The power of quadruple angular correlations combined with a new analysis method was used to identify the first 10+ state at an energy of 19.2(1) MeV in 24Mg. Evidence for the γ decay of this state was also obtained. The results indicate that the rotational band is yrast in 24Mg at spin 10ℏ and is associated with a rotational frequency of ℏω≈2.9 MeV

Amro, H.

Bhattacharyya, P.

Brown, B.A.

Caggiano, J.

Carpenter, M.P.

Devlin, M.

Heinz, A.

Janssens, R.V.F.

Kondev, F.G.

Lauritsen, T.

Lister, C.J.

Sarantites, D.G.

Siem, S.

Sobotka, L.G.

Sonzogni, A.

Wiedenhöver, I.

Wuosmaa, A.H.

Carolina Digital Repository

VOLUME 87, NUMBER 14 P H Y S I C A L R E V I E W L E T T E R S 1 OCTOBER 2001142502-Identification of the Ip 5 101 Yrast Rotational State in 24MgI. Wiedenhöver,1,* A. H. Wuosmaa,1 R. V. F. Janssens,1 C. J. Lister,1 M. P. Carpenter,1 H. Amro,1,†P. Bhattacharyya,2 B. A. Brown,3 J. Caggiano,1 M. Devlin,4,‡ A. Heinz,1 F. G. Kondev,1T. Lauritsen,1 D. G. Sarantites,4 S. Siem,1,§ L. G. Sobotka,4 and A. Sonzogni11Argonne National Laboratory, Argonne, Illinois 604392Purdue University, West Lafayette, Indiana 479073Michigan State University, East Lansing, Michigan 488244Washington University, St. Louis, Missouri 63130(Received 5 February 2001; published 14 September 2001)Spins and parities of high spin states above the particle-binding threshold in 24Mg were determinedwith a basis expansion technique using triple and quadruple angular correlations between a particlesand g rays. The first unambiguous identification of a 101 state is reported. Located at 19.2(1) MeV,this state decays predominantly by a emission, although a candidate g-decay branch with a 5.927 MeVtransition connecting this 101 level to the rotational 81 state at 13.2 MeV was identified as well. Thecorresponding g-a branching ratio is 73 3 1024.DOI: 10.1103/PhysRevLett.87.142502 PACS numbers: 27.30.+t, 07.05.Kf, 21.10.Re, 23.20.EnThe nucleus 24Mg contains a sufficiently small numberof nucleons that its structure can be calculated with theshell model using the full sd-configuration space. Yet, thisnucleus also exhibits collective excitations associated withlarge, prolate deformations. In this context, the identifica-tion of states approaching 12h̄, the maximum spin that canbe generated within the sd shell, is particularly relevant.Their properties test the microscopic basis of collectivemotion; i.e., either they become less collective than lowerlevels as the number of available configurations within thesd shell decreases, or they maintain their collectivity bygathering strength from sizable admixtures from higher ly-ing orbitals, e.g., from the ( fp) shell. Such issues are mostreadily addressed in light nuclei, where calculations remaintractable.The study of levels beyond the established 81 states in24Mg is hampered by the fact that they are particle un-bound by energies $5 MeV. In addition, their deexcita-tion often proceeds through complex paths and, as a result,angular correlation studies are difficult and quantum num-ber assignments problematic. The interpretation of manymeasurements has been carried out by modeling the reac-tion mechanism using calculations of the Hauser-Feshbachtype, see, e.g., [1–3]. With this technique, Lumpkin et al.[1] proposed four candidates for 101 levels between 20.1and 28.2 MeV. Szanto de Toledo et al. [2,3] interpretedthe state at 20.1 MeV as the lowest 101 level. These as-signments, however, remain doubtful as the descriptionsof the data contain adjustable parameters that could not bethoroughly checked with data on levels with establishedcomparable spin values. Here it is shown that the rigorousangular correlation analysis of multistep decay paths re-sults in unambiguous spin and parity assignments to highlying states in 24Mg. In particular, the first firm identifica-tion of a 101 state at 19.2 MeV has been achieved.The experiment was performed at the ATLAS accelera-tor at Argonne National Laboratory. The setup consisted1 0031-90070187(14)142502(4)$15.00of five 16 3 16 silicon strip detectors, located aroundthe target for the detection of a particles, and of theGammasphere array [4] for the coincident detection ofg rays. Excited states in 24Mg were prepared with the12C16O, a24Mg reaction at Ec.m.  26.6 MeV. The aparticles emitted from the 28Si compound nucleus, de-noted as a0, populate the states of interest in 24Mg anddetermine their excitation energy. These particles weremeasured upstream from the target in a segmented annu-lar detector. The resulting excitation-energy spectra werecalibrated with a magnetic spectrometer measurement [5]performed at the same beam energy. The a particles emit-ted from 24Mg states (a1) and their angular distributionswere measured in four segmented silicon detectors posi-tioned at 45± with respect to the beam axis. Subsequentg transitions in 20Ne were measured with Gammasphere.Details about the experiment can be found in Ref. [6].In the analysis, a dynamic quantization axis for the24Mg states was introduced. This procedure is analogousto that described in Ref. [7]. It eliminates the dependenceof the angular correlation on the angle of emission of a0 bytilting the quantization axis slightly away from the beamaxis in a manner depending on the a0 emission angle andangular momentum. The observed a0 correlation patternsconsistently show a population from compound nuclearstates with spin 16 6 1h̄.Considering the case where a1 feeds the 20Ne groundstate, the angular distributions of a1 relative to the quanti-zation axis follow the familiar squared Legendre polynomi-als and provide an effective method for spin determination.Unfortunately, this favorable situation is limited to statesbelow 14 MeV, since decays towards 20Ne excited statesdominate at higher 24Mg excitation energies. The popu-lation of the 21 or 41 levels in 20Ne is characterized byan incoherent superposition of several m-substates wash-ing out the characteristic angular distributions, and mak-ing spin assignments impossible. This difficulty can be© 2001 The American Physical Society 142502-1VOLUME 87, NUMBER 14 P H Y S I C A L R E V I E W L E T T E R S 1 OCTOBER 2001overcome by detecting the direction of the subsequent20Ne, 21 ! 01 g ray [8,9]. This restores coherence tothe 21 m-substate population and reestablishes the charac-teristic oscillatory patterns of the a1 angular distributions.Here, this approach is generalized to states in 24Mg whichdecay to the 41 level of 20Ne. The coherence between the41 m-substates is achieved by detecting the direction ofemission of the entire 41 ! 21 ! 01 g cascade.Under the present coincidence conditions, the a1 par-ticles are emitted from a state of spin IA, m  0 in 24Mgand feed a level of spin IB  01, 21, 41 in 20Ne. Theobserved correlations were found to be consistent with“stretched” a1 decays, i.e., all deexcitations were assumedto correspond to La1  IA 2 IB. Hence, the observedstates in 24Mg must be of natural parity p  21I . Thetriple and quadruple angular correlations can be repre-sented in the form of Eqs. (1) and (2) below, where allterms depending on the a1 angles and quantum numbersare collected in the Al0q0 IA, IB statistical tensors result-ing from the angular momentum coupling between IA, La1 ,and IB. All terms describing the g-ray angular distribu-tions are collected in the Bl0q0 tensors. The exact defini-tion of these A, B2, and B4 terms is given in [6].W ua1ugfg Xl0q0Al0q0IA, 21 ua13 Bl0q02 21, 01 ugfg , (1)W ua1ug1fg1ug2fg2 Xl0q0Al0q0IA, 41 ua13 Bl0q04 41, 21, 01 ug1fg1ug1fg1 . (2)Equations (1) and (2) suggest an expansion of the cor-relation function into the basis Bl0q0i with the coefficientsAl0q0 . Indeed, the Bl0q02 and Bl0q04 tensors form a basis oftheir respective spaces, which is orthogonal in the indicesl0 and q0. l0 is the rank of the orientation tensor of the 21or, respectively, 41 intermediate 20Ne state. The orthogo-nality is then used to generate a basis expansion of theexperimental data, which is obtained by folding the geo-metrical correlations over all available ug angles with therespective basis tensors. The resulting transformed repre-sentations are functions of ua1 only and are expected tofit the calculated Al0q0 IA, 21 or 41 ua1  for all relevantl0q0 indices. Note that Eq. (1) is analogous to the triplecorrelation formula of [8,9].The validity of this new formalism has been thoroughlytested using known 24Mg states [8–10] feeding the 20Ne21 level. This is illustrated in Fig. 1 where the trans-formed experimental data for the 81 state at 16.5(1) MeVare compared with the relevant Al0q0IA, 21 ua1  curves:the distributions calculated for a spin 8 initial state re-produce the data in all l0q0 values, while those calcu-lated for spins 10 and 6 (not shown) can be ruled out. Asingle normalization parameter [NIA] was adjusted in thisanalysis.142502-2FIG. 1. Transformed triple angular correlation data observedfor the a1-g decay of the 16.5(1) MeV state. Plotted arethe data for the most relevant correlations, e.g., l0q0 4, 0 4, 1 4, 2 4, 3. The thick full (dashed) line refers to aIA  8 (10) hypothesis.The method was then extended to the analysis of qua-druple correlations. The correlation data were transformedby folding them with the basis tensors Bl0q04 over all avail-able angles ug1fg1ug2fg2. The most relevant l0q0 in-dices are 8, 0, 8, 1, and 8, 2, and the characteristics ofthe Al0q0 IA, 41 ua1 curves are very similar to those seenin the triple-correlation case. Figure 2 presents the data forthe 19.2(1) MeV state. In this case, the correlation patternfits the distributions calculated for a 101 state very well.Note that this analysis is only possible because of the near4p coverage provided by Gammasphere.Figure 3(a) shows the 24Mg excitation energy spectrumobtained when gating on the a1 decays feeding the 41 statein 20Ne, in coincidence with the 41 ! 21 ! 01 g-raycascade. The lower three histograms [Figs. 3(b)–3(d)]present the normalization parameter NIA as a functionof the excitation energy EX in 24Mg for IA  8, 9, and 10.A large positive value of NIA at the same EX value asa peak in Fig. 3(a) identifies the presence of a state withspin IA. Negative values of NIA arise from levels withspin I fi IA [NIA would be zero if complete 4p coveragewere achieved]. Figure 3(b) confirms that the 17.2 MeVlevel is characterized by 81 quantum numbers, while thetwo peaks at 20.1 and 20.3 MeV [Fig. 3(c)] are dominated142502-2VOLUME 87, NUMBER 14 P H Y S I C A L R E V I E W L E T T E R S 1 OCTOBER 2001FIG. 2. Transformed quadruple angular correlation data ob-served for the a1-g-g decay of the 19.2(1) MeV state. Plottedare the correlation data for l0q0  8, 0 8, 1 8,2 (see text).The thick full (dashed) line refers to a IA  10 (8) hypothesis.by 92 excitations. A clear signal for 101 strength is notedfor the state at 19.2 MeV [Fig. 3(d)] for which the relevantcorrelations were presented in Fig. 2.It is worth noting that the 92 state at 20.2(1) MeVwas mentioned as a candidate for the lowest 101 levelin [1–3], while the present analysis yields an unambigu-ous assignment of IpA  92. In total, new spin and parityassignments were made for nine states between 15.7 and20.3 MeV; these results will be published elsewhere [11].In order to gain more insight into the properties of the19.2(1) MeV 101 state, a search was undertaken for anypossible g-decay branch, as any such transition can beexpected to link levels associated with closely related con-figurations. The data were scanned with the followingcondition on the (a0gg) events: (i) a 19.2 6 0.15 MeVexcitation energy in coincidence with (ii) any of the 24Mgtransitions below the 611 state. The coincident g-ray spec-trum is presented in Fig. 4. Also shown is the correspond-ing background spectrum. A peak of 11 6 4 counts isvisible at 5927(5) keV. This energy matches the valueexpected for the g transition linking the new 19.2 MeV,101 level to the rotational 812 state at 13.212 MeV. The5099 keV g line deexciting this 812 state is also present inthe spectrum. The 5927 keV transition establishes a stateat 19.139(5) MeV matching the energy from the a0 spec-trum. Since the uncertainty in the particle channel is ap-proximately 6100 keV, the presence of a doublet of levelscannot, however, be entirely ruled out. Under the assump-tion that the same state is seen in both decay channels, theg-a branching ratio is 73 3 1024.142502-3FIG. 3. (a) Observed excitation energy spectrum of 24Mg,gated on a1 decays towards the 41 of 20Ne. (b)– (d): Normal-ization parameter NIA as a function of the excitation energyEX for the values of IpA  81, 92, and 101, respectively.Theoretical descriptions of the high spin structure of24Mg have been discussed in detail in Ref. [12]. In par-ticular, this reference addresses the issue that the 812 levelrather than 811 yrast state is a member of the ground staterotational band, a feature which came initially as a sur-prise to experimentalists and theorists alike. The 811 stateFIG. 4. Upper part: g spectrum gated on a 19.2 6 0.15 MeVexcitation energy in coincidence with either the 1369 6 20,2754 6 30, or 3990 6 40 keV ground state band transitions.The decay scheme illustrates the gating conditions with a cross.Lower part: g spectrum gated on background regions; i.e., sumof spectra gated either on (1) a 19.2 6 0.15 MeV excitation en-ergy measured in coincidence with either of the g-backgroundregions 1711 6 20, 3175 6 30, or 4200 6 40 keV or (2) a18.6(15) MeV excitation energy in coincidence with the abovementioned g-peak regions.142502-3VOLUME 87, NUMBER 14 P H Y S I C A L R E V I E W L E T T E R S 1 OCTOBER 2001FIG. 5. Excitation energies of the ground state band in 24Mg,with a rotational reference ErotkeV  187 3 II 1 1 sub-tracted, compared with the results of a sd-shell model calcu-lation with the USD Hamiltonian [13].was described in shell model calculations using empiricalinteractions within the full sd-shell basis. These same in-teractions, labeled PW and CWC in Ref. [12], predict the1011 level around 19.5 MeV with decay properties depend-ing sensitively on the choice of the interaction. While thePW interaction predicts the 101 state to be most stronglyconnected to the K  0 ground state band, the CWC in-teraction favors a strong link with the K  2 band. Inaddition, the same Ref. [12] also discussed the results of aNilsson-Strutinsky calculation where the lowest 101 levelis understood as a member of the ground state band. Inthis context, the present result for the 19.2(1) MeV statefavors its interpretation as a member of the ground staterotational band if the 5927 keV g ray is identified withthe 1011 ! 812 transition.To explore the nature of the new 101 state further,new shell model calculations were performed using theUSD interaction [13] in the full sd-shell basis. The re-sults are compared in Fig. 5 with the data after subtractionof a rotational energy reference defined as ErotkeV 187 3 II 1 1. These calculations reproduce the overallevolution of the ground state band with spin rather well.The predicted energy for the 1011 level of 19.104 MeV isin excellent agreement with the measurement. The cur-vature seen in the figure can be viewed as a signaturefor the onset of band termination, i.e., the level energydecreases with respect to the rotational reference as oneapproaches the 121 state obtained by aligning the spinsof the eight valence nucleons. In fact, the wave func-tion of the USD 101 state is dominated (50%) by the[d527 3 d32] configuration, which can be interpreted as142502-4a particle-hole excitation built from the 811 level which hasa 46% d528 component in its configuration. Thus, the1011 excitation energy is largely determined by the effec-tive d52 2 d32 spin-orbit splitting. Nevertheless, the cal-culation also shows a strong parentage with the rotationalcharacter of the ground state band via its large BE2 tran-sition probability of 22.4e2 fm4 to the 812 state, a valuesignificantly larger than those for decays towards the 811and the 813 levels (5.2 and 11.3e2 fm4, respectively).To summarize, the power of quadruple angular corre-lations combined with a new analysis method has beenutilized to identify the first 101 state at an energy of19.2(1) MeV in 24Mg. Evidence for the g decay of thisstate has also been reported. These results indicate thatthe rotational band is yrast in 24Mg at spin 10h̄ and is as-sociated with a rotational frequency of h̄v  2.9 MeV.This work was supported by the U.S. Department of En-ergy, Nuclear Physics Division, under Contracts No. W31-109-ENG-38 and No. DE-FG05-88ER40406, and by theNational Science Foundation.*Present address: NSCL, Michigan State University, EastLansing, MI 48824.†Present address: Mississippi State University, MississippiState, MS 39372.‡Present address: Los Alamos National Laboratory, LosAlamos, NM 87545.§Present address: University of Oslo, Oslo, Norway.[1] A. H. Lumpkin, G. R. Morgan, J. D. Fox, and K. W.Kemper, Phys. Rev. Lett. 40, 104 (1978).[2] A. Szanto de Toledo, M. Schrader, E. M. Szanto, G. Rosner,and H. V. Klapdor, Nucl. Phys. A315, 500 (1979).[3] A. Szanto de Toledo, T. M. Cormier, M. M. Coimbra,N. Carlin Filho, P. M. Stwertka, and N. G. Nicolis, Phys.Rev. C 30, 1706 (1984).[4] I. Y. Lee, Nucl. Phys. A520, 641c (1990).[5] M. J. Bechara, A. J. Lazzarini, R. J. Ledoux, and E. R.Cosman, Phys. Rev. C 27, 1540 (1983).[6] I. Wiedenhöver et al., Nucl. Phys. A682, 22c (2001).[7] M. Freer, Nucl. Instrum. Methods Phys. Res., Sect. A 383,463 (1996).[8] R. W. Zurmühle, D. P. Balamuth, L. K. Fifield, and J. W.Noé, Phys. Rev. Lett. 29, 795 (1972).[9] L. K. Fifield, R. W. Zurmühle, and D. P. Balamuth, Phys.Rev. C 8, 2217 (1973).[10] K. C. Young, Jr., R. W. Zurmühle, J. M. Lind, and D. P.Balamuth, Nucl. Phys. A330, 477 (1979).[11] I. Wiedenhöver et al. (to be published).[12] R. K. Sheline, I. Ragnarsson, S. Aberg, and A. Watt,J. Phys. G 14, 1201 (1988).[13] B. H. Wildenthal, Prog. Part. Nucl. Phys. 11, 5 (1984);B. A. Brown and B. H. Wildenthal, Annu. Rev. Nucl. Part.Sci. 38, 29 (1988).142502-4

Identification of the Iπ = 10+ yrast rotational state in 24Mg

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Identification of the Iπ = 10+ yrast rotational state in 24Mg

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