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PHYSICAL REVIEW C, VOLUME 63, 061304~R!

Observation of chiral doublet bands in odd-oddNÄ73 isotones

T. Koike, K. Starosta,* C. J. Chiara, D. B. Fossan, and D. R. LaFosseDepartment of Physics and Astronomy, State University of New York at Stony Brook, Stony Brook, New York 11794-380

~Received 17 January 2001; published 3 May 2001!

Three odd-oddN573 isotones, namely128Cs, 130La, and132Pr, have been studied via~HI, xng) reactions.In all three cases,DI 51 side bands of theph11/2nh11/2 yrast bands were discovered. This extends the sys-tematic observation of nearly degenerateph11/2nh11/2 doublet bands in the neighboringN575 isotones; thesewere interpreted as resulting from chiral symmetry breaking in the intrinsic body-fixed frame.

DOI: 10.1103/PhysRevC.63.061304 PACS number~s!: 21.10.Re, 23.20.Lv, 23.90.1w, 27.60.1j

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The observation of nearly degenerate doubletDI 51bands in 134Pr and the surrounding triaxialN575 odd-oddisotones,130Cs, 132La, and 136Pm, has been interpreted athe result of the existence of chirality in the intrinsic bodfixed frame leading to a doubling of states for tph11/2nh11/2 yrast configuration@1,2#. In these triaxial nuclei,left- and right-handed chiral geometries in the body-fixframe can be formed from the mutually perpendicular anlar momenta of theh11/2 particles and the core rotation. Sincthe Fermi level for these nuclei is located in the lower partthe ph11/2 subshell but in the upper part of thenh11/2 sub-shell, theph11/2 and thenh11/2 angular momenta are alignealong the short and long axes of the triaxial core, resptively; this maximizes the overlap of the valence particwave functions and the core and thus minimizes the intetion energy. Likewise, the angular momentum of the rotional core is oriented along the intermediate axis becathe moment of inertia is the largest along this axisirrotational-like flow, which minimizes the rotational energChirality thus attained in the body-fixed frame leads todoubling of states, which manifests in the laboratory fraas degenerate doublet bands. It should be noted, howethat the doublet bands do not represent pure right- or lhanded states, but rather combinations of the two whichstore the chiral symmetry that is broken in the intrinsframe. These chiral effects are dependent on the triashape of the nucleus and a delicate balance of the threegular momenta involved. In fact, the observation of chiproperties represents the first direct evidence for stableaxial shapes in nuclei.

As suggested in Ref.@2#, it is important to explore theextent of these nuclear conditions for chirality to further psue a complete understanding of this novel phenomenoncluding related effects such as collective chiral vibratiorepresenting a weaker symmetry breaking. For this purpexperiments have been performed in the odd-oddN573 iso-tones,128Cs, 130La, and 132Pr, where theph11/2nh11/2 bandsare still yrast.~The spin/parity assignments for the yrast bain 130Cs @3# are based on electron conversion and angudistribution measurements for a series of transitions conning the yrast band to theT1/253.46 min 52 isomeric state,which was rigorously assigned on the basis of atomic-be

*On leave from: Institute of Experimental Physics, Warsaw Uversity, Hoza 69, 00-681 Warsaw, Poland.

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magnetic resonance@4# andb-decay measurements@5#. Sys-tematic trends of the yrast bands inA;130 odd-odd nuclei@6# imply that these bands are built on the same positiparity configuration,ph11/2nh11/2.) An isomer at the band-head in128Cs allows for a particularly sensitive examinatioof possible chiral effects by the use of isomer delayed tging. In all three cases,DI 51 side bands were observeachieving similar doublet-band characteristics as previouseen for theN575 isotones. This Rapid Communication prsents the newN573 results which reveal an extension of thN575 region of nuclear chirality.

Excited states in128Cs, 130La, and132Pr have been populated via the122Sn(10B, 4n) fusion evaporation reaction a47 MeV, 124Te(10B, 4n) at 51 MeV, and117Sn(19F, 4n) at88 MeV, respectively. The targets of122Sn, 124Te, and117Snwere 3.0, 2.2, and 3.6 mg/cm2 thick, respectively, each withlead backing sufficient to stop the recoils in order to reduDoppler broadening of the low-energyg rays of interest. TheFN-tandem injected superconductingLINAC at Stony Brookprovided pulsed beams with a period of 106 ns. A Comptsuppressed HPGe detector array with detectors positione;630°, 690°, and6150° relative to the beam axis waused in conjunction with a 14-element BGO multiplicity fiter. A total of ;5.23107, 5.13107, and 1.313108 time-gated promptg-g events were collected for the128Cs, 130La,and 132Pr experiments, respectively. A pulsed beam-g timeresolution of FWHM;10 ns was maintained over the aceptedg-ray energy range. The energy resolution for theevents was FWHM;2 keV at;550 keV.

Positive-parity side bands are newly identified from tpresent studies in the128Cs and 130La isotones; these sidbands are shown in the partial level schemes in Fig. 1 alwith the correspondingph11/2nh11/2 yrast bands. Previousinformation was available on the yrast bands for these nu@7,8#. A less well-developed side band was observed132Pr, as shown. Most of these132Pr transitions were re-ported in previous works@9,10# without interpretation. As inthe case for theN575 isotones, angular correlation analysalong with timing information uniquely determined that thlinking transitions between the side and yrast bands areDI 51 mixed M1/E2 character. This leads to the currerelative-spin assignments as indicated in Fig. 1 and posiparity for the side bands. The presentation of the leschemes with a common bandhead spin ofI is the same asthat used in Ref.@2#, where also only relative-spin assign

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KOIKE, STAROSTA, CHIARA, FOSSAN, AND LaFOSSE PHYSICAL REVIEW C63 061304~R!

FIG. 1. Partial level schemededuced from the present studfor the N573 isotones 128Cs,130La, and 132Pr are presented inthe format adopted from Ref.@2#.For each isotone, the side bandplaced on the left of theph11/2nh11/2 yrast band.

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ments were made; the systematic band properties as share remarkably similar. Considering all of theN573 and 75isotones, the best consistent choice for the absolute bandspin is I 59 @6#. As pointed out in Ref.@2#, information onthe relative spins is sufficient for the discussion of chiproperties.

Of the nuclei investigated so far regarding chiral doublin the A;130 region, 128Cs is a unique case in that bobands decay mainly through the isomeric state labeled spI,indicated by the thick horizontal line in Fig. 1. Several trasitions below the bandhead were included in the partial lescheme of128Cs to show theg rays used for the isomedelayed tagging. The earlier work@7# had observed this50-ns isomer in 128Cs, but with the 143-keV transitionplaced below the isomer. In the current experiment, the 1keV g ray was observed to be in strong coincidence withprompt in-bandg rays above the isomer, but very weakwith the delayedg rays below the isomer. These observtions, therefore, define the 143-keVg ray as the bottom transition of the yrast band. Delayed tagging on theg rays belowthe isomer reduces the background and enhances bothside-band and the yrast-band transitions as well as theing transitions as shown by the spectrum in Fig. 2. Tpresent128Cs level scheme shown in Fig. 1, along with thoof the otherN573 isotones, is consistent with the systemapattern of theph11/2nh11/2 doublet bands for theN575 odd-odd nuclei. This isomer delayed tagging technique coprove to be advantageous for future experiments involvdetailed studies of the doublet-band transition strengths.

The observed side bands in theN573 isotones sharecommon characteristics with those in theN575 isotones.Figure 3 is a plot of the experimental excitation energversus spin showing near degeneracy for the side bandsthe yrast bands. In all threeN573 cases, the side-band curv~open symbols! is displaced slightly higher in energy abovthe yrast curve~closed symbols!. The amount of displacement, hence the deviation from degeneracy, is approxima200 keV for 128Cs and 400 keV for130La and 132Pr. Thesedoublet bands never achieve equal energies at any ofobserved spins unlike the case of the134Pr nucleus. All ofthe side bands are linked with the yrast bands via miM1/E2 transitions. As argued in Ref.@2#, the ph11/2nh11/2

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configuration is the only reasonable basis for these sbands. Since the yrast-bandph11/2nh11/2 configuration iscomprised of two unique-parity single-particle orbitals~fornuclei between the 50 and 82 proton and neutron closhells!, other possible low-lying positive-parity configurations representing the side bands would necessarily invopositive-parity orbitals~such asd5/2 and g7/2) for both thevalence proton and neutron. No transitions ofM1/E2 multi-polarity, however, would then be allowed between suchband and the yrast band since one-body electromagneticerators do not have transition matrix elements involvingchange of two particles. Thus, as in Ref.@2#, this near de-generacy of the doublet bands is attributed to the doublingstates for theph11/2nh11/2 configuration because of the mutually perpendicular orientation in the body-fixed framethe angular momenta of the two valence particles andcore rotation, which results in the chiral symmetry breakin

FIG. 2. A g-ray spectrum for128Cs obtained by tagging ondelayed transitions, which are labeled as D, below the isomer.numbers correspond to energies in keV and are preceded by Yand L for transitions in the yrast band, the side band, and thlinking the two bands, respectively. Counts per channel have bscaled down by a factor of 2 for energies to the left of the dasline.

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OBSERVATION OF CHIRAL DOUBLET BANDS IN ODD- . . . PHYSICAL REVIEW C 63 061304~R!

Among the N573 isotones,128Cs reveals doublet bandclosest to degeneracy. Reference@2# attributes the small energy displacements between the doublet bands to a collechiral vibration; collective chiral vibrations in relation to chral symmetry breaking would be analogous to collectivetupole vibrations in relation to parity symmetry breaking.

The extendedN573 and 75 systematics of the observdoublet bands with near degeneracy further support tcommon physical origin as the breaking of chiral symmein the body-fixed frame. Since the rotational angular momtum changes gradually with spin, the chiral geometry anddegree of the associated symmetry breaking can changespin; this gives a reasonable explanation for the energiethe doublet band members in134Pr approaching each othewith increasing spin and achieving degeneracy for a smrange of spin starting at (I 16), as shown in Fig. 3. Agradual transition from weaker to stronger chiral symmebreaking seems to evolve with increasing spin in134Pr. In theodd-odd nuclei surrounding134Pr, the symmetry appears tremain moderately broken, as suggested by the small endisplacements as a function of the observed spin.

While experimental studies of doublet bands continue,present experimental results require further theoretical invtigation to address quantitatively these interesting chi

FIG. 3. Experimental excitation energy versus spin plot. Curwith closed~open! symbols connected by dashed lines are ofyrast ~side! bands in theN573 isotones. Similar curves with solilines, representing the fourN575 isotones from Ref.@2#, are plot-ted 1.5 MeV above the reference energy of the correspondingtopes.

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symmetry properties. Currently two theoretical approachave been used to address these experimental results. Mscopic three-dimensional tilted axis cranking~3D TAC! cal-culations@1#, based in a body-fixed rotational frame, habeen successful in elucidating the microscopic origin ofchiral-symmetry breaking in these nuclei. In this model, torientation of the total angular momentumJ, characterizedby the tilting anglesu and w, can be calculated selfconsistently. Aplanar chiral solutions, in which the total agular momentumJ tilts away from all three principal axewith both u andw differing substantially from 0° and 90°were found for theph11/2nh11/2 configuration in134Pr @1# fora range of frequenciesv. The calculations showed that thnucleus was triaxial withg near 30° and that the core rotational vector was aligned along either the6 intermediateaxis, representing the right- and left-handed geometrThese solutions imply chiral symmetry breaking in thetrinsic frame and achieve the doubling of states in the traformation to the laboratory frame where the symmetry hasbe restored. Subsequently, the same 3D TAC approachapplied to all of theN575 odd-odd isotones (Z555–63) of134Pr where doublet bands were observed; results of thcalculations were reported in Ref.@2#. In all five isotones,chiral solutions were found over a limited range inv with atriaxial deformationg;30°. Indicative of the strength ochiral symmetry breaking is the energy difference betwethe Routhian minima and the lowest saddle point atw50°denoted asEb in Ref. @2#. A largeEb confinesJ to one of theminima ~or the rotational angular momentum to the6 inter-mediate axes! corresponding to either the right- or lefhanded solution; this would lead to strong chiral symmebreaking and achieve energy degeneracy for the doubands. A smallEb , on the other hand, would not completeconstrainJ to one of these minima, leading to weaker symmetry breaking and an energy displacement betweendoublet bands; this was discussed in Ref.@2# in terms ofcollective chiral vibrations. The trend of the calculatedEbagrees qualitatively with the observed energy displacemin the N575 isotones; the largestEb was obtained for134Prat v;350 keV/\ in comparison to all the other isotones asfunction of frequency. Such calculations have not been pformed for comparison to the currentN573 isotone results,although experimentally they are similar to theN575 re-sults.

The second approach, a phenomenological partihole plus core coupling model employs weak coupling btween the valence particle/hole and the core; basis stu jp3 j n&LM3uR& are used to diagonalize the Hamiltonian thincludes a triaxial core, a single-particle Hamiltonian, aquadrupole-quadrupole interactions, wherejp , j n , andR arethe angular momenta of the valence proton, the valence ntron, and the core, respectively@11#. This approach is carriedout in the laboratory frame where the Hamiltonian requirestored chiral symmetry. Calculated observables such ascitation energy, total spin, and branching ratios can berectly compared to experimental values, although the cproperties have to be externally provided. Calculations usa rigid triaxial core withg;30° @11# yield degenerate doublet bands consistent with the microscopic 3D TAC calcu

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KOIKE, STAROSTA, CHIARA, FOSSAN, AND LaFOSSE PHYSICAL REVIEW C63 061304~R!

tions discussed above; expectation values of the orientaof the angular momenta obtained with these wave functiagree with the aplanar chiral geometry. Theoretical studusingg-soft triaxial cores have revealed deviations from dgeneracy for the doublet bands@12#. A reduced moment ofinertia along the intermediate axis fromg softness has beesuggested as a possible mechanism for the rotational anmomentum not being completely constrained to the intermdiate axis, thereby mixing the right- and left-handed chisystems and resulting in a weaker symmetry breaking@2#. Itshould be stressed that the observed systematics cannoterly be explained by principal axis cranking. Reference@2#rules out quasiparticle excitations for the side bands inN575 isotones, as well asg vibrations coupled to the yrasband; expected energy differences between the yrast anside bands from these alternative interpretations are mthan twice the experimental values.

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In conclusion, the experimental results for threeN573isotones are presented as an extension of the earlier invgation of chirality in theN575 isotones. In all three cases,DI 51 side band with the sameph11/2nh11/2 configuration asthe yrast band was identified. The128Cs isotone appears especially promising for future experimental studies on tdoublet bands because of the isomer feeding. The smallergy displacements of the side band from the yrast bandply the existence of chiral symmetry breaking in theN573isotones, extending theN575 region surrounding134Prwhere near degenerate doublet bands were interpreted aslective chiral vibrations. Further exploration is important fthe complete definition of theZ,N boundaries of this regionof chirality.

This work was supported by U.S. NSF Grant NPHY9870280. The authors acknowledge helpful theoretdiscussions with Dr. Jing-ye Zhang.

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