The average g factors of the high-energy states of the three superdeformed bands in 194Hg were determined
directly in a transient field experiment. The reaction 150Nd(48Ca,4n)194Hg at a beam energy of 203 MeV was
used to provide recoiling reaction product nuclei with sufficient velocity to traverse a gadolinium ferromagnetic
layer. The resulting g factors g(SD1)50.36(10), g(SD2)50.41(20), and g(SD3)50.71(26) are in
agreement with cranked Hartree-Fock calculations as well as with the picture of a rigid rotation for which g
5Z/A

Benczer-Koller, N.

Broude, C.

Cizewski, J.A.

Hass, M.

Holden, J.

Janssens, R.V.F.

Kumbartzki, G.

Lauritsen, T.

Lee, I.Y.

Macchiavelli, A.O.

Mayer, R.H.

McNabb, D.P.

Satteson, M.

Weissman, L.

Carolina Digital Repository

RAPID COMMUNICATIONSPHYSICAL REVIEW C NOVEMBER 1998VOLUME 58, NUMBER 5First direct measurements ofg factors of the three superdeformed bands of194HgR. H. Mayer,1,* G. Kumbartzki,1 L. Weissman,2,† N. Benczer-Koller,1 C. Broude,2 J. A. Cizewski,1 M. Hass,2 J. Holden,1R. V. F. Janssens,3 T. Lauritsen,3 I. Y. Lee,4 A. O. Macchiavelli,4 D. P. McNabb,1,‡ and M. Satteson1,§1Department of Physics and Astronomy, Rutgers University, New Brunswick, New Jersey 089032Weizmann Institute of Science, Rehovot, Israel 761003Argonne National Laboratory, Argonne, Illinois 604394Lawrence Berkeley National Laboratory, Berkeley, California 94720~Received 2 June 1998!The averageg factors of the high-energy states of the three superdeformed bands in194Hg were determineddirectly in a transient field experiment. The reaction150Nd(48Ca,4n)194Hg at a beam energy of 203 MeV wasused to provide recoiling reaction product nuclei with sufficient velocity to traverse a gadolinium ferromag-netic layer. The resultingg factors g(SD1)50.36(10), g(SD2)50.41(20), andg(SD3)50.71(26) are inagreement with cranked Hartree-Fock calculations as well as with the picture of a rigid rotation for whichg5Z/A. @S0556-2813~98!50711-X#PACS number~s!: 21.10.Ky, 21.10.Re, 25.70.Gh, 27.80.1wr ireofr-extiotglbmtateioa-aryioononncSu-en-ioneificbedllyi.onm-0ndhefidevi-terro-e-t 2idalnetthegne-s avedn-rnalintec-UnivSSuperdeformation in the Hg isotopes and, in particula194Hg, has been extensively studied in recent years. Thsuperdeformed~SD! bands have been identified, lifetimesstates have been measured, and the decays of the yrast~SD1!and one excited superdeformed~SD3! bands have been chaacterized@1–7#.The determination of magnetic moments of nuclearcited states can add an important element in the elucidaof the microscopic structure of these SD states becausecorresponding operator reflects collective as well as sinparticle degrees of freedom. In particular, theg factor of arotational nuclear state in a band with good quantum numK, g5gR1(gK2gR)@K2/I (I 11)#, depends ongR , the ro-tationalg factor and the single-particle contributionsgK .There exist only scant measurements of magneticments of short-lived, high spin states@8–11# and nodirectmeasurement of magnetic moments of superdeformed shas been carried out so far. An indirect measurement demined from the observation of theM1 dipole transitionslinking signature partner bands in193Hg @12# yielded a valuegK520.65(14) consistent with a Woods-Saxon calculatof a 5/22@512# deformed neutron orbital. Similar determintions also exist for193Tl, 193Pb, and195Tl @13–15#.Only the hyperfine interaction in an ion moving throughferromagnetic layer~transient field! can create the necessafield strength to induce a measurable magnetic interactTherefore, only states that are populated while the itraverse a ferromagnetic layer can be probed. In fusievaporation reactions, where nuclei are highly excited ibroad spin and energy range, the specific states of nu*Present address: School of Chemical Engineering, Purdueversity, West Lafayette, IN 47907.†Present address: Katholieke Universiteit, Leuven, Belgium.‡Present address: Lawrence Livermore National Laboratory, Lermore, CA 94550.§Present address: Interventional Innovations Corporation,Paul, MN 55113.PRC 580556-2813/98/58~5!/2640~4!/$15.00ne-nhee-ero-tesr-nn.s-aleitraversing this interaction zone are generally not known.perdeformed bands are populated at very high excitationergies and a very short time after the initial nuclear fusreaction takes place@16#. Thus, it is possible to design thkinematics of the reaction in such manner that specranges of excitation in the nucleus of interest can be pro@9#. The transient field method is, therefore, exceptionawell suited for measuring factors in superdeformed nucleThe experiment was carried out at the 88-Inch Cyclotrat Lawrence Berkeley National Laboratory using the Gamasphere array@17# which consisted, at the time, of 9Compton-suppressed Ge detectors. The reaction150Nd(48Ca,4n)194Hg at 203 MeV was used to populate SD ahigh-spin normal-deformed states in the Hg isotopes. Ttarget consisted of 1 mg/cm2 150Nd evaporated on a2.15 mg/cm2 rolled and annealed gadolinium foil. A layer o40 mg/cm2 of gold was evaporated on the downstream sof the gadolinium layer to provide a perturbation free enronment in which the Hg ions stop. The excited nuclei enthe ferromagnetic foil at an average time of 0.1 ps after pduction, with an average initial energy of 40 MeV and vlocity (v/v0) in52.9 (2.1%c), and exit from the foil 0.5 pslater, with an average velocity (v/v0)out52.0 (1.4%c),wherev0 is the Bohr velocity.During the experiment the beam intensity was kept aparticle nA. The target was cooled to 77 K by flowing liqunitrogen. The gadolinium foil was polarized by an externfield of 0.06 T produced in the gap of a small electromagmounted outside the vacuum chamber. The current inlectromagnet was reversed every five minutes. The matization of the gadolinium foil, measured independently afunction of temperature in an ac magnetometer, wasM50.182(4) T.The nuclear spin precession is obtained from the obserrotation of the angular distribution ofg rays emitted by thedecaying nuclei. This rotation about the direction of the trasient magnetic field, which is the same as that of the extefield direction, causes, for each field flip, a small changethe counting rate in most detectors. Even with a large dei--t.R2640 ©1998 The American Physical Societyp.eaoSdenahnabainnohiinacatdeperbliomredthefpeosseelar-the-ef-geoslue-m-orshetoeces-do-ag-t arendsami-RAPID COMMUNICATIONSPRC 58 R2641FIRST DIRECT MEASUREMENT OFg FACTORS OF . . .tor array such as Gammasphere, such measurements deessentially on the quality of spectra observed in asinglede-tector, albeit gated by all the other detectors in the arrayDouble-gated and triple-gated coincidence spectra wsorted separately for events recorded with the external mnetic field in either the ‘‘up’’ or ‘‘down’’ direction and forindividual detectors in the array. For the extractiondouble-gated spectra, the events were ‘‘unpacked’’@18–20#and the resulting spectra were incremented if at least twocoincidence conditions were satisfied by the remainingtectors. As expected, the lowest members of the SD bawere found to decay while fully stopped. Theg rays fromstates that decayed while in flight were seen to be increingly Doppler shifted and an energy-dependent Doppler-scorrection was applied when gating on these transitioWhile the SD transitions in the SD1 spectra were well estlished, the double-gated coincidence spectra for the SD2SD3 bands had low peak to background ratios.The data were also analyzed by applying triple-gatconditions. In a direct event-by-event sort, one-dimensiospectra for each of the 90 detectors were generated aslined in @18#. Because of the energy dependent Doppler sfor the higher SD transitions, individual gating lists containg up to 15 transitions in the SD bands were used for edetector. The background was determined from double-gspectra generated by the same gate lists@21#. As expected,triple gating reduces the overall intensities in the SD banbut improves the peak to background ratio. The relativerors in the peak sums of double-gated and triple-gated stra are roughly the same, as they are dominated by thespective background subtraction. For the SD1 band, dougated and triple-gated spectra yielded the same precessFigure 1 shows sample spectra of the three superdeforbands in194Hg obtained in asinglebackward detector undethe triple-gate conditions described above.In order to verify the angular distributions of the observtransitions, spectra for detectors with the same azimuangle with respect to the beam axis were added andciency corrected. The relative efficiencies, including the scific absorption caused by the geometry of the angular crelation chamber and magnet, were measured itin situ usingthe activity of the target immediately after the run. Theangular distributions yieldedA2 andA4 coefficients in quali-tative agreement with data obtained by Hackmanet al. @22#,where angular distributions were measured more preciwith single element targets. For the analysis of the currdata, the coefficients of Hackmanet al. for all quadrupoletransitions in the SD bandsA250.352(3) and A4520.103(3) were adopted.For the precession measurements, thez axis is defined bythe direction of the external magnetizing field. The angudistribution forg rays from detectors whose position is chaacterized by the two Euler anglesu andf is given byW~u,f!511A2Q2P2~cosu cosf!1A4Q4P4~cosu cosf!,whereQ2,4 are the geometrical attenuation coefficients.endreg-fD-dss-ifts.-ndgalut-ft-heds,r-c-e-e-ns.edalfi--r-elyntrSymmetric combinations of groups of four detectors atsame6u and6f angles, two forward~2,3! and two back-ward ~1,4!, were used to form double ratios@9#, r i j5(N(u i)↑•N(u j )↓/N(u i)↓•N(u j )↑)1/2, where N(u i)↑,N(u i)↓ are theg-ray rates in detectorsi , j 51, 2, 3, 4 withthe external field in the ‘‘up’’ and ‘‘down’’ direction, respectively. Such double ratios do not depend on the detectorficiency or on beam intensity fluctuations. The averadouble ratior5(r23/r14)1/2 yields an effecte5r21/r11from which the angular precessionDu5e/S is calculated.The logarithmic slopes at the selected anglesS51/W(u,f)3dW(u,f)/du ranged from 0.113–0.594. The double ratir13 and r24 are expected to be close to unity and the vaecheck5r21/r11 with rcheck5(r13/r24)1/2 serves as a consistency check. Similar double ratios were used for the cobinations of three and two detectors. In total 62 detectwere chosen such that 100°<u<160° or 20°<u<80° and0.5°<f<53°. The peak sums for the lowest six~SD1 andSD2! or five ~SD3! band transitions were used to sample taverage effectŝe& for the 15 detector groups and in turncalculate the average precession angle^Du&. It should beemphasized again that these angles correspond to the prsions of states populated while the nuclei traverse the galinium layer.Finally, the averagêg& factors were derived from theformula relating measured precessions to the transient mnetic fieldFIG. 1. Spectra of the lower energy regions of the194Hg SDbands observed in a single backward detector. The lines thalabeled by their energy were analyzed for precession. The diamoindicate SD transitions that were not analyzed because of contnation.msitaedelerdann-srethinheneeeeiccohenosgebyd-tal--the-lofn anntionultsl ofex-re-eforrgetor-bi-blepe-ch.idliselcu-pirforas-f ofnt.ci-da-38.RAPID COMMUNICATIONSR2642 PRC 58R. H. MAYER et al.Du52gmN\ Et intoutB„v~ t !,Z…e2t/tdt,in which the Ziegler stopping powers@23# and the ChalkRiver parametrization of the transient fieldB(v,Z)5154.73Z3(v/v0)3e20.135v/v03M T obtained from data onheavy nuclei@24# were used.This experiment determines the average magneticments of the high-energy states of the three SD band194Hg. The 194Hg nuclei are populated at an average exction energy of 24 MeV. The energy of the first observsuperdeformed state in SD1 at spin;501 lies at 18.6 MeV@1,2#. The decay from the entry states into the superdeformwell is very fast and occurs mostly while the excited nucare still in the150Nd target. Subsequently, theg flux remainsin the corresponding SD bands until the decay-out towathe normal-deformed states occurs at the bottom of the bThe nuclei traverse the gadolinium foil during a time widow of 0.5 ps, during which the averageg factor of thehigher members of the SD band are probed. These stateat an approximate excitation energy 12.2*Eexc*9.8 MeVwhich corresponds to 34\*I *28\ for SD1 and SD2 and33\*I *25\ for SD3.The resulting averageg factors are^g~SD1!&50.36~10!,^g~SD2!&50.41~20!,^g~SD3!&50.72~26!.The quoted errors reflect the counting statistics in theevant detectors and a 5% uncertainty in the calibration oftransient field.These results can be contrasted with the results obtain the same experiment on theg factors of six normal-deformed bands in193,194Hg. In this latter situation,g factorsconsiderably lower than the nominalZ/A were obtained@25#,indicating significant single-neutron contribution to thegfactor of the levels studied, and confirming the validity of tgeneral analytical approach to obtainingg factors from thistype of data.Several models have been used to estimate the magmoments of SD bands in194Hg. As a first approximation,gRcan be assumed to take on the rigid body value,gRB5Z/A50.412. Calculations in the projected Hartree-Fock framwork yield g factors very close togRB @26,27#. Perrieset al.@28# determined the collective gyromagnetic ratiogRIC fromthe Inglis cranking approach applied to the static HartrFock plus BCS and the SkM* force. These authors predgIC50.363 for the yrast SD band in194Hg. Sunet al. @29#have calculated electromagnetic properties and pairingrelations of SD bands on the basis of the projected smodel. They predictg factors whose neutron contributioremains constant as a function of spin at –0.06, but whproton contribution increases slowly with spin in the ran24\&I &44\, reaching a maximum at 0.47, yieldingo-in-disd.liel-eedtic--tr-lle50.41 for the high-spin states in the yrast SD band in194Hg.However, the suggestion of Ref.@29# that the distinction be-tween Coriolis antipairing and gradual high-j orbital align-ment disappears at very large deformation is contradictedthe experimental data@30# on even-even, odd-even, and ododd nuclei. These experiments confirm the modified toRouthian surface~TRS! calculations which attribute the observed rise ofJ (2) with \v to successive alignments of neutrons and protons occupying high-N intruder orbitals, withan additional contribution resulting from the response ofmean field to the alignment process.The present experimentalg factor for the yrast band is ingood agreement withgRIC @28# but lacks the accuracy to exclude the rigid body valuegRB or the projected shell moderesult @29# and there do not yet exist TRS calculationsmagnetic moments.There are no theoretical predictions forg(SD2) org(SD3). However, if the experimentalgR is taken from themeasurement ofg(SD1), the experimentalg(SD2) andg(SD3) can be used to extractgK . Nakatsukaet al. @31#have suggested, on the basis of the latest data on SD3@2#,that SD2 and SD3 represent octupole excitations built oSD minimum with K522. Other possible explanations iterms of aligned quasiparticle excitations@5# might lead todifferent predictions. However, unlessK;I , a determinationof gK for SD2 and SD3 is difficult to extract from the presemeasurements at very high spin because the termI (I 11)strongly attenuates the term (gK2gR) in the expression forthe g factor.This paper presents the first measurement ofg factors inthe SD well, a quest which has had to await the completof large g arrays like Gammasphere. The present resshould be considered as a demonstration of the potentiafuture studies. In this respect, two improvements in theperimental procedure will lead to more accurate measuments of theg factors of SD bands. First, it is clear that thg factors of the lower spin states in the band are criticaldetailed interpretation. Such an experiment using a tawith a gap between the150Nd target and the gadoliniumferromagnetic layer is in progress. Second, it is also imptant to achieve a higher statistical accuracy. Thus, a comnation of a better detector coverage such as will be availawith the future segmented detectors and longer countingriods will improve the statistical accuracy obtainable in suexperiments.In summary, the averageg factors of the high-energystates of the three SD bands in194Hg have been measuredThe^g& factor of the yrast band SD1 is smaller than the rigbody value and agrees with the prediction from an Ingcranking approach. Thêg& of the SD2 and SD3 bands arnot accurate enough to distinguish among theoretical calations.The authors wish to express their gratitude to Leo Saand John Greene for target preparation, to Boris Elkoninthe design of the cooling system, to Randy McLeod forsistance with the data acquisition system and to the stafthe 88-Inch Cyclotron for their help during the experimeThis work was supported in part by the U.S. National Sence Foundation, the Israel-U.S. Binational Science Fountion, and the U.S. Department of Energy W-31-109-ENG-cens,-dsIn-s.tin,tt.ri,RAPID COMMUNICATIONSPRC 58 R2643FIRST DIRECT MEASUREMENT OFg FACTORS OF . . .@1# T. L. Khoo et al., Phys. Rev. Lett.76, 1583~1996!.@2# G. Hackmanet al., Phys. Rev. Lett.79, 4100~1997!, and ref-erences therein.@3# E. F. Mooreet al., Phys. Rev. C55, R2150~1997!.@4# J. R. Hugheset al., Phys. Rev. Lett.72, 824 ~1994!.@5# M. A. Riley, Nucl. Phys.A512, 178 ~1990!.@6# C. W. Beausanget al., Z. Phys. A335, 325 ~1990!.@7# E. Henryet al., Z. Phys. 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First direct measurements of g factors of the three superdeformed bands of 194Hg

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First direct measurements of g factors of the three superdeformed bands of 194Hg

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