Multiple chiral bands in 137 Nd
C. M. Petrache, B. F. Lv, Q. B. Chen, J. Meng, A. Astier, E. Dupont, K. K. Zheng, P. T. Greenlees, H. Badran, T. Calverley, D. M. Cox, T. Grahn, J. Hilton, R. Julin, S. Juutinen, J. Konki, J. Pakarinen, P. Papadakis, J. Partanen, P. Rahkila, P. Ruotsalainen, M. Sandzelius, J. Saren, C. Scholey, J. Sorri, S. Stolze, J. Uusitalo, B. Cederwall, A. Ertoprak, H. Liu, S. Guo, J. G. Wang, X. H. Zhou, I. Kuti, J. Timar, A. Tucholski, J. Srebrny, C. Andreoiu
aa r X i v : . [ nu c l - e x ] A ug Eur. Phys. J. A manuscript No. (will be inserted by the editor)
Multiple chiral bands in Nd C. M. Petrache ∗ , B. F. Lv † , Q. B. Chen , J. Meng , A. Astier , E.Dupont , K. K. Zheng , P. T. Greenlees , H. Badran , T. Calverley , D.M. Cox , T. Grahn , J. Hilton , R. Julin , S. Juutinen , J. Konki , J.Pakarinen , P. Papadakis , J. Partanen , P. Rahkila , P. Ruotsalainen ,M. Sandzelius , J. Saren , C. Scholey , J. Sorri , S. Stolze , J.Uusitalo , B. Cederwall , A. Ertoprak , H. Liu , S. Guo , J. G. Wang ,X. H. Zhou , I. Kuti , J. Tim´ar , A. Tucholski , J. Srebrny , C.Andreoiu Centre de Sciences Nucl´eaires et Sciences de la Mati`ere, CNRS/IN2P3, Universit´e Paris-Saclay, Bˆat. 104-108, 91405 Orsay,France Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China Physik-Department, Technische Universit¨at M¨unchen, D-85747 Garching, Germany State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, China Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan Department of Physics, University of Jyv¨askyl¨a, FI-40014 Jyv¨askyl¨a, Finland Department of Physics, University of Liverpool, The Oliver Lodge Laboratory, Liverpool L69 7ZE, United Kingdom Department of Mathematical Physics, Lund Institute of Technology, S-22362 Lund, Sweden CERN, CH-1211 Geneva 23, Switzerland STFC Daresbury Laboratory, Daresbury, Warrington, WA4 4AD, UK Sodankyl¨a Geophysical Observatory, University of Oulu, FIN-99600 Sodankyl¨a, Finland Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA KTH Department of Physics,S-10691 Stockholm, Sweden Institute for Nuclear Research, Hungarian Academy of Sciences, Pf. 51, 4001 Debrecen, Hungary University of Warsaw, Heavy Ion Laboratory, Pasteura 5a, 02-093 Warsaw, Poland Department of Chemistry, Simon Fraser University, Burnaby, BC V5A 1S6, Canadathe date of receipt and acceptance should be inserted later
Abstract
Two new bands have been identified in
Ndfrom a high-statistics JUROGAM II gamma-ray spec-troscopy experiment. Constrained density functional the-ory and particle rotor model calculations are used toassign configurations and investigate the band prop-erties, which are well described and understood. It isdemonstrated that these two new bands can be inter-preted as chiral partners of previously known three-quasiparticle positive- and negative-parity bands. Thenewly observed chiral doublet bands in
Nd representan important support to the existence of multiple chi-ral bands in nuclei. The present results constitute themissing stone in the series of Nd nuclei showing mul-tiple chiral bands, which becomes the most extendedsequence of nuclei presenting multiple chiral bands inthe Segr´e chart.
The nuclei of the A ≈
130 mass region constitute thelargest ensemble of chiral nuclei [1] in the chart of thenuclides [2]. Reviews of the experimental results andtheir theoretical interpretation can be found in Refs. [3,4,5,6,7]. Bands built on configurations involving three-, four- and six-quasiparticles have been observed in thismass region (
La [8],
Ce [9],
Nd [10,11], Nd ∗ corresponding author: [email protected] † corresponding author: [email protected] [12,13] and Nd [14,15,16]). The present work is de-voted to the study of chirality in
Nd, the odd-evenneighbor of
Nd and
Nd, in which multiple chiraldoublet (M χ D) [17] bands have been recently identi-fied [11,12,13]. Prior to this work, the
Nd nucleushas been investigated both experimentally [18,19,20,21,22] and theoretically [23]. Two new dipole bandsare identified at medium spins, which are interpreted aschiral partners of previously known three-quasiparticlepositive- and negative-parity bands. The interpretationof the three-quasiparticle bands and the chirality, pre-viously investigated using the interacting boson modelplus broken pairs [23], are revisited. The resemblancebetween the new negative-parity chiral doublet of
Ndwith that known in
Nd and
Ce, gives strong sup-port to the interpretation in terms of chiral vibration atlow spin, and to the invoked transition between chiralvibration and chiral rotation in the odd-even Nd nu-clei [24]. The existence of two chiral doublet bands in
Nd also gives a strong support to the existence of theM χ D phenomenon in the A ≈
130 mass region, whichpresents, in addition to
Ce, in the most extendedsequence of nuclei including both odd-even and even-even nuclei, from
Nd to
Nd. The band structureis discussed within the constrained covariant densityfunctional theory (CDFT) framework [17,25] and theparticle rotor model (PRM) recently developed to in- clude multi- j configurations, which is a powerful tool inthe investigation of the 3D chiral geometry in nuclei [13,26,27]. The present experimental results are obtainedfrom the same data set from which were obtained theresults of Refs. [11,12,22,28,29]. High-spin states in
Nd were populated using the
Mo( Ar,3n) reaction at a beam energy of 152 MeV,provided at the Accelerator Laboratory of the Univer-sity of Jyv¨askyl¨a, Finland. A self-supporting enriched
Mo foil of 0.50 mg/cm thickness was used as a tar-get. The JUROGAM II array [30] consisting of 24 cloverand 15 coaxial tapered germanium detectors placed atthe target position was used to detect prompt γ -rays.A total of 5 . × prompt γ -ray coincidence eventswith fold ≥ E γ - E γ - E γ ) and four-dimensional ( E γ - E γ - E γ - E γ ) matriceswere analyzed using the radware [33,34] analysis pack-age.The partial level scheme of Nd showing in red thenewly identified bands is given in Fig. 1. Spin and parityassignments for newly observed levels are based on the measured two-point angular correlation (anisotropy) ra-tios R ac [35,36]. To extract the R ac values, the datawere sorted into γ - γ matrices constructed by sortingprompt coincidence events with the detectors mountedat (133 . ◦ and 157 . ◦ ) versus (all angles) and (75 . ◦ and104 . ◦ ) versus (all angles) combinations, by setting thesame energy gates on the (all angles) projection spec-trum in both matrices, and projecting on the other axis.Then, the R ac ratio was calculated using the extractedrelative intensities of the γ -rays of interest ( I γ ) fromthese spectra, normalized by the different efficiencies ofthe two sets of detectors. To determine the efficiency atdifferent angles, we combined all tapered germaniumdetectors mounted at 133 . ◦ and 157 . ◦ in one ring,and all clover detectors mounted around 90 ◦ (75 . ◦ and104 . ◦ ) in one ring, respectively. The R ac values forstretched dipole and quadrupole transitions are around0.8 and 1.4, respectively, have been deduced from theanalysis of strong E2, E1, and M1 transitions in ‘36 Nd.More details of the experimental setup and data anal-ysis can be also found in Ref. [28]. The γ -ray energies(E γ ), level energies (E i ), relative intensities (I γ ), R ac values, multipolarities, and assigned spin-parity of thedifferent γ -ray transitions of Nd are listed in Table1. Nd D1D2 D5D4D3 D6
Fig. 1 (Color online) Partial level scheme of
Nd showing, in addition to the previously known bands D1, D2 and D5, thenewly identified bands D3 and D6, and 594-, 875-, 883- and 1165-keV transitions (marked in red).
Energy(keV)
Band D3
500 582
Band D6 C oun t s
218 354265295139 435 ,
436 596 669482310264 706 a)b)
488 883475396382 457 500196 295 382382 463382 457 10091053549328364373*407 582602* 669706 749779196 10381036672 1064996939601 ,
605 699614
Fig. 2 (Color online) Gamma-ray spectra for bands D3 and D6 of
Nd obtained by double-gating on selected in- and out-of-band transitions: 436, 482, 488, 1036, 1038 keV for band D3, and 310, 382, 457, 996, 1009, 1053 keV for band D6. Newlyidentified transitions are indicated in red color. The contaminant transitions of 373 and 602 keV belonging to
Nd populatedby the strongest reaction channel are indicated with an asterisk. C oun t s Double gate on 436 keV and 482 keVDouble gate on 436 keV and 437 keV / Energy (keV) / a)b)
218 1038196214218264295 328364 407 602488 582601549488 669 706749* 939 106410381036779 / / / / / / , / *373** 482407 435 , Fig. 3 (Color online) Gamma-ray spectra for band D3 of
Nd obtained by double-gating on 436 keV and 437 keV in panela), and on 436 keV and 482 keV in panel b). Newly identified transitions are indicated in red color. The contaminant transitionsof 373 and 602 keV belonging to
Nd populated by the strongest reaction channel are indicated with an asterisk. C oun t s Double gate on 396 keV and 1050 keVDouble gate on 354 keV and 396 keV
Energy (keV) / a)b) Fig. 4 (Color online) Gamma-ray spectra for the 996- and 1050-keV transitions connecting bands D5 and D6 of
Nd,obtained by double-gating on 354 keV and 396 keV in panel a), and on 396 keV and 1050 keV in panel b). Newly identifiedtransitions are indicated in red color.
Table 1: Experimental information including the γ -ray energies,energies of the initial levels E i , intensities I γ , R ac , multipolarities,and the spin-parity assignments to the observed states in Nd. γ -ray energy a E i (keV) Intensity b R acc Multipolarity J πi → J πf Band D1 − → − − → − − → − − → − − → − − → − − → − − → − − → − − → − − → − Band D2 + → + + → + + → + + → + + → + + → + + → + + → + Table 1 –
Continued γ -ray energy a E i (keV) Intensity b R acc Multipolarity J πi → J πf + → + + → + + → + + → + + → + + → + − → − + → + + → + + → + + → + + → − + → + + → + + → − + → − + → + + → + + → + + → + + → + + → + < + ) → + + → − Table 1 –
Continued γ -ray energy a E i (keV) Intensity b R acc Multipolarity J πi → J πf Band D3 + → + + → + + → + + ) → + < + ) → (39/2 + )601.4 4711.7 0.42(15) 31/2 + → + + → + + → + + → + + → + Band D4 − → − − → − − → − − → − − → − − → − − → − − → − − → − − → − − → − − → − Table 1 –
Continued γ -ray energy a E i (keV) Intensity b R acc Multipolarity J πi → J πf < − ) → − − → − − → − − → − − → − − → − − → − − → − − → − Band D5 − → − − → − − → − − → − − → − − → − − → − − → − − → − − → − − → − − → + − → − − → − Table 1 –
Continued γ -ray energy a E i (keV) Intensity b R acc Multipolarity J πi → J πf − → + < − → − − → − − → − − → − − → − − → − − → − − → − − → − − → − − → − Band D6 − → − − → − − → − − → − − → − − → − − → − − → − ≤ − → − − → − a The error on the transition energies is 0.2 keV for transitions below 1000 keV of the
Nd reaction channel, 0.5keV for transitions above 1000 keV, and 1 keV for transitions above 1200 keV. b Relative intensities corrected for efficiency, normalized to the intensity of the 699.4-keV transition. The transitionintensities were obtained from a combination of total projection and gated spectra. c The R ac has been deduced from two asymmetric γ - γ coincidence matrices sorted with all detectors on one axis,and detectors around 90 ◦ and at backward angles, respectively, on the other axis. The tentative spin-parity of thestates are given in parenthesis. The bands D1, D2, D4 and D5 were previously re-ported in Ref. [21]. Their spins and parities were wellestablished on the basis of directional correlation ra-tios from oriented states reported in Ref. [21]. In thepresent work, we mainly focus on the newly observedbands D3 and D6. In addition, the following new tran-sitions have been identified in the previously reportedbands: 1164.8 keV on top of band D2, 875.3 keV con-necting band D2 to band D1, 882.9 keV in band D4,and 594.5 keV connecting band D4 to band D5.The positive-parity band D3 consisting of six lev-els with spins from 31 / + to (41 / + ), inter-connectedby the 435-, 482- 436-, 488- and 549-keV dipole transi-tions, has been newly identified. It decays to band D2by five transitions of 601, 605, 672, 1036 and 1038 keV,which are assigned M1 and E2 characters. The alter-native E1 or M2 characters are less probable becausethe existence of several E1 transitions would imply ei-ther enhanced dipole moments which are not expectedto be present in this nucleus, and the existence of sev-eral M2 transitions would imply large change of angu-lar momentum and change of parity, which hardly cancompete with collective E2 transitions at high spins.Fig. 2(a) shows the newly identified in-band and out-of-band transitions of bands D3. It should be pointedout that the contaminant transitions of 373 and 602keV belonging to Nd populated by the strongest re- action channel, are present in Fig. 2(a) due to the usedsum of gates on transitions with energies close to thoseof transitions in
Nd (481 keV of band D2, 485 keVof band D1, 486 keV of band N1, 487 keV of bands D4and L3, 488 keV of γ -band, 1039 keV of band T2, allreported in Ref. [28]); however, the spectrum is domi-nated by the 196-, 218-, 295-, 328-, 407, 582-, 669- and706-keV transitions of Nd, giving clear evidence forthe assignment of the new band structure to
Nd. Theexistence of three transitions with energies around 436keV, one in band D2 and two in band D3 is demon-strated in Fig. 3, where one can see the presence of the435-keV peak is the double-gated spectrum on the 436-and 437-keV transitions. The spins and parity of bandD3 are assigned based on the R ac values of the 605-, 1036-, and 1038-keV connecting transitions to bandD2, in particular those of 1038 and 1036 keV whichhave E2 character (see Table 1).The negative-parity band D6 consisting of five lev-els with spins from 33 / − to 41 / − , inter-connected bythe 310-, 382-, 457- and 500-keV dipole transitions, hasbeen also newly identified. It decays to band D5 by sixtransitions of 614, 699, 996, 1009, 1050 and 1053 keV,which are assigned M1 and E2 character based on con-siderations similar to those of band D3. A double-gatedspectrum showing the newly identified in-band and out-of-band transitions of band D6 is given in Fig. 2(b). In order to identify the weak 996- and 1050-keV connect-ing transitions between the bands D6 and D5 not clearlyseen in the spectrum of Fig. 2(b), double-gated spectralike those of Fig. 4 were used. Based on the R ac valuesof the 1053- and 699-keV decay-out transitions whichclearly indicate their quadrupole and dipole nature, re-spectively (see Table 1), a spin 33/2 and negative parityhave been assigned to the band-head of band D6. TheR ac values of three other inter-band transitions betweenbands D5 and D6 have also been measured, confirmingthe spin and parity assignment to the levels of band D6. We investigated the structure of the bands discussedin the present work using the constrained CDFT andPRM. The unpaired nucleon configurations, quadrupoledeformation parameters ( β, γ ) obtained by CDFT withPC-PK1 interaction [37] as well as the quadrupole de-formation parameters ( β ′ , γ ′ ), moments of inertia J (unit ¯ h / MeV), and Coriolis attenuation factors ξ usedin the PRM calculations are listed in Table 2. For eachconfiguration, a normalization of PRM energy of theband-head of each band to the experimental values hasbeen done. However, for the chiral doublet bands, onlythe band-head of the yrast band has been normalizedbecause the energy difference between the doublet bandsis given by the model. (a) Nd D1 (Exp) D1 (PRM) E ( I )- . I ( I + ) ( M e V ) (b) D2 (PRM) D3 (PRM)
D2 (Exp) D3 (Exp) (c)
D4 (Exp)
D4 (PRM-3qp) D4 (PRM-5qp)
Spin I ( ) (d)
D5 (PRM-3qp) D5 (PRM-5qp) D6 (PRM)
D5 (Exp) D6 (Exp)
Spin I ( )
Fig. 5 (Color online) Comparison between the experimentalenergies relative to a rigid rotor (symbols) and the particle-rotor calculations (lines) for the bands discussed in thepresent work.
The calculated excitation energies relative to a rigidrotor are shown in Fig. 5. As one can see in Fig. 5(a), agood description of band D1 built on the νh / [505]11 / − Nilsson orbital is obtained. The excitation energies ofbands D2 and D3, as well as those of the bands D5and D6, are very similar. These four bands correspond,one to one, to the bands identified in
Nd [11]. How-ever, the agreement between the theoretical curves andthe data points is poor at lower spins, in particular forband D2, due to strong mixing with many other statespresent in the same energy region, not all shown in Fig.1 but reported previously in Ref.[21], which is beyondthe PRM calculation. Table 2
The unpaired nucleon configurations, quadrupole deformation parameters ( β, γ ) obtained by CDFT as well as thequadrupole deformation parameters ( β ′ , γ ′ ), moments of inertia J (unit ¯ h / MeV), and Coriolis attenuation factors ξ used inthe PRM calculations for bands D1-D6.Band Unpaired nucleons ( β, γ ) ( β ′ , γ ′ ) J ξ D1 ν (1 h / ) − (0 . , . ◦ ) (0 . , . ◦ ) 16 . . ν (1 h / ) − ⊗ π (1 h / ) π (1 g / ) − (0 . , . ◦ ) (0 . , . ◦ ) 26.0 0.94D4-low ν (1 h / ) − (0 . , . ◦ ) (0 . , . ◦ ) 26.0 1.00D4-high ν (1 h / ) − ⊗ π (2 d / ) (0 . , . ◦ ) (0 . , . ◦ ) 33.0 1.00D5, D6 ν (1 h / ) − ⊗ π (1 h / ) (0 . , . ◦ ) (0 . , . ◦ ) 27.5 1.00D5-high ν (1 h / ) − ⊗ π (1 h / ) π (2 d / ) (0 . , . ◦ ) (0 . , . ◦ ) 33.0 0.91 The previous interpretation of the three-quasiparticlenegative-parity bands in
Nd [21], as well as the pro-posed chiral interpretation of the same bands [23], arerevised. We invert the configurations assigned to bandsD4 and D5: the new configuration assigned to band D4below the crossing at I = 41 / h is νh − / , while thatof band D5 below the crossing at I = 37 / h is νh − / ⊗ πh / . These revised configuration assignments betteraccount for the B ( M /B ( E
2) values of the bands asshown in Fig. 6, where the experimental values are de-termined by assuming zero mixing ratios of the dipoletransitions, assumption based on the DCO (DirectionCorrelations from Oriented states) published previouslyin Ref. [21], which are compatible with pure M R ac values deduced in thepresent work, which are compatible with zero mixing ratios for all M1 transitions. The B ( M /B ( E
2) valuescould be extracted for several states of band D5, butonly for one state of band D4, because of the too weakand therefore unobserved E2 crossover transitions de-exciting the other states. In fact, the observation of E h / sub-shell. The missing E h / sub-shell. On the other hand, themissing E Nd D1 (Exp) D1 (PRM) B ( M ) / B ( E ) ( N / e b ) (a) (b) D2 (Exp) D2 (PRM) D3 (PRM) (c)
D4 (Exp) D4 (PRM-3qp) D4 (PRM-5qp)
Spin I ( ) (d)
D5 (Exp) D5 (PRM-3qp) D5 (PRM-5qp) D6 (PRM)
Spin I ( )
Fig. 6 (Color online) Comparison between experimental ra-tios of transitions probabilities B(M1)/B(E2) (symbols) andthe particle-rotor calculations (lines). As there are no experi-mental values for bands D3 and D6, only the calculated onesare drawn in panels (b) and (d), respectively.
As one can see in Fig. 6, a reasonably good agree-ment is obtained for the B ( M /B ( E
2) values of bothbands D2 and D5, giving credit to the assigned config-urations. For band D2, the calculated B ( M /B ( E νh − / ⊗ πh / ( g / ) − configuration, which gives abetter agreement with the experiment than the config-uration with one proton in the d / orbital, suggestingtherefore the predominance of the proton g / orbitalin the mixed π ( d / , g / ) configuration involved in thebands D2 and D3.From the single-particle alignments i x as function ofthe rotational frequency ¯ hω shown in Fig. 7, we observe h - ω (MeV)0481216 A li gn m e n t i x ( h - ) D1D2D3D4D5D6
Fig. 7 (Color online) The experimental quasi-particle align-ments for the chiral rotational bands of
Nd. The Harrisparameters used, chosen to result in a flat alignment of bandD2, are J = 11 ¯ h MeV − and J = 20 ¯ h MeV − . The twosequences of a given band with even/odd spins are drawnwith the same color and with filled/open symbols, respec-tively. Dashed and continuous lines are used to indicate neg-ative and positive parity, respectively. large values of i x for all bands D2-D5, with a differenceof 2¯ h between D2 and D3, as well as between D5 andD6, due to either different Fermi levels for protons andneutrons implying the occupation of different Nilssonorbitals, and/or different moments of inertia inducedby the active quasiparticles. However, this 2¯ h differ-ence between the doublet bands can be interpreted aspossibly resulting from the presence of chiral vibration,like in the case of the Nd nucleus (see e. g. [10,11]).The ≈ h alignment difference between band D2and band D1 based the one-quasiparticle νh − / con-figuration, clearly indicates a 3-quasiparticle configura- tion for band D2, with two more nucleons placed in theopposite-parity proton orbitals h / and ( d / , g / ),leading to the νh − / ⊗ π [ h / ( d / , g / ) − ] configura-tion. The i x values of ≈ h and ≈ h of the negative-parity bands D5 and D6, respectively, are larger thanthose of the positive-parity bands D2 and D3, clearly in-dicating the presence in their configurations of two moreprotons in the πh / orbital, leading to the νh − / ⊗ πh / configuration.A sudden increase of the single-particle alignment of2¯ h is observed in both bands D4 and D5 at slightly dif-ferent rotational frequencies, which was investigated bycalculating different possible additional aligned quasi-particles. A similar crossing could exist in band D6, butcould be sharper and not observed in the present exper-iment in which the weak band D5 has been observed upto lower spin than band D5. It appears that the align-ment of two protons in the πd / orbital well reproducesboth the excitation energies and the B ( M /B ( E
2) ra-tios for both bands D4 and D5, as shown in Figs. 4and 6. We therefore assign νh − / ⊗ πd / and νh − / ⊗ πh / ⊗ πd / configurations to bands D4 and D5 abovethe crossing, respectively.The configuration νh − / ⊗ π [ h / ( d / , g / ) − ] as-signed to band D2, is similar to that assigned to thecorresponding bands of Nd [11] and
Ce [9]. Thealignment of the new band D3, larger by 2¯ h than that A n g u l a r m o m e n t u m () i-axis s-axis l-axis RD2 J (h ) J (h )J (g ) D3 Spin I ( ) A n g u l a r m o m e n t u m () i-axis s-axis l-axis RD5 J (h ) J (h )D6
Spin I ( )
Fig. 8 (Color online) The root mean square componentsalong the intermediate (i-, squares), short (s-, circles) andlong (l-, triangles) axes of the rotor R , valence protons J π ,and valence neutrons J ν angular momenta calculated as func-tions of spin by PRM for the chiral partners D2, D3 and D5,D6. One should note that there are three panels for the con-figuration assigned to bands D2 and D3, which involves threedifferent orbitals πh / , πg / and νh / , and only two pan-els for the configuration assigned to bands D5 and D6, whichinvolves two protons and one neutron placed in the πh / and νh / orbitals, respectively. of band D2, is different from the nearly identical align-ments of the corresponding positive-parity bands in Nd and Ce. On the other hand, the same 2¯ h difference inalignment is present in the negative-parity chiral dou-blet D5 and D6 of Nd [11], which was interpreted aschiral vibration [10]. A similar difference of 2¯ h betweenthe i x values of bands D5 and D6 is also observed. Thisstrongly supports the interpretation in terms of chiralvibrations of both doublet bands (D2, D3) and (D5,D6) of Nd.Finally, the composition of the angular moments inthe different assigned configurations has been investi-gated, in particular for the two pairs of doublet bands(D2, D3) and (D5, D6), which are shown in Fig. 8. Onefirst observes a similar composition of the angular mo-mentum in the two partners of each doublet, which isshared between the three axes of the triaxial core, inagreement with the chiral interpretation. For the (D2,D3) doublet bands the component along the long axisis larger, due to the summed contribution of the high-
Ωπg / [504]7 / + and νh / [505]11 / − orbitals, while forthe (D5, D6) doublet bands the component along theshort axis is larger, due to the summed contribution oftwo protons in the low- Ω πh / [550]1 / − orbital. In summary, we have identified two new bands in
Nd,which are interpreted as chiral partners of two pre-viously known three-quasiparticle bands involving one h / neutron and two protons placed either in opposite-parity or identical-parity orbitals. Two pairs of chiralbands are therefore present in Nd, like in the caseof
Nd and
Ce, bringing support to the M χ D phe-nomenon currently explored in the A = 130 mass re-gion. The difference in the aligned single-particle spinbetween the partners is interpreted as due to chiralvibration. The configuration of the doublet bands areinvestigated theoretically using the constrained CDFTand PRM, which reveals the chiral geometry in bothchiral doublets. The present results extend the limits ofthe region of M χ D phenomenon in the A = 130 massregion, which includes now four Nd nuclei, from Ndto
Nd. The present results encourage further investi-gations of possible candidates for multiple chiral bandsin other isotopes from this and other mass regions.
This work has been supported by the Academy of Fin-land under the Finnish Centre of Excellence Programme(2012-2017); by the EU 7th Framework ProgrammeProject No. 262010 (ENSAR); by the National KeyR&D Program of China (Contract No. 2018YFA0404400and No. 2017YFE0116700), by the National NaturalScience Foundation of China (Grants No. 11621131001and No. 11875075); by the GINOP-2.3.3-15-2016-00034,National Research, Development and Innovation Of- fice NKFIH, Contracts No. PD 124717 and K128947;by the Polish National Science Centre (NCN) GrantNo. 2013/10/M/ST2/00427; by the Swedish ResearchCouncil under Grant No. 621-2014-5558; and by the Na-tional Natural Science Foundation of China (Grants No.11505242, No. 11305220, No. U1732139, No. 11775274,and No. 11575255), and by the National Sciences andEngineering Research of Canada. The use of germa-nium detectors from the GAMMAPOOL is acknowl-edged. The work of Q.B.C. is supported by DeutscheForschungsgemeinschaft (DFG) and National NaturalScience Foundation of China (NSFC) through fundsprovided to the Sino-German CRC 110 “Symmetriesand the Emergence of Structure in QCD” (DFG GrantNo. TRR110 and NSFC Grant No. 11621131001). I.K.was supported by National Research, Development andInnovation Office NKFIH, contract number PD 124717.The authors are indebted to M. Loriggiola for his helpin target preparation. References
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