponding to the in-band transitions of band D1-chiral and to the connecting transitions to band D1 are indicated with asterisks. 200 300 400 500 600 700 800 900 1000 1100 Ener gy ( keV ) 0 5 10 15 950 1000 1050 5 10 15 Double gate 345-249 keV 10-3 Counts 693 520 824 814 1060 750 355 542 * 495 200 653 426 989 * * 10-2 Counts 183 249 308 292 374 318 466 350 390 565 434 602 661 770 801 857 886 645 274 945 1060 1031 488 962 1024 404 501 * 449 * * * * FIG. 9. Double-gated spectrum on the 249- and 345-keV transitions of band D3, showing the connecting transitions of band D3- chiral to band D3, which are indicated with asterisks. IV. DISCUSSION The 136Nd nucleus, with 60 protons and 76 neutrons is expected to have a small deformation, ε2≈0.15–0.20. Thus it is convenient to express the single-particle states in terms of j-shell quantum numbers. In the CNS formalism the nucleus rotates about one of its principal axes and the pairing is neglected. The deformation is optimized for each single-particle configuration explored. The configurations are labeled by the number of particles in low-j and high-jorbitals, respectively, in the different Nshells. The configurations can be defined relative to a 132Sn core as π(g)−p1(dg)p2(h11/2)p3ν(sd)−n1(h11/2)−n2(hf )n3(i13/2)n4, for which we will use the shorthand notation [(p1)p2p3, n1n2(n3n4)]. The pseudospin partners d5/2g7/2(dg), s1/2d3/2(sd), and h9/2f7/2(hf ) are not distinguished in the CNS formalism. Note that all particles are listed, i.e., not only the particles considered as active (unpaired). Note also that the labels do not refer to the pure jshells, but rather to the dominating amplitudes in the Nilsson orbitals. In some cases, for an odd number of particles in a group, the signature will be specified as a subscript +(α=+1/2) or − 200 300 400 500 600 700 800 900 1000 1100 Ener gy ( keV ) 0 5 10 15 20 25 30 900 950 1000 1050 1100 1 2 3Double gate 357-309 keV 10-3 Counts 693 1032 520 863 838 746 1071 785 445 582 * 986 542 426 933 501 998 1006 998 * * 10-3 Counts 230 276 338 318 374 402 488 436 390 631 466 602 661 770 824 886 923 737 962 1060 945 1022 1032 1069 1071 1060 1006 986 962 1050 923 908 1022 * * * * * FIG. 10. Double-gated spectrum on the 309- and 357-keV transitions of band D4. The peaks corresponding to the connecting transitions of band D4-chiral to band D4 are indicated with asterisks. 044304-15 B. F. LV et al. PHYSICAL REVIEW C 98, 044304 (2018) 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 Ener gy ( keV ) 0 5 10 15 20 1050 1100 1150 1200 1250 1300 1350 0 2 4 6 8Gates on 463-230-388-345-284 keV 10-3 Counts 886 1144 628 1047 1030 1106 920 263 702 * 1222 602 345 818 526 1222 384 * * 10-2 Counts 388 232 355 318 374 412 600 428 473 735 519 770 845 1093 663 1093 1167 784 284 1167 1135 1372 1327 580 1200 1260 504 671 * 567 * * * * 1061 * * * * * 1125 * * 430 * 1306 977 FIG. 11. Sum of spectra obtained by double-gating on all combinations of the 230-, 284-, 345-, 388-, and 463-keV transitions of band D5. The peaks corresponding to the in-band transitions of band D5-chiral and to the connecting transitions to band D5 are indicated with asterisks. (α=−1/2). In the present calculations for 136Nd we have used the A=130 parameters [86,87]. The lowest proton configuration has ten protons in the πg7/2and πd5/2orbitals which are strongly mixed. Higher angular momenta from proton configurations can be obtained by exciting one, two, or three protons from the πg7/2and πd5/2to the πh11/2orbitals. The lowest observed bands have active neutron holes in the νd3/2and νs1/2orbitals which are also strongly mixed. Higher angular momenta from neutron configurations can be obtained with one, two, or three active holes in the νh11/2orbital. Many more excited states and very high angular momenta can be obtained from neutron excitations above the N=82 shell gap into the νf7/2,νh 9/2 and νi13/2orbitals and proton excitations from the πg9/2 orbital across the Z=50 shell gap. The level scheme of 136Nd presents a very rich and complex structure at low and medium spins, and several rotational FIG. 12. γ-Time matrix for the clovers at the focal plane. The transitions marked with asterisks represent the β-decay contaminants from the nuclei produced in this experiment: 665 keV, 783 keV, 828 keV and 872 from the β-decay of 135Ce, 761 keV and 925 keV from the β-decay of 137Nd. 01 02 0 Spin, I [h -] -2 -1 0 1 2 E - Erld(def) (MeV) GSB γ-band N1 N2 (a)136Nd 10 20 30 40 Spin, I [h -] 0 1 2 3 E - Erld(def) (MeV) L1 L2 L3 L4 L5 L6 L7 L8 L9 T1 T2 T3 T4 (b) 136Nd 10 15 20 25 30 35 Spin, I [h -] 1 2 E - Erld(def) (MeV) D1 D1-chiral D2 D2-chiral D3 D3-chiral D4 D4-chiral D5 D5-chiral D6 (c) 136Nd FIG. 13. Energies relative to a standard rotating liquid drop reference calculated for the experimental bands observed in 136Nd. With an odd number of h11/2neutron holes, two signature degenerate bands are formed which are drawn with the same color and filled/open symbols for even/odd spins, respectively. bands observed up to very high spin. We will discuss here the majority of the observed bands (N, L, D, and T) using the cranked Nilsson-Strutinsky (CNS) model [86–89]. A detailed discussion of the dipole bands in the framework of TACCDFT, 3DTAC-CDFT, and Mj-PRM models was published recently [9,10]. In the present work we will discuss the 044304-16 EVOLUTION FROM γ-SOFT TO STABLE … PHYSICAL REVIEW C 98, 044304 (2018) -2 -1 0 1 2 3 E−Erld(def) [MeV] (a) Exp. 136Nd GSB γ-band N1 N2 -2 -1 0 1 2 3 E−Erld(def) [MeV] (b) CNS calculations [10 0,42] [82,42] [9+,-1-,42] [10 0,3-3+,-] 0 102030 Spin, I [h -] -2 -1 0 1 2 3 Etheo.−Eexp. [MeV] (c) Difference CNS calc. - Exp. GSB-[10 0,42] γ-band-[82,42] N1-[9+,-1-,42] N2-[10 0,3 -3+,-] FIG. 14. The observed low-spin bands of 136Nd are shown relative to a rotating liquid drop reference in panel (a), with the calculated configurations assigned to these bands given relative to the same reference in panel (b). Panel (c) provides the difference between calculations and experiment. properties of the dipole band configurations resulting from the CNS calculations. Before discussing the various observed structures, it is instructive to draw the observed bands relative to a rotor reference: the resulting figures reveal not only the relative excitation of the bands, but also details which otherwise are hard to observe in the E-Iplots. However, the multitude of bands identified in 136Nd makes their visualization in a single figure cumbersome. We therefore divided them in three groups, which are drawn in the panels of Fig. 13 as follows: the GSB, γband, and bands N1, N2 in panel (a); the medium- and high-spin bands L and T in panel (b); the five dipole bands D1–D5, their chiral partners D1-chiral to D5-chiral, and band D6 in panel (c). In panel (a) of Fig. 13 one can see the up-sloping pattern with increasing spin of all the bands, which is induced by the large difference between the moments of inertia of the low-spin bands and that of the rotating liquid drop. One can observe the change of slope of the γband above spin 10+, and of the even-spin branch of band N1 above spin 18+, which are evidently induced by configuration and/or deformation changes. In panel (b) of Fig. 13 one can observe the yrast nature of band L1 in the spin range 10¯hto 20¯h, while just above 10+ the lowest excited band is L7. There are three positive-parity -1 0 1 2 3 E−Erld(def) [MeV] L1 L2 L3 L4 L5 L6 L7 L8 L9 -1 0 1 2 3 E−Erld(def) [MeV] (b) CNS calculations (a) Exp. 136Nd [82,42] [9-1-,3+3-] [7+3+,42] [7-3+,42] [10 0,24] [9-1+,3-3-] [82,24] 10 20 Spin, I [h -] -1 0 1 2 3 Etheo.−Eexp. [MeV] (c) Difference CNS calc. - Exp. L1-[82,42] L2-[82,42] L3-[9-1-,3+3-] L4-[82,42] L5-[7+3+,42] L6-[7-3+,42] L7-[10 0,24] L8-[9-1+,3-3-] L9-[82,24] FIG. 15. The same as in Fig. 14 but for the medium-spin bands L. yrare bands L2, L3, and L4, two nearly degenerate negativeparity bands L5 and L6 connected to band L1, and two yrare positive-parity bands L8 and L9 which decay to band L7. At spins higher than 20+there are four bands, labeled T1–T4 to emphasize their interpretation in terms of triaxial bands (see the following sections). Band T2 develops over the largest spin interval, from 15+to 39+; at the highest spins it develops up to ≈1.7 MeV above yrast, which is a feature similar to that observed in the neighboring 137Nd [70]. The bands T1, T3, and T4 have a nearly flat behavior, with moments of inertia which are similar to that of the liquid drop in the observed spin interval. In panel (c) of Fig. 13 one can see the well known parabolic behavior of the E-Erld plots, which is induced by the mismatch between the calculated moment of inertia of the drop and that of a given band: for a perfect matching one would have a flat horizontal line (see, e.g., [20]). The chiral doublets are drawn with the same color, but different symbols (circles for the yrast, squares for the yrare bands). The spin of the minimum of each parabola is indicative of the total singleparticle spin of the contributing nucleons in the configuration. All bands show nearly degenerate branches with even and odd spins, which indicate the presence in the configurations of one unpaired high-Nilsson orbital. One can observe that the chiral doublets develop only at high spins for the bands D2, D3, D4, that the energy separation is different for the different doublets, and that the chiral doublet observed over the largest spin interval is that of band D5. 044304-17 B. F. LV et al. PHYSICAL REVIEW C 98, 044304 (2018) TABLE II. Configuration assignments and deformation information for the bands of 136Nd. Band Intensity (%) Parity CNS Configuration States Deformation (ε2,γ) GSB 100 +[10 0,42] 0+-10 +(≈0.16,≈−20◦) γband 6 +[82,42] 2+-20 +(≈0.20,≈26◦) N1 9 −[9+,−1−,42] 5−-20 −(≈0.18,≈25◦) N2 5 −[10 0,3−3+,−]6 −-14 −(≈0.16,≈−25◦) L1 34 +[82,42] 10+-26 +(≈0.20,≈25◦) L2 6 +[82,42] 14+-20 +(≈20,≈25◦) L3 2 +[9−1−,3+3−]13 +-21 +(≈0.16,≈−25◦) L4 3 +[82,42] 12+-22 +(≈0.20,≈25◦) L5 1.4 −[7+3+,42] 17−-23 −(≈0.20,≈25◦) L6 1.2 −[7−3+,42] 16−-20 −(≈0.20,≈20◦) L7 7.5 +[10 0,24] 10+-16 +(≈0.15,≈−35◦) L8 0.2 +[9−1+,3−3−]13 +-18 +(≈0.17,≈−33◦) L9 0.7 +[82,24] 18+-22 +(≈0.18,≈27◦) T1 3 +[7−3−,3−3−]20 +-32 +(≈0.18,≈−35◦) T2 0.7 −[82,3+3+]15 −-(39 −)(≈0.19,≈26◦) T3 0.6 −[82,3−3−]26 −-(37 −)(≈0.17,≈−30◦) T4 0.7 −[7+3−,24] 24−-(38 −)(≈0.20,≈−70◦) D1 1.7 +[9−1+,−,3+3−]11 +-20 +(≈0.18,≈−25◦) D2 1.9 +[7+3+,3−3+,−]15 +-26 +(≈0.20,≈21◦) D3 2.6 −[82,3+3+,−]13 −-23 −(≈0.20,≈25◦) D4 2.9 −[82,3−3+,−]14 −-25 −(≈0.20,≈25◦) D5 8.4 +[82,3−3+,−(1−0)] 15+-29 +(≈0.23,≈27◦) D6 1.2 −[7+3+,3−3+,−(1−0)] 21−-31 −(≈0.23,≈25◦) A. The low- and medium-spin bands The γband of 136Nd exhibits a crossing at Iπ=10+ similar to that observed in the neighboring 134Nd nucleus [37]. The B(E2; 2+ 2→0+) and B(E2; 2+ 2→2+ 1) values extracted from the relativistic Coulomb excitation measurement reported in Ref. [80] clearly show the large triaxiality (γ≈ 23◦) and pronounced γsoftness of 136Nd at low spins. The γsoftness is well documented in the A=130 mass region, in particular in the 134Nd nucleus, for which the measured transition probabilities are in good agreement with the O(6) symmetry of the interacting boson model, which is adequate for the description of γ-soft nuclei [100]. Above the crossing at Iπ=10+,theγband exhibits a regular increase of the transition energies as expected for a rotational band, but also several transitions towards the bands L1 and L2, which is a clear indication of mixing with the configurations of these bands. The same behavior of the γbands has been reported in 134Nd [37]. As one can see in panels (c) of Figs. 14 and 15, the bands L1, L2, L4 and the high-spin part of the γ band are all well reproduced by the [82,42] configuration, which involves a pair of aligned h11/2protons. The calculated deformations in the observed spin range show their enhanced quadrupole deformation (ε2≈0.20) relative to that of the GSB (ε2≈0.16), and their pronounced triaxiality γ≈+25◦ (see Table II). As one can see Fig. 14, a nice global agreement with the experimental bands N1 and N2 is obtained if one assigns the [9+,−1−,42] configuration [or π(dg)1h1⊗ν0interms of spherical single-particle orbitals, where ν0 represents the vacuum for neutrons] to band N1 and the [10 0,3+3+,−] configuration [or π0⊗νh−1(sd)−1in terms of spherical singleparticle orbitals, where π0 represents the vacuum for protons] to band N2. The bands have different deformations, which are induced by the different types of active nucleons: band N1 has higher quadrupole deformation (ε2≈0.18) than band N2 (ε2≈0.16), and positive triaxiality (γ≈+25◦) which is opposite to that of band N2 (γ≈−25◦). The larger quadrupole deformation and positive triaxiality of band N1 are induced by the low-h11/2proton present in its configuration. The high-h11/2neutron present in the configuration of band N2 induces a smaller increase of the quadrupole deformation and negative triaxiality. Interestingly enough, the high-spin part of band N1, which exhibits a change of slope in the E-Erld plot of Fig. 13, is nicely reproduced by the [9+,−1−,42] CNS configuration, which shows a jump from the minimum at positive triaxiality (ε2≈0.18, γ≈+25◦) to the minimum at negative triaxiality (ε2≈0.17, γ≈−85◦), indicating a drastic change of the rotation axis, from the intermediate to the long axis, respectively. The medium-spin bands L5 and L6 are the continuation of the odd- and even-spin cascades composing band N1. They have the same neutron configuration as band N1 and two additional h11/2aligned protons, which in CNS notation leads to the [7+,−3+,42] configuration. They have pronounced triaxiality and, as expected due to the presence of three low- h11/2protons, larger quadrupole deformation (ε2≈0.20) than band N1 (ε2≈0.18). Band L7 is based on the [10 0,24] configuration with two h11/2aligned neutrons. It has a smaller deformation (ε2≈ 0.15) than the GSB and negative triaxiality (γ≈−35◦), induced by the presence of two high-h11/2neutrons. The continuation of band L7 to higher spins is band L9, to which we assign the [82,24] configuration involving two h11/2 044304-18 EVOLUTION FROM γ-SOFT TO STABLE … PHYSICAL REVIEW C 98, 044304 (2018) -1 0 1 2 3 E−Erld(def) [MeV] T1 T2 T3 T4 -1 0 1 2 3 E−Erld(def) [MeV] (b) CNS calculations (a) Exp. 136Nd [7-3-,3-3-] [82,3+3+] [82,3-3-] [7+3-,24] 20 30 40 50 Spin, I [h -] -1 0 1 2 3 Etheo.−Eexp. [MeV] (c) Difference CNS calc. - Exp. T1-[7-3-,3-3-] T2-[82,3 +3+] T3-[82,3 -3-] T4-[7+3-,24] FIG. 16. The same as in Fig. 14 but for the bands T. aligned protons, which induce a larger quadrupole deformation (ε2≈0.18) and positive triaxiality (γ≈+27◦). Band L8 has odd spins and is linked to band L7 by weak I=1 transitions, which most probably have M1/E2 character. A possible configuration for band L8 is [9−1+,3−3−], which is quite different from that of band L7 to which it decays and can explain the weak connecting transitions. B. The T bands In the high-spin region we observed four bands that are called T bands to underline their pronounced triaxiality, which distinguish them from the other high-spin bands based on nearly axial shapes and are dominated by highly-deformed (HD) configurations. Band T1 decays only to bands L1 and L4, which are well reproduced by the [82,42] configuration involving two h11/2aligned protons. As it is not linked through several transitions to the other bands, one reasonably can assume that its configuration is quite different from the configurations of the medium-spin bands. One possible configuration is [7−3−,3−3−], which involves one h11/2proton and one h11/2neutron. The band T2 is observed over a wide spin range from I=15 to I=39, and decays only to band L1. Its increasing excitation energy relative to the other high-spin bands (see Figs. 13 and 16) is an intriguing behavior that was recently observed in a band in the neighboring 137Nd nucleus [70] and interpreted in terms of rotation of an oblate shape. A possible configuration for band T2 of 136Nd is [82,3+3+], which -1 0 1 2 3 E−Erld(def) [MeV] (a) Exp. 136Nd D1 D2 D3 D4 D5 D6 -1 0 1 2 3 E−Erld(def) [MeV] (c) Diffference CNS calc. - Exp. (b) CNS calculations [9-1+,-,3+3-] [7+3+,3-3+,-] [82,3+3+,-] [82,3-3+,-] [82,43+,-(1-0)] [7+3+,43+,-(1-0)] 10 20 30 40 Spin, I [h -] -1 0 1 2 3 Etheo.−Eexp. [MeV] D1-[9-1+,-,3+3-] D2-[7+3+,3-3+,-] D3-[82,3+3+,-] D4-[82,3-3+,-] D5-[82,43+,-(1-0)] D6-[7+3+,43+,-(1-0)] FIG. 17. The same as in Fig. 14 but for the bands D. involves one more neutron in the h11/2orbital. The calculated deformation is (ε2≈0.19,γ ≈+26◦)uptoIπ=19−, while in the range Iπ=21−to Iπ=39−the deformation changes gradually from (ε2≈0.17,γ≈−20◦)to(ε2≈0.09,γ≈ −54◦). This decreasing quadrupole deformation and increase of the triaxiality with increasing spin is a behavior similar to band O of 137Nd [70]. The bands T3 and T4 have possible configurations [82,3−3−] and [7+3−,24], respectively. Their quadrupole deformations decrease gradually with increasing spin at quasiconstant triaxiality, from (ε2≈0.20,γ≈−70 ◦)to(ε2≈ 0.12,γ≈−68◦) for band T3, and from (ε2≈0.17,γ≈ −30◦)to(ε2≈0.12,γ≈45◦) for band T4. C. The dipole bands The CNS configurations assigned to the dipole bands of 136Nd are shown in Fig. 17, and are in global agreement with those calculated with the CDFT model in Ref. [10]. Of course, only the configurations of the yrast partners of the chiral doublets can be described by the CNS model, which assumes the rotation around one of the principal axes. As one can see in Table II, all dipole bands D1–D6 have a pronounced triaxiality, close to the maximum of 30◦. The calculated triaxiality is positive for all bands excepting for band D1. The configuration assignment is quite straightforward, being based on the measured energies, spin-parities, and decay patterns. The configuration assignments are as follows: 044304-19 B. F. LV et al. PHYSICAL REVIEW C 98, 044304 (2018) (1) Band D1, having positive parity, decays to band L7 and the bottom of band L1, which are based on νh2 11/2 and πh2 11/2configurations, respectively. The assigned [9−1+,−,3+3−] configuration is the simplest singleparticle excitation leading to a low-lying positiveparity band, which, however, maintains one low- proton and one high-neutron in the h11/2orbitals to assure the perpendicular geometry of the angular momenta required by dipole and chiral bands. (2) Band D2, having positive parity, develops above spin I=15+and has a fragmented decay to many lowlying bands, including band D1. A two-quasiparticle excitation with respect to band D1 appears as the natural choice, and we therefore assign the [7+3+,3−3+,−] configuration, involving two additional h11/2protons relative to band D1. (3) Bands D3 and D4, having negative parity, are connected through several transitions and decay via a multitude of transitions towards the low-lying bands. Their spins and excitation energies are similar to those of band D2. The most probable configurations are [82,3+3+,−] and [82,3−3+,−], which are in good agreement with experiment. (4) Band D5 is the strongest dipole band, has positive parity, and decays mainly to band L1. Its properties are nicely reproduced by the [82,43+,−(1−0)] configuration which involves one neutron in the intruder (h9/2,f 7/2) orbital. As a consequence, its quadrupole deformation is larger (ε2≈0.23) than those of bands D1–D4, due to the polarizing force of the (h9/2,f 7/2) intruder orbital. (5) Band D6 is the highest excited dipole band, has negative parity, and decays to band L6. We assign it the [7+3+,43+,−(1−0)] configuration, which has one neutron excited from the h11/2to the (h9/2,f 7/2) intruder orbital relative to band L6. V. SUMMARY Summarizing, we performed a study of the triaxial nucleus 136Nd up to very high spin. The configuration assignment is based on CNS calculations. Five pairs of chiral pairs of rotational bands were identified in 136Nd. It is the first time that chiral bands have been observed in an even-even nucleus. The present work aims to the complete spectroscopy of 136Nd, which, based on the present experimental information, is known in detail from low to very high spins, being one of the best studied nuclei in the A=130 mass region. ACKNOWLEDGMENTS This work has been supported by the China Scholarship Council (CSC), CSC No. 201604910533; by the Academy of Finland under the Finnish Centre of Excellence Programme (2012–2017); by the EU 7th Framework Programme Project No. 262010 (ENSAR); by the GINOP-2.3.3-15-2016-00034, National Research, Development and Innovation Office NKFIH, Contract No. PD 124717; by the Polish National Science Centre (NCN) Grant No. 2013/10/M/ST2/00427; by the Swedish Research Council under Grant No. 621-2014- 5558; and by the National Natural Science Foundation of China (Grants No. 11505242, No. 11305220, No. U1732139, No. 11775274, and No. 11575255). A.H. would like to thank the Slovak Research and Development Agency under Contract No. APVV-15-0225, and Slovak grant agency VEGA (Contract No. 2/0129/17). The use of germanium detectors from the GAMMAPOOL is acknowledged. The authors are indebted to M. Loriggiola for his help in target preparation. [1] P. Möller, R. Bengtsson, B. G. 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