Subpicosecond lifetimes of states in shears band 1 in 97Pb were measured by means of the recoil distance method employing Gammasphere and the New Yale Plunger Device. The extracted reduced matrix elements, B(M1), show a clear sensitivity to the crossing of different shears configurations reflecting the closing and reopening of the shears blades. The energies and B(M1) values in the band crossing region are successfully described in the framework of the semiclassical model of the shears bands. The relevance of core rotation contributions are shown. The results point to the existence of shears states with an angular momentum coupling angle larger than 90°

Beausang, C.W.

Carpenter, M.P.

Cooper, J.R.

Dewald, A.

Janssens, R.V.F.

Kemper, G.

Klug, T.

Krücken, R.

Lister, C.J.

Novak, J.R.

von Brentano, P.

Wiedenhöver, I.

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 20011Crossing of Shears Bands in 197Pb: BM1 Values and Semiclassical DescriptionJ. R. Cooper,1 R. Krücken,1 C. W. Beausang,1 J. R. Novak,1 A. Dewald,2 T. Klug,2 G. Kemper,2 P. von Brentano,2M. P. Carpenter,3 R. V. F. Janssens,3 C. J. Lister,3 and I. Wiedenhöver3,*1A. W. Wright Nuclear Structure Laboratory, Yale University, New Haven, Connecticut 065202Institut für Kernphysik, Universität zu Köln, Köln, Germany3Argonne National Laboratory, Argonne, Illinois 60439(Received 25 April 2001; published 5 September 2001)Subpicosecond lifetimes of states in shears band 1 in 197Pb were measured by means of the recoil dis-tance method employing Gammasphere and the New Yale Plunger Device. The extracted reduced matrixelements, BM1, show a clear sensitivity to the crossing of different shears configurations reflectingthe closing and reopening of the shears blades. The energies and BM1 values in the band crossingregion are successfully described in the framework of the semiclassical model of the shears bands. Therelevance of core rotation contributions are shown. The results point to the existence of shears stateswith an angular momentum coupling angle larger than 90±.DOI: 10.1103/PhysRevLett.87.132503 PACS numbers: 27.80. +w, 21.10.Ky, 21.10.Re, 23.20.–gThe so-called shears mechanism seems experimentallywell established as the mechanism governing the mag-netic dipole M1 bands in the neutron-deficient Pb iso-topes [1–4]. In particular, recent lifetime measurements[5–8] have unambiguously shown that the reduced tran-sition matrix elements BM1 characteristically decreasewith increasing angular momentum. Experimental BM1values and transition energies closely follow predictions ofthe tilted-axis-cranking (TAC) [9] model, which providesa microscopic interpretation of the dipole bands.The underlying configuration of the shears bands isbased on the perpendicular coupling of the angular mo-menta of high-j, high-K proton particles and high-j, low-Kneutron holes. This coupling scheme was confirmed bythe results of a recent g-factor measurement in 193Pb [10].With increasing angular momentum the quasiparticle angu-lar momenta jp , jn align gradually with the total angularmomentum vector J. This motion resembles the closingof the blades of a pair of shears, lending the name “shearsbands” to the observed bands [4].In order to describe the rotational-like behavior of thesebands it was suggested that the spherical symmetry of thesystem is broken by the anisotropic current distribution ofthe orbital motion of the high-j quasiparticles. An orienta-tion of the system can be defined and rotational motion canoccur. The large magnetic dipole component perpendicu-lar to the total angular momentum can be viewed as ro-tating around J, and this rotating magnetic dipole inducesenhanced M1 transitions. This motion has been named“magnetic rotation” [11] as opposed to the more famil-iar “electric rotation” of a quadrupole deformed chargedensity leading to rotational bands with enhanced elec-tric quadrupole E2 transitions. In another approach therotational-like pattern can be explained in terms of the in-teraction of the quadrupole moments of the quasiparticleconfigurations with the quadrupole vibrational field of thecore, which leads to a parabolic spin dependence of thelevel energies [12–15].32503-1 0031-90070187(13)132503(4)$15.00A remarkable result of the previous investigation of197Pb was the observed rise in the BM1 values of shearsband 1 in 197Pb (the band is labeled according to Ref. [16])at the point of a small up bend in the spin vs rotational fre-quency plot [6]. At the same time band 2 in 197Pb, whichdoes not exhibit an up bend, showed the usual decreasein BM1 values associated with the shears mechanism.It was speculated that the rise of BM1 values in band1 may reflect the reopening of the shears blades due to aband crossing [1,6]. Clark and Macchiavelli [1] provided aschematic prediction of the behavior of the BM1 valuesdue to the crossing of the different shears configurations.In this Letter we report on results from a subpico-second lifetime measurement on states in shears band 1of 197Pb [16–19] that for the first time reveal the details ofthe band crossing of different shears configurations. Afterpresenting the experimental procedure and data analysis,band-mixing calculations are presented that are based onthe description of the shears configurations by a semiclas-sical approach [14,15,20].Excited states in 197Pb were populated in the reaction176Yb26Mg, 5n197Pb at a beam energy of 130 MeV. Thebeam was delivered by the ATLAS accelerator of Ar-gonne National Laboratory. The g rays emitted by theexcited 197Pb nuclei were detected by the Gammaspherearray [21]. The 1 mgcm2 thick 176Yb target foil was sup-ported by a 1.5 mgcm2 Ta layer that faced the incomingbeam. The recoiling nuclei left the target with a velocityof y  0.01c and were stopped in a 5 mgcm2 thick Austopper foil. Target and stopper foil were mounted insidethe New Yale Plunger Device (NYPD) [22]. An average of150 3 108 events with at least four Compton suppressedgamma-ray energies were collected at each of ten distances[1, 2, 3, 4.5, 6.5, 9, 12, 16, 22, and 32 mm, with respectto the electrical contact of the foils]. The separation ofthe foils was kept constant to within a few percent by afeedback system [23] that relies on the capacitance be-tween the foil and distance corrections by a piezoelectric© 2001 The American Physical Society 132503-1VOLUME 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 2001crystal. This stabilization is crucial since the uncertaintyof the distance difference enters into the uncertainties ofthe lifetimes.For each distance separate background-subtracted,double-gated spectra were sorted for each level of interestin the band and each of the Gammasphere detector rings at35± (combination of detectors positioned at 32± and 37±),54± (50± and 58±), 126± (combination of 122± and 130±),146± (143± and 148±), and 163±. Figure 1 shows samplespectra. Intensities of the unshifted and Doppler-shiftedcomponents were extracted for the depopulating andpopulating transitions of each of these levels. The gat-ing conditions required coincidences with higher lyingtransitions, thus selecting the decay path of the nucleiand eliminating any contributions of side feeding in thelifetime analysis.Lifetimes for the levels of interest were extracted usingthe differential decay curve method (DDCM) [24,25]. Allof the measured lifetimes are in the range from 0.5 to1.1 ps indicating the difficulty of the present experiment.[The recoil distance method (RDM) is commonly usedto measure lifetimes above 1 ps.] The measurement ofsuch short lifetimes was possible only due to the effectivepopulation times of the levels of interest, on the order of2 ps. Because of the short lifetimes one can no longermake the usual assumption that the slowing down time inthe stopper foil can be neglected [26]. Correction factorswere calculated, as suggested by Dewald [26], which varysmoothly from 50% at 0.5 ps to 30% at 1.1 ps. Table Isummarizes the lifetimes and BM1 values obtained inthis experiment. The BM1 values are shown as a functionof level spin in Fig. 2.The BM1 values first fall with increasing spin as ex-pected for a shears configuration but rise in the spin regionFIG. 1. Gated spectra for the detector ring at 126± at distancesof 1.0, 4.5, 12, and 32 mm. The positions of shifted (dashedline) and unshifted (solid line) components are indicated for the3122!2922(270.5 keV), 4122!3922(293.8 keV), and 4722!4522(285.2 keV) transitions.132503-2of the first band crossing. The increase of the BM1 val-ues in the first band crossing region lends support to thelarge BM1 values found above this first crossing in theDSAM experiment of Ref. [6].In order to understand the experimental BM1 valueswe employ a semiclassical model [14,15,20] in which theshears bands result from the simple recoupling of the angu-lar momentum vectors generated by the proton-particle andneutron-hole configuration, respectively. The quasiparticleangular momenta jp and jn are coupled by the shears an-gle u to the total angular momentum J (see inset of Fig. 2).The interaction leading to the closing of the shears bladescan be described by a simple quadrupole-quadrupole in-teraction, which may originate from the interaction ofthe quadrupole moment of the quasiparticle configurationswith the vibrational field of the core [12,13,15]. Thus, theenergy states for the unperturbed shears configuration aregiven byEJ  E0 1 V2P2cosu , (1)withcosu JJ 1 1 2 jn jn 1 1 2 jp  jp 1 12pjn jn 1 1jp jp 1 1. (2)We use the quasiparticle configurations A11pi132h9211 ≠ ni21132, ABC11 pi132h9211 ≠ni23132332, and ABCEF11 pi132h9211 ≠ ni23132 3 f52p32392 [16,19] as unperturbed configurations.For each configuration V2 is calculated as nV0, withn being the number of quasiparticles involved in theshears, e.g., n  3 for the A11 configuration. A value ofV0  0.48 MeV, which is well within the range deducedin Ref. [15], was found to best reproduce the data. Athree band mixing calculation was performed, in whichthe values of E0 and the interaction between the bandswere fitted to reproduce the energies of the experimentallyTABLE I. Mean level lifetimes t and reduced matrix elementsBM1 for the states in shears band 1 of 197Pb from the presentwork. The corrected lifetimes tcorr were calculated from theuncorrected tuncorr according to [26] to account for the effectsof the slowing process in the stopper foil.Spinp Eg tuncorr tcorr BM1h̄ (keV) (ps) (ps) m2N2922 152.6 0.8 (2) 1.1 (3) 3.8 (9)3122 270.5 0.47 (12) 0.71 (19) 2.5 (4)3322 359.1 0.39 (10) 0.60 (16) 1.6 (3)3522 369.8 0.29 (8) 0.49 (15) 1.8 (4)3722 385.0 0.8 (4) 1.0 (5) 0.8 (4)3922 365.2 0.6 (3) 0.8 (4) 1.1 (4)4122 293.8 0.47 (14) 0.7 (2) 2.1 (5)4322 227.6 0.52 (17) 0.8 (3) 3.1 (12)132503-2VOLUME 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 2001FIG. 2. BM1 values as a function of level spin for shearsband 1 in 197Pb. The results of this work (filled circles) and aprevious DSAM experiment [6] (filled triangles) are comparedto the results of our band-mixing calculations (solid line) usingthe semiclassical model [14,15,20]. As an inset the coupling ofproton and neutron quasiparticle angular momenta to the totalangular momentum J is shown.observed band. The reasonable agreement between theexperimental energies and the results of the mixingcalculations can be seen in Fig. 3. Interactions of 0.7and 0.1 MeV were used for the mixing of configurationsA11ABC11 and ABC11ABCEF11, respectively. Theinteraction of 0.7 MeV seems rather large but doesprovide the best fit of the experimental energies using theparametrization of the unperturbed bands.At this point we would like to remark that within thepresent model it is impossible to describe the crossingbetween the A11 and ABC11 configurations without theintroduction of a small amount of rotational angularmomentum from the core. This is apparent when oneconsiders that the A11 configuration can only generate aFIG. 3. Experimental (filled squares) and calcualted (solidline) angular momentum vs rotational frequency (gamma-rayenergy) for shears band 1 in 197Pb.132503-3total angular momentum of 17.5 h̄ while mixing betweenthe A11 and ABC11 configuration occurs up to a spin of21.5 h̄. The difference in angular momentum has to comefrom the core rotation. Therefore, we have included thecore rotation [20] into our calculations, which leads to amodification of Eq. (1) toEJ  E0 1 R22core 1 V2P2cosu . (3)Here R is the core angular momentum along the total angu-lar momentum vector and core is the core moment of in-ertia. The value of core  3h̄2MeV was extracted fromenergy fits to shears bands from 193Pb to 199Pb.The decomposition of our mixing calculations is sum-marized in Fig. 4. In the bottom panel of Fig. 4 the con-tributions of the core angular momentum are plotted asa function of the total angular momentum. One can seethat near the band head of the A11 configuration core ro-tation does not play a role, while a contribution of about4 h̄ is needed at spin 21.5 h̄. Generally, the contributionof the core rotation increases almost linearly with spin foreach configuration [20]. This is in general agreement withthe results of TAC calculations, which are discussed inRef. [16]. It is interesting to note that one actually needsa negative spin contribution of the core rotation near theband head in order to successfully describe the lowest ob-served states for configuration ABC11.Figure 4 also shows the squared mixing amplitudes ofthe three unperturbed configurations in the wavefunctionsof the observed states (top) as well as the opening angle ofthe unperturbed shears configurations (middle) as a func-tion of the total angular momentum. One can see that theFIG. 4. Top: Squared mixing amplitudes a2 of the shearsconfigurations A11 (solid line), ABC11 (dashed line), andABCEF11 (dash-dotted line) as a function of the total angularmomentum J . Middle: Opening angle u for each shearsconfiguration as a function of J including the core contributionsR to J . Also shown is the opening angle of configurationA11 (dotted line) if no core rotation is included. Bottom:Contribution of the core rotational angular momentum R to thetotal angular momentum for each shears configuration.132503-3VOLUME 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 2001A11 configuration (including core rotation) terminates atspin 21.5 h̄. In the middle panel we have also indicatedthe opening angle for the A11 configuration if no core ro-tation were included in order to stress its importance fora correct description of the bands. It is notable that forconfiguration ABC11 we require opening angles u . 90±at the lowest angular momenta.BM1 values for each transition were calculated usingthe relationship [14]BM1 34pm2 38pg2effj2p sinup . (4)The calculated BM1 values for band 1 in 197Pb are shownin Fig. 2 in comparison to the data. A value of geff  0.9was used for the effective g factor of all three configura-tions. This value best reproduced the data and is close tothe value of geff  0.92 shown to reproduce on averagethe BM1 values in the Pb region [14]. The agreementof the three band mixing calculations and the experimentaldata is remarkable.In summary, we have measured subpicosecond lifetimesof states in shears band 1 of 197Pb using the recoil dis-tance method. The experiment was performed using theNYPD in conjunction with Gammasphere. The absoluteBM1 values deduced from the lifetimes show a charac-teristic pattern that reflects the crossing of the A11 andABC11 configurations. At higher spins the ABC11 con-figuration is crossed by the ABCEF11 configuration wherethe BM1 values from a previous DSAM experiment showa characteristic rise. The BM1 values indicate that withincreasing spin the blades of the A11 configuration close.At the crossing point a mixing occurs between an almostclosed A11 shears configuration and the ABC11 configu-ration with a coupling angle of larger than 90± at the bandhead, leading to a jump in the BM1 values. The cross-ing of the ABC11 and ABCEF11 configurations does notoccur as close to the termination point and band head ofthe respective configurations. Thus the change in BM1values is not quite as dramatic.We have shown that the semiclassical model by Macchi-avelli et al. [14,15,20] provides an excellent quantitativedescription of the energies and BM1 values if a certainamount of core rotation is included. Our results show therelevance of core rotation contributions and suggest the ex-istence of states with shears angles larger than 90±.Finally, we would like to point to the possibility touse the shears bands to study in detail the particle-corecoupling mechanism [12,13]. We hope our article will en-132503-4courage such work as well as more detailed theoretical pre-dictions of the strength of this coupling.We would like to acknowledge significant contributionsby R. M. Clark and A. O. Macchiavelli. This work wasfunded in part by the U.S. DOE under Grant No. DE-FG02-91ER-40609 and Contract No. W-31-109-ENG-38as well as the German Federal Minister for Education andResearch (BMBF) under Contract No. 06OK958.*Present address:NSCL, Michigan State University, EastLansing, MI.[1] R. M. Clark and A. O. Macchiavelli, Annu. Rev. Nucl. Part.Sci. 50, 1 (2000).[2] S. Frauendorf, Rev. Mod. Phys. 73, 463 (2001).[3] R. M. Clark et al., Nucl. Phys. A562, 121 (1993), andreferences therein.[4] G. Baldsiefen et al., Nucl. Phys. A574, 521 (1994), andreferences therein.[5] R. M. Clark et al., Phys. Rev. Lett. 78, 1868 (1997).[6] R. M. Clark et al., Phys. Lett. B 440, 251 (1998).[7] R. Krücken et al., Phys. Rev. C 58, R1876 (1998).[8] G. Kemper et al., Eur. Phys. J. A11, 121 (2001).[9] S. Frauendorf, Nucl. Phys. A557, 259c (1993).[10] S. Chmel et al., Phys. Rev. Lett. 79, 2002 (1997).[11] S. Frauendorf, Z. Phys. A 358, 163 (1997).[12] V. Paar, Nucl. Phys. A331, 16 (1979).[13] K. Heyde, P. van Isaker, M. Waroquier, J. L. Wood, andR. A. Meyer, Phys. Rep. 102, 291 (1983).[14] A. O. Macchiavelli et al., Phys. Rev. C 57, R1073 (1998).[15] A. O. Macchiavelli et al., Phys. Rev. C 58, R621 (1998).[16] A. Görgen et al., Nucl. Phys. A683, 108 (2001).[17] J. A. Becker et al., Nucl. Instrum. Methods Phys. Res.,Sect. B 79, 313 (1993).[18] J. R. Hughes et al., Phys. Rev. C 48, R2135 (1993).[19] G. Baldsiefen et al., Nucl. Phys. A587, 562 (1995).[20] A. O. Macchiavelli et al., Phys. Lett. B 450, 1 (1999).[21] I. Yang Lee, Nucl. Phys. A520, 641c (1990).[22] R. Krücken, in Proceedings of the International Sympo-sium on Advances in Nuclear Physics, Bucharest, Roma-nia, 1999, edited by D. Poenaru and S. Stoica (WorldScientific, Singapore, 2000), p. 336.[23] R. Krücken, J. Res. Natl. Inst. Stand. Technol. 105, 53(2000).[24] A. Dewald, S. Harissopulos, and P. von Brentano, Z. Phys.A 334, 163 (1989).[25] G. Böhm, A. Dewald, P. Petkov, and P. von Brentano, Nucl.Instrum. Methods Phys. Res., Sect. A 329, 248 (1993).[26] A. Dewald (private communication); B. H. Saha, diplomathesis, University Köln, 2000 (unpublished).132503-4

Crossing of shears bands in 197Pb: B(M1) values and semiclassical description

http://cdr.lib.unc.edu/downloads/1257b3574

Crossing of shears bands in 197Pb: B(M1) values and semiclassical description

Abstract

Similar works

Full text

Available Versions

Carolina Digital Repository