The ground state rotational bands of the N = Z nuclei 72Kr, 76Sr, and 80Zr have been extended into the angular momentum region where rotation alignment of particles is normally expected. By measuring the moments of inertia of these bands we have observed a consistent increase in the rotational frequency required to start pair breaking, when compared to neighboring nuclei. 72Kr shows the most marked effect. It has been widely suggested that these “delayed alignments” arise from np-pairing correlations. However, alignment frequencies are very sensitive to shape degrees of freedom and normal pairing, so the new experimental observations are still open to interpretation

Balamuth, D.P.

Bauer, R.

Becker, J.A.

Bernstein, L.A.

Carpenter, M.P.

Durell, J.

Fischer, S.M.

Fotiades, N.

Freeman, S.J.

Garrett, P.E.

Hausladen, P.A.

Janssens, R.V.F.

Jenkins, D.

Leddy, M.

Lister, C.J.

Ressler, J.

Sarantites, D.G.

Schwartz, J.

Seweryniak, D.

Svelnys, D.

Varley, B.J.

Wyss, R.

Carolina Digital Repository

VOLUME 87, NUMBER 13 P H Y S I C A L R E V I E W L E T T E R S 24 SEPTEMBER 2001Alignment Delays in the N 5 Z Nuclei 72Kr, 76Sr, and 80ZrS. M. Fischer,1 C. J. Lister,2 D. P. Balamuth,3 R. Bauer,4 J. A. Becker,4 L. A. Bernstein,4 M. P. Carpenter,2 J. Durell,5N. Fotiades,6 S. J. Freeman,5 P. E. Garrett,4 P. A. Hausladen,3 R. V. F. Janssens,2 D. Jenkins,2,3 M. Leddy,5 J. Ressler,7J. Schwartz,2 D. Svelnys,1 D. G. Sarantites,8 D. Seweryniak,2 B. J. Varley,5 and R. Wyss91Department of Physics, DePaul University, Chicago, Illinois 606142Physics Division, Argonne National Laboratory, Argonne, Illinois 604393Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 191044Physics Division, Lawrence Livermore National Laboratory, Livermore, California 945505Department of Physics, University of Manchester, Manchester M13 9PL, United Kingdom6Department of Physics and Astronomy, Rutgers University, New Brunswick, New Jersey 089037Department of Chemistry, University of Maryland, College Park, Maryland 207428Department of Chemistry, Washington University, St. Louis, Missouri 631309Royal Institute of Technology, KTH-Frescati, Frescativ 24, 104 05, Stockholm, Sweden(Received 22 March 2001; published 4 September 2001)The ground state rotational bands of the N  Z nuclei 72Kr, 76Sr, and 80Zr have been extended intothe angular momentum region where rotation alignment of particles is normally expected. By measuringthe moments of inertia of these bands we have observed a consistent increase in the rotational frequencyrequired to start pair breaking, when compared to neighboring nuclei. 72Kr shows the most markedeffect. It has been widely suggested that these “delayed alignments” arise from np-pairing correlations.However, alignment frequencies are very sensitive to shape degrees of freedom and normal pairing, sothe new experimental observations are still open to interpretation.DOI: 10.1103/PhysRevLett.87.132501 PACS numbers: 27.50.+e, 21.30.Fe, 23.20.Lv, 24.10.– iShort range correlations of fermions to form bosonlike“Cooper pairs” are known to have a dramatic influenceon physical observables in materials, causing effects suchas superfluidity and superconductivity. The nature of thesecorrelations is described by the Bardeen-Cooper-Schrieffer(BCS) pairing theory. Their strength has been extensivelyinvestigated through the destruction of the pair field bytemperature or by magnetic fields. In nuclei, similar cor-relations play a crucial role in nuclear structure, especiallyof even-even nuclei where all the particles can be paired.The conditions for BCS-type pair fields are not always sat-isfied in nuclei, due to their small size leading to low leveldensities, and because the absolute number of particles in anucleus is relatively small. However, it is well known thatin most nuclei the observed properties can be describedonly if a pairing field is assumed. Experimentally, themost clear-cut way to investigate nuclear pairing is throughtransferring pairs of particles using light-ion transfer reac-tions such as p, t or t, p and measuring the probabilityof levels near the Fermi surface being occupied by scat-tered pairs [1]. Less directly, as pairing reduces the mo-ment of inertia of deformed nuclei by about a factor of 2compared to the rigid body value, the variation of the mo-ment of inertia with angular momentum has been a usefultool for investigating the strength of pairing fields, in closeanalogy with the destruction of superconductivity by mag-netic fields.The effect of Coriolis forces on the pair field in well-deformed nuclei has been extensively investigated bothexperimentally and theoretically, and models with goodpredictive power have been developed [2–5] which cal-132501-1 0031-90070187(13)132501(4)$15.00culate the frequencies where pairs break. In heavy nucleiseparate neutron and proton pair fields exist, each consist-ing of pairs of identical particles in time reversed orbitswhich are coupled to angular momentum J  0h̄, andisospin T  1. In light nuclei, the neutron and protonFermi surfaces can be equal (N  Z nuclei) and neutron-proton pairs should also be involved, either coupled toJ, T  0, 1 (as in “normal” pairing) or with an isospin an-tisymmetric wave function with T  0 and J fi 0, or both.The properties of np pairs have attracted interest over theyears from Elliott [6], Goodman [7], Pittel [8], and oth-ers. Until recently, a serious impediment to progress hasbeen the inaccessibility of intermediate-mass N  Z nu-clei; they lie far from stability, and can be produced onlywith low cross-sections when stable beams and targets areinvolved.Advances in experimental technique have opened up theN  Z line between 56Ni and 100Sn to observation. Con-siderable interest has turned to the issue of np pairing.An extensive review of recent calculations is presented inRef. [7]. One particular line of investigation [7,9–12] in-volved consideration of the robustness of the various pairfields against rotation, and the realization that T  0 pairsare less easily destroyed by Coriolis forces, so it may bemore important at high angular momentum when otherfields are quenched. As these pairs are not easily bro-ken, irregularities in the moment of inertia (“alignments”or “backbends”) are predicted to be delayed to higher ro-tational frequencies [10,11] or may disappear altogether[12]. At present, many calculations are schematic andreach widely differing conclusions on the role and relative© 2001 The American Physical Society 132501-1VOLUME 87, NUMBER 13 P H Y S I C A L R E V I E W L E T T E R S 24 SEPTEMBER 2001importance of T  0 and T  1 np pairs. In this Letterwe report on new experiments aimed at studying g raysfrom rotational bands of N  Z nuclei in the middle ofthis region where deformations are large b2  0.4 andthere should be sufficient valence particles to support pair-ing fields. At the outset of this study, no data on the angu-lar momentum region of interest existed. The goal was toidentify levels above the region of spin where pair breakingis normally found, i.e., in the J  8 to 14h̄ regime whereg92 particles in this mass region normally align. Further,we wanted to study several nuclei systematically, in orderto look for consistently delayed alignments which may beexpected if a new collective pair field was in action. Thisresearch extends the work of deAngelis et al. [13], whosuggested an np-pairing driven delayed alignment in 72Kr.72Kr was produced in the 40Ca40Ca, 2a reaction at160 MeV. Gamma rays were detected using the Gam-masphere detector, consisting of 101 Compton-suppressedhigh-purity germanium detectors. Channel selection wasachieved using the Microball CsI light-charged particle de-tector. The efficiency for 2a detection was measured tobe 16%. The cross section for 72Kr production was es-timated to be 120 mb. 76Sr and 80Zr were produced bythe inverse 24Mg54Fe, 2n and 24Mg58Ni, 2n reactions at180 and 200 MeV respectively. In these cases, channelselection was achieved using the Argonne fragment massanalyzer (FMA) with an ion chamber at the focal plane toallow the atomic numbers to be inferred from energy lossmeasurements. The FMA efficiency was about 12%, andthe production cross sections were consistent with a previ-ous measurement [14] of approximately 10 mb.Spectra of g rays from the ground state bands of 72Kr,76Sr, and 80Zr are shown in Fig. 1. A tabulation of therelevant g-ray energies and intensities can be found inTable I. In the upper panel, Fig. 1a, the 2a-gg gatedspectrum clearly shows the 72Kr ground state sequenceextending above spin J  26. The assignments of deAn-gelis et al. [13] were confirmed to spin J  14, but thehighest transition they reported, a 1368 keV g ray, wasnot found to be a member of the yrast cascade. Instead,the band continues to spin 18 where an irregularity is clear,before smoothly continuing to the highest spin we observe,at J  26. In addition, above spin J  12, we find afork in the ground state rotational band, with a more ir-regular second sequence apparently becoming yrast. Thissequence appears to be a more spherical irregular “ter-minating” configuration, and does not enter into the fol-lowing discussion of rotational alignment. In Fig. 1b theground state sequence of 76Sr is shown. The best data onthe ground state band come from applying mass, energyloss, and single g gates. The dramatically lower crosssection for strontium production is clearly evident. How-ever, the band can be extended above spin J  16, a con-siderable advance over the original study [14] which waslimited to J  4. 76Sr gated ggg data indicate a ten-tative 18 ! 16 transition of 1666 keV. Figure 1c showsa 80Zr gated g singles spectrum with contributions from132501-2050100150050100Counts / 3 keV0 500 1000 1500 2000Energy  (keV)0100200 72Kr a)76Sr b)80Zr c)2624836988931067121813491498612 71079299611851355150916621739183019152034213628953777910051179FIG. 1. Gamma-ray spectra of the ground state cascades inN  Z nuclei: (a) 72Kr (2a-gated ggg data, sum of gggates with one transition below and one transition above J  14,production cross section 120 mb); (b) 76Sr (AQ  7624and dEdx gated gg data, sum of g gates for transitions belowJ  10, 20 mb); (c) 80Zr (AQ  8025 and dEdx gated gsingles, 10 mb).yttrium and strontium isobars subtracted. The data seton 80Zr is smaller than that for 76Sr, as the experimentwas a trial run for this kind of study, the acquisition timeshorter, and the cross section slightly lower. The 80Zr ggcoincidence data were very sparse, and could not be com-pletely separated from 80Y, which is produced 400 timesmore intensely and has transitions of similar energies to80Zr. However, the data were sufficient to verify the cas-cade coincidence relationship of the five transistions inFig. 1c and Table I. Transitions of 1300 and 890 keV,visible in Fig. 1c, appear to be associated with 80Zr but donot form part of this sequence, perhaps belonging to the gband. Clearly, a further study of 80Zr to obtain more datais both feasible and desirable.The method of converting the sequence of g raysinto moments of inertia is well established [2]. Twomoments are frequently considered: the kinematic mo-ment, J 1, which is the slope of an energy vs spin2plot and is numerically equal to the recipe used in older“backbending” analyses; and its derivative, the dynamicmoment of inertia J 2. In the heavy deformed nucleiof the rare earth and actinide regions, the deformation is132501-2VOLUME 87, NUMBER 13 P H Y S I C A L R E V I E W L E T T E R S 24 SEPTEMBER 2001TABLE I. Ground state cascades for the nuclei 72Kr, 76Sr, and 80Zr. Data were 2a-gated ggg triples for krypton, mass and chargegated gg doubles for strontium, and mass and charge gated g singles for zirconium. The intensities for 72Kr were from g triplesdata and thus have been normalized to the 8 ! 6 transition, which is estimated to be half the 2 ! 0 flux. Transitions identified byan asterisk (*) have measured g-ray angular distributions consistent with quadrupole radiation.72Kr 76Sr 80ZrJi Eg keV I arb. Eg keV I arb. Eg keV I arb.2 710.1(2)* 200 261.5(3)* 100 288.9(2)* 1004 611.8(2)* · · · 483.2(3)* 76(6) 536.9(3)* 80(10)6 791.5(2)* · · · 697.9(5)* 67(11) 779.2(5) 60(10)8 995.6(2)* 100 893.3(5)* 33(6) 1005(1) 43(8)10 1185.0(3)* 76(12) 1067(1)* 33(8) 1179(1) 25(5)12 1354.9(3)* 61(11) 1218(1) 21(6)14 1508.9(3)* 65(12) 1349(1) 21(8)16 1662.0(6)* 39(10) 1498(2) 15(8)18 1738.6(6)* 26(9) (1666) ,1020 1829.7(1) 36(12)22 1915(1) 25(9)24 2034(1) 19(6)26 2136(2) 9(4)quite constant and stable, and so changes of the moment ofinertia directly give information on the pair field. Further,for rigid shapes, a core moment of inertia can be fitted (areference) and the total angular momentum then decom-posed into “core” and “aligned particle” components. Inthe mass A  80 region, it has long been known that thesepremises are less valid [3] as the alignment of particlescan have a significant polarizing effect on the core [15,16].Consequently, the extraction of the crossing frequency,alignment, and interaction strengths need to be treatedwith caution. Despite these concerns, the reduction of thedata to kinematic and dynamic moments of inertia servesas a useful basis for interpretation and comparison withneighboring nuclei. Such a comparison is shown in Fig. 2where we present J 1 (top panels) and J 2 (bottom132501-3panels) for each of the nuclei of interest, compared to itsnearest neighbors with N  Z 1 2 [17] and N  Z 1 4[18–20].Sharp upbends are found in 74,76Kr at h̄v  0.65 MeVassociated with simultaneous proton and neutron align-ment. An important recent study of 74Kr shows thatthe nucleus shrinks 30% in quadrupole deformationduring this process and at higher frequencies, shiftingthe neutron crossing down in frequency to overlap theproton alignment [15]. In 72Kr, no sudden discontinuitiesof this type are found at low frequency, just a moregradual interaction at h̄v  0.85 MeV. It is unclearwhy an analogous alignment to 74,76Kr is not seen in72Kr, perhaps suggesting that new correlations are in play.We performed a traditional rigid-cranking analysis, with0102030J     (MeV/ h   )0.0 0.4 0.802040 J     (MeV/ h   )0.0 0.4 0.8 1.20.0 0.4 0.8hω (MeV)(1)(2)22///Kr Sr ZrKr Sr ZrFIG. 2. The kinematic moments of inertia J 1 (top panels) and dynamic moments of inertia J 2 (bottom panels) of the groundstate bands of 72Kr, 76Sr, and 80Zr calculated according to Ref. [2]. Tentative data points are marked with open symbols. The dashedcurves are the moments of inertia for isotopes with N  Z 1 2, and the dotted curves for isotopes with N  Z 1 4.132501-3VOLUME 87, NUMBER 13 P H Y S I C A L R E V I E W L E T T E R S 24 SEPTEMBER 2001normal pairing fields, and found that it is possible to shiftthe alignments up to high frequency only by invoking anunrealistically large deformation b2 . 10.45, or byinvoking a highly deformed, collectively rotating oblateshape with jb2j . 0.3. The latter seems unlikely asthe band has almost the same moment of inertia as itsneighbors which are known to be prolate at intermediatespin. Data on 73Kr [21] show that the odd-A nucleushas an alignment pattern very similar to 74Kr, furtherhighlighting the unique nature of the band crossing in72Kr. In strontium isotopes the effect is more subtle as theinteraction between ground-state and aligned bands is verylarge, so no abrupt irregularities are seen in either N  Zor N  Z 1 2, 4 isotopes. Only the dynamic moments ofinertia reveal the crossing location and frequency. 78,80Srhave very similar proton crossings at h̄v  0.55 MeV.76Sr has an interaction of similar strength to its isotopes,but again shifted upwards, to h̄v  0.62 MeV. Finally,in the zirconium isotopes, where sharp alignment irreg-ularities are known in 84Zr and heavier nuclei, arisingfrom proton pair breaking below h̄v  0.5 MeV, wefind that the 80Zr ground state band is smooth to thehighest frequency we observe (h̄v  0.6 MeV), againindicating an alignment delay. However, we note that82Zr [17] shows similar behavior, so the situation is evenless clear-cut. A recent experiment [22] has identifiedthe ground state sequence in 88Ru which reveals anothersmoothly spaced sequence of transitions extending beyondthe rotational frequency where alignment is expected.Thus, in cases from N  Z  36 to 44, there is consistentevidence that particle alignments are all shifted to higherfrequency than is expected from systematic trends, and forN  Z  36, 38 the crossing frequency has been located.There has been considerable theoretical speculation thatsuch shifts may be an experimental manifestation of nppairing. To understand our observations a self-consistentanalysis is needed, building on both the new N  Z mea-surements and the extensive data with N . Z. Carefulstudies of the N  Z 1 2 nuclei [15,17] which can beproduced hundreds of times more prolifically, and are moreextensively known, strongly constrain our interpretations.It is already clear that the situation is more complicatedthan originally perceived. In the nuclei under study, theband crossings are not a clean experimental probe of pair-ing, as the nuclei are easily polarized by changing thepopulation of individual orbits, so “rigid-core” assump-tions are not valid. Further, there is a close link be-tween the equilibrium shapes and pairing. Modification ofthe strength and type of pair fields, especially introducingpairs not coupled to J  0, will change the deformation,as J  0 coupling favors more spherical shapes to maxi-mize degeneracy and overlap. Many theoretical groups areworking on this interesting problem.In conclusion, we have experimentally demonstrated aconsistent shift to higher frequencies of the alignment ofg92 particles in the ground state bands of N  Z nuclei132501-4from krypton to zirconium. A similar observation hasvery recently been made for N  Z ruthenium [22]. Theeffect is most striking for 72Kr, more modest in 76Sr, anda limit in 80Zr and 88Ru. Considerable progress is stillneeded to reach an unambiguous understanding of theseresults. In experiment, progress can be made on even-even nuclei through measuring the transitional collectivityof the new bands and extending the data on the heaviersystems, while studying the odd-odd N  Z nuclei canimprove our understanding of np coupling. In theory, fullyself-consistent analyses of shapes and pair fields across theentire region are badly needed.This research was supported by grants from the DOE,NSF, Research Corporation, and European funding agen-cies. We note, in particular, U.S. DOE Nuclear PhysicsDivision Grant No. W-31-109-ENG38 which supportedGammasphere at the ATLAS facility. A later Gammas-phere experiment has confirmed our yrast sequences for72Kr [23].[1] D. Bes, R. A. Broglia, O. Hansen, and O. Nathan, Phys.Rep. 34C, 53 (1977).[2] R. Bengtsson and S. Frauendorf, Nucl. Phys. A327, 139(1979).[3] W. Nazarewicz, J. Dudeck, R. Bengtsson, T. Bengtsson,and I. Ragnarsson, Nucl. Phys. A435, 397 (1985).[4] W. Satula and R. Wyss, Phys. Scr. T56, 159 (1995).[5] R. Palit, J. A. Sheikh, Y. Sun, and H. C. Jain, Nucl. Phys.A686, 141 (2001).[6] J. P. Elliott et al., Phys. Lett. 97B, 169 (1980); Nucl. Phys.A609, 1 (1996).[7] A. L. Goodman, Adv. Nucl. Phys. 11, 263 (1979); Phys.Rev. C 58, R3051 (1998); 60, 014311 (1999).[8] J. Dobes and S. Pittel, Phys. Rev. C 57, 688 (1998); Balk.Phys. Lett. 1, 3 (1998).[9] K. Nichols and R. A. Sorensen, Nucl. Phys. A309, 45(1978).[10] S. Frauendorf and J. A. Sheikh, Phys. Rev. C 59, 1400(1999); Phys. Scr. T88, 162 (2000); Nucl. Phys. A645,509 (1999).[11] W. Satula and R. Wyss, Phys. Lett. B 393, 1 (1997).[12] A. L. Goodman (to be published).[13] G. deAngelis, Phys. Lett. B 415, 217 (1997).[14] C. J. Lister et al., Phys. Rev. Lett. 59, 1270 (1987); Phys.Rev. C 42, R1191 (1990).[15] A. Algora et al., Phys. Rev. C 61, 031303 (2000).[16] A. Harder et al., Phys. Rev. C 55, 1680 (1997).[17] D. Rudolph et al., Phys. Rev. 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Alignment delays in the N = Z nuclei 72Kr, 76Sr, and 80Zr

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Alignment delays in the N = Z nuclei 72Kr, 76Sr, and 80Zr

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