The evolution of the quasicontinuum spectrum with neutron number has been investigated in the sequence of isotopes Dy152,154,156. The three nuclei display a pronounced collective E2 component. In Dy154 this component shows a splitting into two distinct parts, signifying a structural change along the cascade above the yrast line. The E2 and statistical components are reproduced in simple -cascade calculations; in Dy152 and Dy156 only rotational bands are included, whereas in Dy154 additional vibration-like transitions are required to reproduce the two E2 peaks

Ahmad, I.

Daly, P.J.

Dichter, B.K.

Drigert, M.W.

Emling, H.

Garg, U.

Holzmann, R.

Janssens, R.V.F.

Khoo, T.L.

Ma, W.C.

Piiparinen, M.

Quader, M.A.

Trzaska, W.

Carolina Digital Repository

VOLUME 62, NUMBER 5 PHYSICAL REVIEW LETTERS 30 JANUARY 1989Structure in the E2 Quasicontinuum Spectrum of ' 4DyR. Holzmann, ~'~ T. L. Khoo, W. C. Ma, t ~ I. Ahmad, B. K. Dichter, 'H. Emling, ' and R. V. F. JanssensArgonn, e National Laboratory, Argonne, I/linois 60439M. W. Drigert and U. GargUniversity ofNotre Dame, Notre Dame, Indiana 46556M. A. Quader, P. J. Daly, M. Piiparinen, ' and W. Trzaska 'Purdue University, West Lafayette, Indiana 47907(Received 18 May 1988)The evolution of the y quasicontinuum spectrum with neutron number has been investigated in the se-quence of isotopes ' " ' Dy. The three nuclei display a pronounced collective E2 component. In"Dy this component shows a splitting into two distinct parts, signifying a structural change along the ycascade above the yrast line. The E2 and statistical components are reproduced in simple y-cascade cal-culations; in ' Dy and ' Dy only rotational bands are included, whereas in ' Dy additional vibration-like transitions are required to reproduce the two E2 peaks.PACS numbers: 23.20.Lv, 21.10.Pc, 27.70.+qHot nuclei provide opportunities to study several as-pects of physics. In nuclear structure it is interesting toexamine the change of shapes, thermal shape fluctua-tions, and the melting of shell eA'ects with increasingtemperature. Calculations based on the Landau theoryof phase transitions ' and the finite-temperatureHartree-Fock-Bogoliubov method predict that nucleiwhich are prolate along the yrast line become triaxialwith increasing excitation energy above the yrast line, U,and undergo a phase transition to oblate shape at a criti-cal temperature T„. There is also a possibility to learnabout chaos in a quantum system, since the excursionfrom the cold yrast line with increasing U represents atransition from order to chaos. For example, it is of in-terest to search for signatures of order at high excitationenergy and to study the role of collectivity and spin inpreserving order. 'Several experiments have investigated the shapes ofrotating nuclei at high temperature (U) 40 MeV) byexamining the giant-dipole-resonance component of they spectrum, but manifestations of phase transitionshave proven elusive. Striking shape changes may also beexpected at significantly lower U in transitional nuclei,where the structure along the yrast line has been ob-served ' to vary rapidly with both spin I and neutronnumber Ã. Indeed, T,„ is predicted to decrease quicklywith the approach towards the transitional region. Al-ternative methods have to be developed for the study ofthe interesting nuclear physics near a predicted phasetransition in the lower U domain, where photon emissionin the giant dipole region is negligible.To probe nuclear behavior in the U =1-8-MeV range,we have measured quasicontinuous spectra of y rayswhich connect excited states in the region of high-leveldensities. We have found evidence for structuralchanges in the quasicontinuum states and, perhaps, alsofor the large Auctuations which are expected near aphase transition.A solid understanding of structural change with I andU requires knowledge of the Bow pattern of the de-exciting y cascade. Our approach starts with experimen-tal determination of the initial and end points of thequasicontinuum cascade. With these points as con-straints, Monte Carlo calculations of the y cascade,which reproduce all observed spectral features, are usedto indicate the U-I region being studied. Although theactual decay pathway is not delineated completely fromexperiment, this approach nevertheless provides the bestdefinition to date. Our analysis suggests that thequasicontinuum E2 spectrum probes mainly states withU —1-7 MeV.In this Letter we report on the quasicontinuum spectrain the transitional nuclei ' ' Dy. The results, togetherwith our previous data on ' Dy, elucidate the evolutionof E2 continuum properties in a sequence of isotopeswith increasing ground-state deformation.The nuclei ' ' Dy were produced in theSn( S,4n) reactions with beams provided by theArgonne superconducting linac, ATLAS. The I-mg/cmtargets were evaporated on a 25-mg/cm Pb backing, re-sulting in stopping times of —1.6 ps for the nuclei recoil-ing with an initial velocity of v/c —0.020. Prompt y-ycoincidences were measured in eight Compton-sup-pressed Ge detectors placed at 34, 90', and 146 withrespect to the beam axis. High multiplicity events wereselected with the requirement that at least two out of anarray of fourteen bismuth-germanate crystals fired.From the coincidence data, clean ' "Dy and ' Dy spec-520 1989 The American Physical SocietyVOLUME 62, NUMBER 5 PHYSICAL REVIEW LETTERS 30 JANUARY 1989Eb„m (MeV)&I. „,) (h)(E,„„„)(MeV)(M stat)(~quad)(~total)Qr (e b)a2,tr (h MeV ')152D a16046.725.64.01.95.330.57 0+2.5~/(7 ~ 1)76.0154D16550.226.93.91.69.128.86.5+ 1'~/(7+ 1)72.0'156D15548.825.43.91.110.327.86.0+ 1.5W/(7+ 1)75.5TABLE I. Average entry points and multiplicities of the y-ray quasicontinuum components measured in theSn( S,4n) ' ""Dy reactions. The average entryspins and energies have been determined by the addition of theangular momenta and energies removed by each one of thespectral constituents, including the discrete lines. The parame-ters used in our y-cascade model to reproduce the data are alsolisted, where g, is the electric quadrupole moment, a is thelevel-density parameter, and 2,& is the eAective moment of in-ertia.0.4—0.2—0 . a,0.4—0.2—00) 0Q)~ p4—Y)(f)o 0.2U)CLI I IiI I I II 52DyDyDy500 IOOO I 500 2000 2500E (keV)'From Ref. 9.I ncludes discrete lines.'Properties of initial rotational cascade; in the second stage, corre-sponding to E* & 17 MeV, E~ =780 keV with a 500-keV spread(FW H M), and B(E2 ) =300 Weisskopf units.FlG. 1. Measured (Q) quasicontinuum E 2 y spectra inDy. Discrete lines have been subtracted and the spec-tra corrected for Doppler shifts and angular-distributioneAects. Calculated spectra are shown as histograms.tra were generated by gating on low-lying lines for eachdetector angle. These spectra were corrected for neu-tron-induced background' and unfolded. The strongdiscrete lines and the statistical y rays were subtracted,yielding the true y quasicontinuum spectra, which couldthen be decomposed into dipole and quadrupole partswith use of their different angular distributions. Foreach spectral component, the average multiplicity, andtotal spin and energy removed were determined, allowingthe entry spin and excitation energy to be specified. (De-tails of the analysis are described in Ref. 9.) The resultsare summarized in Table I, including data on ' Dy.Figure 1 shows the E 2 continuum spectra for the threeDy isotopes investigated. In ' Dy and ' Dy one broadpeak can be discerned, diff'ering in multiplicity and ener-gy, whereas in' Dy two distinct parts are observed.There have been earlier indications" ' of structure inthe quasicontinuum spectra of translational nuclei.However, the spectral shape and the extent of thequasicontinuum contribution were not known sincediscrete lines, which are largely responsible for structurein the total y spectra below 1 MeV, were not subtracted.For example, double bumps were observed in the totalspectra of ' ' Er, but the lower bump is drastically re-duced after subtraction' of discrete lines, and the resi-duum has almost no E2 contribution, ' as in the isotoneDy; see Fig. 1 and Ref. 9. In the present work, twobroad E2 peaks remain in the ' Dy after yrast transi-tions have been subtracted, unambiguously demonstrat-ing that both peaks must be due to transitions above the0.4 —(a0.2—~ ~II I I 1nrtRI BI&go~ ~(b)I.O)Q) 00.4~ 0.2I—0m 0.40.2—0 500 IOOOMeVSMeVi i 4 kl500 2000nfu &4~"s e~ ~n n~, I0 500 IOOO I 500 20000.5,POo~I.O ~~I.O—, 0.5E (MeV)FIG. 2. (a) Measured (Q) quasicontinuum E2 spectra for' "Dy at beam energies of 148, 155, and 165 MeV, aftercorrection for Doppler shift and angular anisotropy. Simulatedspectra are shown as histograms. The measured average entryand end spins of the quasicontinuum E2 cascades are (50.2,30.0) h, (42.7, 25.1)h, and (35.9, 21.2)h at 165, 155, and 148MeV, respectively. (b) Measured (~) and simulated (histo-grams) backward/forward E2 intensity ratios, which reflect theDoppler shifts. Some estimated errors are shown.yrast line. The average multiplcity and energy of theupper peak both increase with beam energy [Fig. 2(a)],consistent with a rotational origin. In contrast, the low-energy peak stays remarkably constant; in particular, itsaverage energy of 780 keV does not change noticeably521VOLUME 62, NUMBER 5 PHYSICAL REVIEW LETTERS 30 JANUARY 1989when the average input spin decreases from 506 at abeam energy of 165 MeV to 366 at 148 MeV. Theseobservations demonstrate that the transitions associatedwith the upper peak precede the ones giving rise to thelower peak. Quasicontinuous dipole transitions are alsoobserved in ' ' Dy, which probably follow the E2 cas-cades. The dipole multiplicities decrease with increas-ing neutron number (see Table I).The emission times of the y rays were extracted fromthe observed Doppler shifts with knowledge of theslowing-down process in the Pb-backed targets. Themeasured backward/forward intensity ratios, whichrefiect the Doppler shifts, are shown in Fig. 2(b) forDy. The upper edges of both E2 peaks are nearly ful-ly shifted, proving that the lifetimes of the levels involvedare much shorter than the slowing-down time of therecoiling nuclei, i.e., (&1.6 ps. Hence both peaks origi-nate from fast stretched-quadrupole transitions.The appearance of two broad peaks in ' Dy resultsfrom a redistribution of transition energies along the ydeexcitation pathway; in the later decay stage transitionenergies are shifted downwards, causing the clusteringaround 780 keV and the dip around 1.1 MeV. The twopeaks provide clear signature for a change in nuclearstructure above the yrast line. In ' Dy the collectiveF2 cascade is similar (see Table I) to that of the firstpart in ' Dy. However, in ' Dy the collective flow ter-minates, on average, at U =1-1.5 MeV and I—346, asaligned-particle configurations dominate in the vicinityof the yrast line and dipole transitions emerge. (Hencea rapid decrease of the E2 quasicontinuum intensity atlow energies occurs. ) Aligned-particle configurations arenot dominant along the yrast line in ' Dy, allowing theE2 cascade to continue to U —0.7 MeV and I—266,and this results in a larger E2 multiplicity. Only a sin-gle peak is observed, implying rotational behaviorwherein the transition energy decreases with spinthroughout the quasicontinuum cascade.These conclusions were derived with the aid of MonteCarlo calculations of the y cascade, which take into ac-count the competition of statistical E 1 and. collective E2decay at high excitation energy. The calculations repro-duced simultaneously all observed features of the E2and statistical components, i.e., their multiplicities, spec-tral shapes, Doppler shifts, and entry points into theyrast region. The only free parameters are the level-density parameter, the average eAective moment of iner-tia J,g, and the average electric quadrupole moment ofthe rotational bands responsible for the E2 peak. Thissimple model can reproduce the data for ' Dy andDy (Fig. 1) but is unable to reproduce the splitting ofthe E2 component seen in ' Dy. However, by our as-suming a change from rotational to vibrationlike behav-ior for excitation energy E* & 17 MeV, the observedfeatures at all beam energies could be reproduced (seeFig. 2) with one common set of parameters (Table I).[The term vibrationlike refers to the assumption of tran-sition energies which, instead of increasing with spin asfor a rotor, remain constant at an average value of 780keV, with a spread of 500 keV (FWHM); vibrationalmotion is not implied. ] A collective 8(E2) of 300Weisskopf units (with an estimated 30% uncertainty)was required to reproduce the measured Doppler shiftsof the lower E2 peak [Fig. 2(b)], as well as the spectralshapes and yrast feeding. The simulations suggest thatthe lower peak arises from states with U —1-5 MeV andl —(30-40)h„(25-38) l'i, and (21-33)0 for beam ener-gies of 165, 155, and 148 MeV, respectively. While re-quiring a structural change below E*=17 MeV repro-duces the data, this does not mean that a sharp transitionnecessarily occurs, or that a difI'erent boundary profile inE*-Ispace could not also reproduce the data. However,it was not possible to reproduce the data at all beam en-ergies by switching to vibrationlike motion below a fixedspin value, or by retaining rotational motion and increas-ing S,g for E*( 17 MeV.It was suggested in Ref. 12 that the bumps in the totaly spectra in transitional Er nuclei are due to shell effects,the lower bump attributed to valence nucleons and theupper one to orbits of the next major shell. In ' "Dy, in-spection of the yrast transitions shows that they pile upto make the predominant contribution to the low-energybump region. This results from structural changesoccurring near the yrast line, which are clearly ofvalence origin. %e have now determined the extent towhich the shell effects persist above the yrast line by iso-lating the quasicontinuum E2 component, and havefound that such structural changes occur for U up to 5MeV.These changes are probably connected with variationsof the nuclear shape. In the course of a prolate to oblateshape change near the yrast line, many triaxial bandsmay occur. ' As U increases, the mixing among theclosely lying families of states could give rise to apotential-energy surface soft in the P-y plane, which inturn could account for the vibrationlike transitions asso-ciated with the lower-energy E2 peak. A more generalviewpoint based on theories of shape changes at hightemperature may be taken. In a transitional nucleussuch as ' By, the shape transition from triaxial to ob-late is predicted to occur at low U, even at the yrast linefor I~ 386, in fair agreement with an established ob-late region for I between 325. and 386. For all bom-barding energies the y cascades cross the predicted phasetransition boundary of Ref. 8, which resembles that cal-culated for the isotone ' Yb. The large shape fluctua-tions expected' in the transition region give a potential-energy surface Aat in the P-y plane and perhaps vibra-tionlike transitions.The higher E2 peak exhibits collective behavior, seem-ingly contradicting mean-field theory, ' which predictsthat the first part of the cascade flows through noncollec-VOLUME 62, NUMBER 5 PHYSICAL REVIEW LETTERS 30 JANUARY 1989tive oblate states. Fluctuations in the P-y plane couldaccount for the collectivity. However, the observed ro-tational behavior (E, rs'-I) may not be easy to explain inthis context, and one may speculate about the additionalrole' of orbitals from the next higher shell in collectivemotion at the higher spins.In the three Dy isotopes studied, the E 2 properties arevery similar at high I ()40A, ) and U (up to —7 MeV).However, there are clear diff'erences observed in the E2properties for I (40h, and U (5 MeV, reIIecting thepersistence of shell effects and some degree of order upto U-5 MeV. In the chaotic limit, no diff'erences withneutron number would have been observed. While thesystem is clearly ordered at the yrast line, evidence forchaotic behavior has been found' at low spin for U-8MeV and even for U as low as —1-3 MeV in somecases. The persistence of elements of order up to U —5MeV at I—(20-40)h is interesting in this context andone may speculate on the role of collectivity in preservingorder.In summary, excited states with U up to —7 MeVhave been investigated in ' ' ' Dy. A collective, pre-sumably prolate, E2 component has been observed in allcases. In ' Dy this persists towards the yrast region. InDy it terminates at higher I and U as aligned-particleconfigurations in the yrast region are encountered. InDy, this collective structure changes to one which hasa vibrationlike behavior, with the transition energiesremaining nearly constant with spin, and gives rise to alower-energy peak. This work demonstrates that thequasicontinuum E 2 spectrum can reveal structuralchanges in excited states to higher excitation energy thanhas been observed before.We acknowledge helpful discussions with Y. Alhassid,A. Goodman, and F. S. Stephens. This work was sup-ported by the Department of Energy, Nuclear PhysicsDivision, under Contracts No. W-31-109-ENG-38 andNo. DE-FG02-87ER40346, and by the National ScienceFoundation under Grant No. PHY84-16025."' Present address: Gesellschaft fur SchwerionenforschungDarmstadt. m. b.H. , Darmstadt, D-6100, West Germany.Present address: Tsinghua University, Beijing, People' sRepublic of China.' Present address: Panametrics Inc. , Waltham, MA 02254.Present address: Idaho National Engineering Laboratory,Idaho Falls, ID 83415.' Present address: University of Jyvaskyla, Jyvaskyla, SF-40720, Finland.'Y. Alhassid, S. Levit, and J. Zingrnan, Phys. Rev. Lett. 57,539 (1986), and Nucl. Phys. A469, 205 (1987).~A. Goodman, Phys. Rev. C 35, 2338 (1987), and 38, 1092(1988).3T. H. Seligmann, J, J. M. Verbaarschot„and H. A. Weiden-miiller, Phys. Lett. 167B, 365 (1986).4A. Y. Abul-Magd and H. A. Weidenmuller, Phys. Lett.162B, 223 (1985).SK. Snover, Annu. Rev. Part. Nucl. Sci. 36, 545 (1986), andreferences therein.6W. C. Ma et al. , Phys. Rev. Lett. 61, 46 (1988).H. W. Cranmer-Gordon et al. , Nucl. Phys. A465, 506(1987).8Y. Alhassid and B, Bush, private communication; J. M.Manoyan, Ph. D. thesis, Yale University, 1987 (unpublished).9R. Holzmann et al. , Phys. Lett. B 195, 321 (1987).' R. Holzmann et al. , Nucl. Instrum. Methods Phys. Res. ,Sect. A 260, 153 (1987).t tM. A. Deleplanque et al. , Phys. Rev. Lett. 43, 1001 (1979).'2M. A. Deleplanque et al. , Phys. Rev. Lett. 51, 1854 (1983).'3G. Bogaert et al. , Z. Phys. A 324, 107 (1986).t4P. 3. Twin, in Proceedings of the Niels Bohr CentennialConference on Nuclear Structure 1985, Copenhagen, Denmark, 1985, edited by R. A. Broglia, G. B. Hagemann, and B.Herskind (North-Holland, Amsterdam, 1985).'sC. Baktash et al. , Phys. Rev. Lett. 54, 978 (1985).' R. U. Haq, A. Pandey, and 0. Bohigas, Phys. Rev. Lett. 48,1086 (1982).

Structure in the E2 quasicontinuum spectrum of Dy154

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Structure in the E2 quasicontinuum spectrum of Dy154

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