An excited superdeformed band in 194Hg, observed to decay directly to both normal-deformed and superdeformed yrast states, is proposed to be a Kπ = 2− octupole vibrational band, based on its excitation energies, spins, and likely parity. The transition energies are identical to those of the yrast superdeformed band in 192Hg, but originate from levels with different spins and parities. The evolution of transition energies with spin suggests that cancellations between pairing and particle alignment are partly responsible for the identical transition energies

Ackermann, D.

Agrawala, S.

Ahmad, I.

Amro, H.

Blumenthal, D.J.

Calderin, I.J.

Carpenter, M.P.

Døssing, T.

Fisher, S.M.

Hackman, G.

Hannachi, F.

Janssens, R.V.F.

Khoo, T.L.

Korichi, A.

Laurtisen, T.

Lee, I.Y.

Lopez-Martens, A.P.

Macchiavelli, A.O.

Moore, E.F.

Nakatsukasa, T.

Nisius, D.

Reiter, P. Chard C.

Young, J.

Copenhagen University Research Information System

Spins, Parity, Excitation Energies and Octupole Structure of an Excited Superdeformed Band in 194 Hg and Implications for Identical Bands - Reply

Lauritsen, T.

Lopez-Martens, A.

Agarwala, S.

Fischer, S.M.

Reiter, P.

Carolina Digital Repository

VOLUME 79, NUMBER 21 P H Y S I C A L R E V I E W L E T T E R S 24 NOVEMBER 1997Spins, Parity, Excitation Energies, and Octupole Structure of an Excited Superdeformed Bandin 194Hg and Implications for Identical BandsG. Hackman,1 T. L. Khoo,1 M. P. Carpenter,1 T. Lauritsen,1 A. Lopez-Martens,2 I. J. Calderin,1 R. V. F. Janssens,1D. Ackermann,1 I. Ahmad,1 S. Agarwala,1 D. J. Blumenthal,1 S. M. Fischer,1 D. Nisius,1 P. Reiter,1 J. Young,1H. Amro,1,3 E. F. Moore,3 F. Hannachi,2 A. Korichi,2 I. Y. Lee,4 A. O. Macchiavelli,4T. Døssing,5 and T. Nakatsukasa61Argonne National Laboratory, Argonne, Illinois 604392Centre de Spectrometrie Nucleaire et de Spectrometrie de Masse, IN2P3-CNRS, F-91405 Orsay, France3North Carolina State University, Raleigh, North Carolina 27695 and TUNL, Durham, North Carolina 277084Lawrence Berkeley National Laboratory, Berkeley, California 947205Niels Bohr Institute, DK-2100 Copenhagen 0, Denmark6UMIST, Manchester M60 1QD, United Kingdom(Received 8 July 1997)An excited superdeformed band in194Hg, observed to decay directly to both normal-deformed andsuperdeformed yrast states, is proposed to be aKp ­ 22 octupole vibrational band, based on itsexcitation energies, spins, and likely parity. The transition energies are identical to those of the yrastsuperdeformed band in192Hg, but originate from levels with different spins and parities. The evolutionof transition energies with spin suggests that cancellations between pairing and particle alignment arepartly responsible for the identical transition energies. [S0031-9007(97)04582-1]PACS numbers: 21.10.Re, 21.10.Hw, 23.20.Lv, 27.80.+wInn)n.SDty11]b-reors.y-fc-ereegytalh-di-ci-heofThe potential energy surface in a number of nuclei han excited minimum (false vacuum) at large deformatioThe lowest states in the superdeformed (SD) minimulie among hot normal-deformed (ND) states several Meabove the ND yrast line at low spin, but are isolateby a barrier. As a consequence, they are cold orderstates, characterized by good quantum numbers such aKand signature, in addition to spin and parity. A majotheme of nuclear structure studies is to understand tmicroscopic structure of cold SD bands. However,has not been possible to perform standard spectroscotests of theory, i.e., to confront theory with experimentaenergies and interband transition rates of stateswithspecific spins and parities. This is because energies anspinyparity quantum numbers have been determined fjust two SD bands (in194Hg [1] and 194Pb [2]), although,175 SD bands have been found in theA ­ 150 and190 regions. These fundamental properties are necessfor a rigorous test of theory, e.g., of predictions ooctupole susceptibility (reviewed in Ref. [3]) and of lowlying octupole vibrations [4,5] in SD nuclei.There are many pairs of SD bands, in nuclei with diferent mass numbers, which have many transitions wequal energy (within 1 keV) or which have identical dynamic moments of inertia,J s2d (e.g., see Refs. [6,7]).(J s2d ­ 4yDEg , whereDEg is the spacing between con-secutive SD-band transitions.) This unexpected phenomnon has stimulated many explanations [7], but it is stnot understood. The degeneracy may be due to a symetry (which has yet to be identified) or to accidentacancellations of several effects [8]. An understandingthis phenomenon requires knowledge of the spins, paties, quadrupole moments, and microscopic structures4100 0031-9007y97y79(21)y4100(4)$10.00asn.mVdedsrheitpicldoraryf-f-ith-e-illm-lofri-ofthe identical bands, besides just transition energies.this Letter, we report on the spins, parity, and excitatioenergies of an excited SD band in194Hg, labeled band 3by Ref. [9]. (A preliminary report has been given [10].We suggest that the band is built on an octupole vibratioIts transition energies are equal to those in the yrastband in192Hg, but the emitting states have opposite pariand spins differing by1h̄.Two experiments were performed at Gammasphere [with the 150Nd(48Ca,4n)194Hg reaction, using 202 MeVbeams provided by the Lawrence Berkeley National Laoratory 88” Cyclotron. The targets consisted of,1 mgycm2 of isotopically enriched Nd evaporated on,13 mgycm2 Au foils. In the two experiments, Gammasphecomprised 85 and 92 Compton-suppressed Ge detectIn the second experiment, improved (“electronic honecomb”) Compton suppression yielded a,40% improve-ment in sensitivity in fourfold coincidences. A total o5.1 3 109 events were available for analysis after seletion of prompt, high-multiplicity events. The data wersorted by setting coincidence gates on either two or thtransitions in the known SD bands in194Hg as describedin Ref. [12]. Figures 1(a) and 1(b) show theg rays co-incident with triplets and pairs of transitions from SDband 3, respectively, clearly revealing two high-energamma rays at 4978 and 5030 keV in Fig. 1(b). The tocoincidence data and the energy difference of the higenergy transitions show that the two high-energy linesrectly connect the112 SD level to the101 and121 NDyrast states, as shown in the level scheme (Fig. 2). Coindences with the 262-keV intraband transition show that t,5 MeV lines decay out of the same level as the bulkthe decay, which consists of unresolved quasicontinuumg© 1997 The American Physical SocietyVOLUME 79, NUMBER 21 P H Y S I C A L R E V I E W L E T T E R S 24 NOVEMBER 1997ndhe30.iesonthatnisesthensernd 3d8]SDeictu-g]FIG. 1. (a) Low- and (b) high-energy portions of the spectcoincident with, respectively, triplets or pairs of transitionfrom band 3. Note the presence of band 1 lines (B1) in (a).(c) Pairwise coincidence spectrum obtained with one gatethe 4978-keV line and another on band-3 transitions, showtransitions from the101 and 81 ND levels [13]. (d),(e)Portions of triple-coincidence spectra, showing the 832 a839-keV interband lines; (d) from a gate on the 343-keV ban3 line and double gates on higher-lying band-3 transitions a(e) from a gate on the 296-keV band-1 line and double gatesband-3 transitions.rays [14]. There is also evidence for direct decay branchfrom band 3 to band 1, e.g., the 832- and 839-keV linesFigs. 1(d) and 1(e).For the 4978-keV transition, the angular distributiocoefficient was measured to beA2 ­ 20.38s25d, whichis consistent with an anti-stretched dipole assignment arules out a stretchedE2 or DI ­ 0 dipole character(A2 , 10.35). Decay out of SD states [14] is a statisticaprocess analogous to [1]g decay following neutroncapture, where the observed [15] ratio ofE1 to M1 ratesis ,5 for the primaryg rays, which are related to our1-step decay lines. Hence, the,5 MeV transitions mostlikely have E1 multipolarity, leading to negative parityfor band 3. For an excited SD band, this is the first tim(a) that the excitation energies, spins, and likely parhave been determined and (b) that decay branches to byrast SD and ND states have been established.The enhanced statistics from this work confirms thlevel scheme for SD band 1 first proposed in Ref. [1shows additional decay branches and provides betterA2values [10]. The observed 1-step decays from bandand 3 go to ND states of opposite parity, consolidating tassignments of opposite parity to those bands. No 1-stransitions from another excited band, labeled band 2 [rasoningndd-ndonesinnndleityothe],s 1hetep9],FIG. 2. Partial level schemes for the decay of SD bands 1 a3 in 194Hg. Dashed lines indicate tentative assignments. Ttransition intensities (in brackets) are normalized to 100 andfor the full-strength transitions in bands 1 and 3, respectivelyhave been identified, but its intraband transition energ[16] (midway between those of band 3), equal populatiintensity, and probable even spins (see below) suggestit is the signature partner of band 3.At the lowest observed frequencies, the excitatioenergy of band 3 above that of the vacuum band 1only 0.7 MeV (see Fig. 2) and it is extrapolated to b,0.8 MeV at zero frequency. In BCS theory, the lowe2-quasiparticle (qp) excitation energy should be twice tpairing gapD, or ,1.6 MeV for typical values [17] ofD used in calculations which provide good reproductioof the J s2d values of SD bands in theA , 190 region.Since the experimental energies are significantly lowthan those expected for 2-qp states, we suggest that bais not a 2-qp neutron configuration [9], but is insteaa collective vibrational band. Indeed, Refs. [4,5,1have proposed that the lowest excited states in theminimum are octupole vibrations in190 194Hg (and alsoin 192 198Pb. Our data support this interpretation: thexperimental Routhian (orbital energies in the intrinsframe) is close to the calculated one for the lowest ocpole band in194Hg, with Kp ­ 22 (see Fig. 3), and theparity of the band is assigned as negative. A low-lyinexcited SD band in190Hg has also been proposed [4,19to be an octupole vibrational band.4101VOLUME 79, NUMBER 21 P H Y S I C A L R E V I E W L E T T E R S 24 NOVEMBER 1997le,ngheaserotdeofFIG. 3. Routhians for theoretical octupole vibrations (opeand filled circles for signature 1 and 0) and negative par2-qp states (lines) compared with experimental data (opsquares) for band 3. The calculation was performed withoctupole coupling constant 1.05 times the harmonic oscillavalue, which also gives good agreement forJ s2d —see Fig. 1 inRef. [4].The transitions connecting bands 3 and 1 must hastretchedE1 character because of the spins and (likelparities of the initial and final states. The measuredBsE1dvalues are,1025 Weiskopf units (W.u.), which are sig-nificantly stronger than those (,1027 W.u.) for the 1-steptransitions to the ND yrast states. TheBsE1d values sup-port the octupole-vibration assignment. Coriolis couplinwith the lower-K octupole components provides a naturexplanation for the observedE1 transitions, which wouldotherwise beK forbidden between states withKp ­ 22and01. They can proceed through admixtures ofKp ­12 and, particularly,Kp ­ 02, which has the dominantE1 strength [4,20]. The octupole band in190Hg is pre-dicted [4] to have a largerKp ­ 02 admixture, whichexplains its higherE1 strength (,1023 W.u.) [21]. Theemerging systematics of low-lying excited bands andE1rates in194Hg, 190Hg [19,21], and196Pb [22] lend credenceto the predictions [4,5] that octupole vibrations constituthe lowest excited states in the SD minimum of even-evmass-190 nuclei.Since the spins for bands 1 and 3 are now knowboth the dynamical and kinematic moments of inertia,J s2dand J s1d, can be determined as a function of rotationfrequency (̄hv ­ Egy2)—see Fig. 4(a). Extrapolationsof J s1d and J s2d to zero frequency show a significanconvergence for each of the bands. This can be understfrom familiar expressions based on the Harris expansioJ s2d ­ J0 1 3J1v2, (1)Ix ­ J0v 1 J1v3 1 i , (2)J s1d ­ Ixyv ­ J0 1 J1v2 1 iyv . (3)SinceJ s2d ­ dIxydv, integration of Eq. (1) gives Eq. (2),wherei is a constant of integration. By comparing Eqs. (24102nityenantorvey)galteenn,altoodn,)FIG. 4. (a) J s2d (circles) and J s1d (triangles) for bands 1(filled symbols) and 3 (open symbols) in194Hg. The extrapo-lations tov ­ 0 (thin lines) are from fits with Eqs. (1) and (3).The solid line showsJ s2d for the vacuum SD band in192Hg.(b) Ix 2 J0v for 194Hg band 3 and192Hg vacuum band.Ix ­ fIsI 1 1d 2 K2g1y2, where Kp ­ 2 and 0, respectively.The termJ0v has been subtracted to amplify the ordinate scausing theJ0 value of 192Hg. Inset: the spin differenceDIxfor the two bands. The dashed line is an extrapolation usiEq. (2).or (3) to the data, we obtain­ 0. Hence, atv ­ 0, bothJ s1d andJ s2d have the same value, namelyJ0 [see Eqs. (1)and (3)], explaining the convergence seen in Fig. 4(a).In Ref. [23] a procedure was proposed to deduce tspins of SD bands from Eqs. (1) and (2). However, it wnecessary to make an assumption thati ­ 0 and there wascriticism [24] about its validity. Bands with known spins(194Hg bands 1 and 3 and194Pb band 1 [2]) indeed havei ­ 0. This occurs because Routhians generally have zslope, i.e., no alignment, atv ­ 0. Common exceptionsare high-N configurations which can exhibit alignmeneven at zero frequency, so thati fi 0. We suggest anempirical guideline that it is safe to assumei ­ 0 whena band hasJ0, J1 values nearly equal to those of a banknown to havei ­ 0. With this guideline, Eq. (2) yieldseven spins for194Hg band 2 and the192Hg vacuum band.Finally, we discuss the implications of our results on thorigin of identical bands. Band 3 of194Hg has transitionenergies which are identical to those of the vacuum bandVOLUME 79, NUMBER 21 P H Y S I C A L R E V I E W L E T T E R S 24 NOVEMBER 1997r-tac-n-nspt.,/i.v.192Hg for a large range ofEg (382–854 keV). The presentresults, together with the observation of equal quadrupomoments [25], provide the most comprehensive collectioof information about the properties of identical bandThis allows a critical question to be addressed: do staemitting equal-energy transitions have the same spineven nuclei), parity, and quadrupole moments?The spins and parity of the vacuum SD band of192Hghave not been determined from experiment. HoweveEq. (2) gives even spin values, as discussed above. Fthermore, a “ground” band with pair correlations in the Sfalse vacuum should have even spins and positive parityas observed for the vacuum bands of194Hg (see Fig. 2and Ref. [1]) and194Pb (Ref. [2]). On the other hand, thelevels of band 3 have odd spin and negative parity. Hencthere is reasonable confidence that,for this particular pairof identical bands, transitions of equal energy originatfrom states with different spin and parity.At low v, the transition energies of the identical banddiverge andJ s2d for band 3 is larger than for the vac-uum bands of192,194Hg (see Fig. 4). Reference [26] hasshown that the largerJ s2d for the excited SD band can beexplained by a reduction of pairing from blocking. Theextrapolated value ofJ s2d at v ­ 0 supports this inter-pretation. Here,Ix (defined in the Fig. 4 caption) andiare zero, i.e., there is no single-particle contribution to thspin. Hence, as the quadrupole moments for both banare the same [25], a significant part of the,7% excess ofJ s2d for band 3 must be due to a reduction of pairing.SincedIxydv ­ J s2d, band 3 has a largerIx at low v.This is illustrated in Fig. 4(b), whereIx 2 J0v is plottedfor both bands, withJ0 taken as the Harris parameter fo192Hg. The difference in spinDIx increases from zero; butthe growth then slows for̄hv . 0.15 MeV (see inset), asdIxydv for 192Hg increases due to alignment of high-Norbitals [9,27]. In other words, the unit spin differencand identical transition energies result from a complicatemechanism involving both pairing and particle alignmeni.e., from accidental cancellations,in agreement with thesuggestions of Refs. [17,26]. However, an explanatiobased on a symmetry cannot be ruled out since that costill be the root cause of these cancellations.The above interpretation shows thatDIx cannot be at-tributed solely to particle alignment (a few-particle effectin band 3. Reduced pairing (a collective effect) plays aimportant role and there is, in fact, smaller particle alignment in band 3 at lowv. This interpretation contradictsthe proposal by Ref. [28], which attributes the additionaspin of band 3 to pseudospin alignment. It is also hardenvisage pseudospin alignment in an octupole vibrationband, which is a complicated (but coherent) superpositiof 2-qp states. In any event, pseudospin alignment arisifrom two particles in a pseudospin doublet [28] would givthe wrong (positive) parity for band 3.lens.tes(inr,ur-D—e,esedsredt,nuld)n-ltoalonngeIn summary, we have determined the spins, likely paity, excitation energies, and someBsE1d values of mem-bers of band 3 in194Hg. These properties indicate thathis excited SD band is aKp ­ 22 octupole vibrationalband. Its transition energies are equal to those of the vuum band in192Hg. However, it has opposite parity anda spin differenceDIxsvd which grows from 0 (atv ­ 0)and saturates at1h̄. The evolution ofDIxsvd andJ2svdshows that the integer spin difference and identical trasition energies result in part from accidental cancellatiobetween the effects of pairing and particle alignment.This research is supported in part by the U.S. Deof Energy, under Contracts No. W-31-109-ENG-38No. DE-AC03-76SF00098, and No. W-7405-ENG-48.[1] T. L. Khoo et al., Phys. Rev. Lett.76, 1583 (1996).[2] A. Lopez-Martenset al., Phys. Lett. B380, 18 (1996);K. Hauschildet al., Phys. Rev. C55, 2819 (1997).[3] P. A. Butler and W. Nazarewicz, Rev. Mod. Phys.68, 349(1996), and references therein.[4] T. Nakatsukasaet al., Phys. Rev. C53, 2213 (1996).[5] T. Nakatsukasaet al., in Proceedings of the Conferenceon Nuclear Structure at the Limits, Argonne, 1996, ANLPHY-97/1, p. 111.[6] R. V. F. Jansssens and T. L. Khoo, Annu. Rev. Nucl. Sc41, 321 (1991).[7] C. Baktash, B. Haas, and W. Nazarewicz, Annu. ReNucl. Sci.45, 485 (1995).[8] I. Ragnarsson, Nucl. Phys.A520, 67c (1990).[9] M. Riley et al., Nucl. Phys.A512, 178 (1990).[10] G. Hackmanet al., in Ref. [5], p. 1.[11] I. Y. Lee et al., Nucl. Phys.A520, 641c (1990).[12] G. Hackmanet al., Phys. Rev. C55, 148 (1997).[13] H. Hübel et al., Nucl. Phys.A453, 316 (1986).[14] R. G. Henry et al., Phys. Rev. Lett.73, 777 (1994);T. Lauritsenet al., in Ref. [5], p. 35.[15] L. M. Bollinger and G. E. Thomas, Phys. Rev. C2, 1951(1970).[16] R. Krückenet al., Phys. Rev. C54, R2109 (1996).[17] R. Wyss and W. Satuła, Phys. Lett. B351, 393 (1955).[18] P. Fallonet al., Phys. Rev. C55, R999 (1997).[19] B. Crowell et al., Phys. Lett. B333, 320 (1994); A. N.Wilson et al., Phys. Rev. C54, 559 (1996).[20] T. L. Khoo et al., Nucl. Phys.A202, 289 (1973).[21] H. Amro et al. (to be published).[22] S. Bouneauet al., in Ref. [5], p. 105.[23] J. E. Draper et al., Phys. Rev. C42, R1791 (1990);J. Beckeret al., ibid.46, 889 (1992).[24] R. Wyss and S. Pilotte, Phys. Rev. C44, R602 (1991);C. L. Wu et al., Phys. Rev. Lett.66, 1377 (1991);C. Baktashet al., Nucl. Phys.A555, 375 (1993).[25] E. F. Mooreet al., Phys. Rev. C55, R2150 (1997).[26] P. Fallonet al., Phys. Lett. B276, 427 (1992).[27] E. F. Mooreet al., Phys. Rev. Lett.64, 3127 (1990).[28] F. S. Stephenset al., Phys. Rev. Lett.64, 2623 (1990);65,301 (1990).4103

Spins, parity, excitation energies, and octupole structure of an excited superdeformed band in 194Hg and implications for identical bands

Dossing, T.

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Spins, parity, excitation energies, and octupole structure of an excited superdeformed band in $^{194}$Hg and implications for identical bands

Spins, parity, excitation energies, and octupole structure of an excited superdeformed band in $^{194}$ Hg and implications for identical bands

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Spins, parity, excitation energies, and octupole structure of an excited superdeformed band in 194^{194}194Hg and implications for identical bands

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Spins, parity, excitation energies, and octupole structure of an excited superdeformed band in $^{194}$ Hg and implications for identical bands