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Vol. 42 (2011) ACTA PHYSICA POLONICA B No 3–4PROMPT HIGH ENERGY DIPOLE γ EMISSION?A.
Vol. 42 (2011) ACTA PHYSICA POLONICA B No 3–4PROMPT HIGH ENERGY DIPOLE γ EMISSION?A. Corsia, A. Giaza, A. Braccoa, F. Cameraa, F.C.L. CrespiaS. Leonia, R. Nicolinia, V. Vandonea, O. Wielandb, G. BenzonibN. Blasib, S. Brambillab, B. Millionb, S. Barlinic, L. BardellicM. Binic, G. Casinic, A. Nanninic, G. Pasqualic, G. PoggicS. Carbonic, V.L. Kravchukd, M. Cinauserod, M. DegerlierdF. Gramegnad, T. Marchid, D. Montanaria,e, G. BaioccofM. Brunof , M. D’Agostinof , L. Morellif , S. Sambif , G. VanninifM. Ciemalag, M. Kmiecikg, A. Majg, K. MazurekgW. Meczynskig, S. Myalskig, D. Santonocitoh, R. AlbahC. Maiolinoh, M. Colonnah, M. Di Toroh, C. RizzohaDipartimento di Fisica, Università di Milano and INFN Sezione di Milano, ItalybINFN Sezione di Milano, ItalycDipartimento di Fisica, Università di Firenze and INFN Sezione di Firenze, ItalydINFN Laboratori Nazionali di Legnaro, ItalyeDipartimento di Fisica, Università di Padova and INFN Sezione di Padova, ItalyfDipartimento di Fisica, Università di Bologna and INFN Sez. di Bologna, ItalygThe Henryk Niewodniczański Institute of Nuclear Physics PAN, Krakow, PolandhINFN Laboratori Nazionali del SUD, Italy(Received January 28, 2011)Version corrected according to Erratum, Acta Phys. Pol. B 44, 675 (2013)The study of the collective properties of a nuclear system is a powerfultool to understand the structure which lies inside the nucleus. A success-ful technique which has been used in this field is the measurement of theγ-decay of the highly collective Giant Dipole Resonance (GDR). In fact,GDR can be used as a probe for the internal structure of hot nuclei and,in addition, constitutes a clock for the thermalization process. Using thefusion–evaporation reaction, it has been recently possible to study (i) theyield of the high-energy γ-ray emission of the Dynamical Dipole whichtakes place during the fusion process and (ii) the degree of isospin mixingat high temperature in the decay of 80Zr. In the first case it is impor-tant to stress the fact that the predictions of the theoretical models mightdiffer depending on the type of nuclear equation of state (EOS) and onthe N–N in-medium cross-section used in the calculations while, in thesecond physics case, the data are relative to the heaviest N = Z nucleuswhich has been possible to populate in the I = 0 channel using fusion–evaporation reaction. Both experiments were performed at the Laboratori? Presented at the Zakopane Conference on Nuclear Physics “Extremes of the NuclearLandscape”, August 30–September 5, 2010, Zakopane, Poland.(619)620 A. Corsi et al.Nazionali di Legnaro using the HECTOR-GARFIELD array. The high-energy γ-rays were measured in coincidence with light charged particlesand fusion–evaporation residues.DOI:10.5506/APhysPolB.42.619PACS numbers: 24.30.Cz, 25.70.–z, 23.20.–g1. IntroductionHeavy-ion reactions are a powerful tool to study the structure of thenucleus and the dynamics of the nuclear reactions. During heavy-ion colli-sions, in the complete fusion channel, a variety of single and collective modesof the nucleons takes place leading to the formation of a compound nucleus(CN). The CN is a long-lived system, at thermal equilibrium, whose featuresand decay mode do not depend on the reaction entrance channel except forparity, energy and angular momentum conservation [1].At the very early stage of the fusion process, when two heavy ions in-teract, the density of neutron excess changes very rapidly in time untilit reaches an equilibrium value. This process, known as charge or N/Zequilibration, is relevant when projectile and target have a large differencein the N/Z ratio. In such a scenario, it has been predicted that the chargeequilibration should take place with a collective motion known as Dynam-ical Dipole (DD) since it appears as a dipole oscillation that is a source ofγ-rays emission [2–4]. The description of the Dynamical Dipole requires asimportant input parameters the N–N collision cross-section and the nuclearequation of state with its symmetry term. In fact, being the DD emissionrelated to an isospin oscillation in the neck region between projectile andtarget, it is affected by the value of symmetry energy at densities lower thanthe saturation one.During the thermalization process, the last degrees of freedom to attainequilibration in the CN are the collective ones, i.e. the Giant Resonances.The E1 γ-rays emission associated with the statistical decay of the GiantDipole Resonances is a probe of the bulk properties of the nuclei. It de-pends on the structure of initial and final states and on the selection rulesassociated with the specific transition. In particular, the transitions froma Iinitial = 0 to a Ifinal = 0 state (with I isospin quantum number) are for-bidden in self-conjugate nuclei. Such a selection rule can be used to studythe role of the nuclear interaction in compound nucleus formation usingthe GDR decay from an I = 0 CN [5–7]. In fact, the hindrance of GDRγ-decay from I = 0 CN is due to a partial restoration of isospin symmetry athigh nuclear temperature (T ), since the excited compound nucleus lifetimeis too short for the relatively weak Coulomb interaction to mix states withdifferent isospin.Prompt High Energy Dipole γ Emission 621In both the physics cases previously mentioned, the measurement ofprompt γ radiation in heavy-ions fusion–evaporation reactions and the iden-tification of the reaction channel, are necessary. This has been possible usingthe GARFIELD-HECTOR array [8–12] at the Laboratori Nazionali di Leg-naro described in Section 2. In Section 3 the experimental results on themeasurement of the Dynamical Dipole γ-ray yield in the reaction 16O+116Snat 12 MeV/u are discussed. These data integrate those taken at 8.1 and15.6 MeV/u already published [19]. In Section 4 the data relative to themeasurement of isospin mixing for 80Zr at high temperature are discussed.It is important to stress that this nucleus is the heaviest N = Z isotope inwhich isosopin mixing was measured with this technique. The used reactionis 40Ca+40Ca → 80Zr (E? = 83 MeV) which produces 80Zr in the I = 0channel while the reference fusion–evaporation reaction was 37Cl+44Ca →81Rb at E? =83 MeV which produces 81Rb in the I = 7/2 channel.2. The experimental apparatusThe experiments presented in this work were performed at LaboratoriNazionali di Legnaro. The high energy γ-rays were measured (using theHECTOR array [8, 9]) in coincidence with the evaporation residues (usingan array of phoswich detectors [10]), the light charged particles (using theGARFIELD array [11, 12]) and the pre-equilibrium neutrons (using a part ofthe HELENA array [13]). The time reference of the experiments was givenby the accelerator radiofrequency or by an array of fast scintillators placednear the target (from the HELENA array [13]).The HECTOR array is composed of 8 BaF2 scintillators, each of '3000 cm3 of volume, placed in the backward direction relative to the beam.The absolute full energy peak efficiency of the array was ' 1% at 15 MeV.The BaF2 intrinsic time resolution was 600 ps and the energy resolution was' 12% at 1.3 MeV. In this experimental campaign HECTOR scintillatorsoperated under the high vacuum (10?5 mbar) of the GARFIELD scatteringchamber (a cylinder of ' 3 m of diameter and ' 5 m of length). To avoidoverheating of the electronics, the voltage dividers were placed outside thechamber and the signals from the photomultipliers were sent via dedicatedcables. The detectors were calibrated with standard sources for low energyγ-rays and using the 15.1 MeV γ rays emitted in the reaction 11B (19.1 MeV)+d =12C+n+ γ [14–18].GARFIELD is a high-granularity 4pi array dedicated to charged-particleidentification. Charge identification can be achieved with ?E–E, isotopeidentification with the pulse shape analysis of the signal coming from thestop scintillator detector (E). In the experiments only the forward chamber,covering angles 0? < φ < 360? and 30? < θ < 85?, was used.622 A. Corsi et al.PHOSWICH scintillators were arranged in 4 boxes surrounding the beamline at a distance of ' 160 cm from the target and covering a polar anglebetween 5? and 13?. Inside one of the PHOSWICH boxes a fast plastic scin-tillator of small dimensions was also placed to detect the elastically scatteredbeam. These PHOSWICH detectors consist of three coupled stages of scintil-lators followed by one photomultiplier. The scintillation light of the differentstages has different decay constants and can be consequently identified andseparated in the digitized pulses.Additional BaF2 scintillators from HELENA array were also employed.In the experimental setup 5 detectors were placed close to the target toprovide an alternative time reference with respect to radio-frequency. Inforward direction, 7 detectors at ' 80 cm from the target were used tomeasure neutrons via time of flight.3. Dynamical dipole emissionAs previously mentioned, during heavy-ion fusion-evaporation reactionsthe density of neutron excess changes very rapidly in time until it reachesan equilibrium value. This process is particularly relevant if the collidingnuclei have a different N/Z ratio; in this case, it has been predicted that theequilibration should take place with a collective oscillation [2–4].As both high energy γ-rays emitted in the hot GDR statistical decay andin the pre-equilibrium DD emission have a dipole nature and their energyspectra are centred in the interval 10–15 MeV, it is extremely difficult, if notimpossible, to directly measure the DD emission yield from only one fusion–evaporation reaction. The typical experimental procedure relies on the factthat DD emission is not expected in N/Z symmetric fusion–evaporation re-actions. Consequently, the measurement of the DD yield requires a secondreference fusion–evaporation reaction producing the same compound nucleusat the same excitation energy and angular momentum but in an N/Z sym-metric channel. The comparison between the γ-ray spectra measured in theN/Z symmetric and N/Z asymmetric channel will evidence the DD contri-bution.Since 1993, a series of experiments [19, 23–28] has measured an extrayield in γ emission that has been associated with the Dynamical Dipole (DD)emission. The available data are concentrated mainly in the A ' 132 massregion and seem not to follow [19, 27] the theoretical predictions concerningthe DD intensity dependence on the beam energy. In particular, a verypronounced rise and fall behaviour, not fully accounted for by theory, hasbeen measured in the systems 32S+100Mo [25] and 36Ar+96Zr [26] (see theleft panel of Fig. 1). Qualitatively, an increase of the DD yield with beamenergy is expected as the dynamics in the neck region between projectile andtarget, where the DD oscillation develops, becomes faster. A decreasing yieldPrompt High Energy Dipole γ Emission 623for higher beam energies is similarly expected due to the damping related tofast processes like pre-equilibrium neutron emission and p–n direct collisionsthat reduces the N/Z asymmetry and damps the isovector oscillation. TheDD yield dependence with beam energy is the result of the interplay betweenthese two phenomena.1.4 10-3?O+Sn exp1.2 10-3? asy-stiff EOS1.0 10-3asy-soft EOS?8.0?10-46.0 10-4?4.0?10-42.0 10-4? 6 8 10 12 14 16 18 20Elab (MeV/nucleon)Fig. 1. The Dynamical Dipole γ emission yield measured in mass region A ' 132for beam energies ranging from 6 to 15 MeV/u. Right panel: data reported forthe reactions 32S+100Mo [25] and 36Ar+96Zr [26, 27]. Left panel: data reported inRef. [19] for the reaction 16O+116Sn at 8.1, 12 and 15.6 MeV/u. The diamond inthe plot, at 12 MeV/u is still a preliminary result [20, 22]. In both plots theoreticalcalculations are connected with dotted or dashed lines.The measured DD total yield measured in the reaction 16O+116Sn isshown in the left panel of Fig. 1. The data points at 8.1, 15.6 MeV/u werealready discussed in Ref. [19]. The one at 12 MeV/u is preliminary andprovides a measurement of the Dynamical Dipole emission in the regionbetween the data points previously taken [20, 22]. The beam energy waschosen to have information exactly where data from [25] disagree from cal-culations. In the present data analysis the fusion–evaporation reaction usedto tune the statistical model calculations was 64Ni+68Zn (Elab = 4.7, 6.2and 7.8 MeV/nucleon) [8].The integrated DD yield measured in the 16O+116Sn reaction and plottedin the left panel of Fig. 1 shows the same rise and fall behaviour as reportedin Ref. [27] and in the right panel. Even though the analysis of the measureddata and of the theoretical calculations are still in a preliminary phase, asfar as the reaction at 12 MeV/u is concerned, the “rise and fall” trend of theDD multiplicity as a function of beam energy is clearly seen in the measureddata but not in the results of theoretical calculations. The different EOSparametrizations used in the calculations [4, 29] do not seem to produceeither a better agreement with measured data or the large differences in thetotal yield as in the case of Ref. [4]. This is probably due to the much largerN/Z asymmetry in the reaction channel of Ref. [4].mγ624 A. Corsi et al.This difference between the expected and measured DD total γ-ray yieldcalls for further investigation, e.g. performing new theoretical calculationswith different parametrization of N–N cross-section and a more detaileddescription of the pre-equilibrium particle emission. The angular distribu-tion of γ-rays measured in the backward hemisphere (covered by HECTORdetectors) will be extracted from data at 12 MeV/u and the comparisonwith the one obtained within theoretical model will provide a much deeperdetailed check of the model.4. Isospin mixingIn the isospin formalism, neutrons and protons are assumed to be twodifferent states of the nucleon with values 1/2 and ?1/2 of the projectionIz of the isospin operator I. According to this definition, the projectionof isospin for a nucleus can be written as: Iz = (N ? Z)/2. The groundstate of most even–even and odd–odd mass nuclei has isospin I = Iz. Theconsequence which is relevant for this work is that N = Z nuclei are in aI = 0 state. This makes possible the formation of a CN in an I = 0 statethrough the use of N = Z isotopes as projectile and target.In the nuclear ground state isospin symmetry is largely preserved andthe degree of mixing is given by the mixing parameter α2 [6, 7] defined as∑2 |〈I = I0 + 1|H 2C?I=1|I = I0〉|α = ,(EI=I0+1 ? EI=I0)2I=I0+1where H is the isovector part of the Coulomb potential.Isospin symmetry breaks as energy is given to the nuclear system. Infact, nuclear levels come closer and develop a finite width making more ef-fective the mixing between levels of different I induced by Coulomb force.In compound nuclei, if the excitation energy is high enough, the mixingprocess can be interrupted by statistical decay with the consequent restora-tion of isospin symmetry [5–7, 30]. In such a situation, where the mixingis expected to be small, α2 parameter can be approximated as the ratiobetween the Coulomb spreading width Γ ↓ (which represents the time-scaleover which the symmetry violation occurs) and the compound decay widthΓCN [6]. Practically, in the hot CN the degree of isospin mixing is given bythe interplay between Γ ↓ and ΓCN. The higher is the excitation energy, thestronger is expected to be the restoration of isospin symmetry.As discussed in Introduction, due to the E1 nature of the γ decay, theGDR is a good probe for the measurement of isospin mixing. The exper-imental procedure requires two fusion evaporation reactions producing thesame compound at the same excitation energy and angular momentum (asPrompt High Energy Dipole γ Emission 625in the case of Section 3). One reaction is used to tune the statistical modelcalculations, the other one to measure the isospin mixing. The analysismethod that has been used in this work is based on the assumption thatthe statistical decays of 81Rb (at E? = 83 MeV) (produced via the reaction37Cl+44Ca) and that of 80Zr (at E? = 83 MeV) (produced via the reaction40Ca+40Ca) have the same features. This condition was verified as the mea-sured energy spectra of light charged particles (alpha and protons) have thesame slope for both 81Rb and 80Zr compound nuclei [21, 22].The spectra displayed in Fig. 2 show the high energy γ-rays measuredin both reactions. The results of statistical model calculations are indicatedwith a continuous line. The spectra in Fig. 2 were measured in coincidencewith fusion–evaporation residues and were analysed with a version of CAS-CADE Statistical Model code which includes isospin physics [6, 22, 31, 32].Phase-space population modified by the kinematic selection induced byPHOSWICH geometrical efficiency has been adopted instead of the stan-dard one.10-2 10-2 8 810-3 10-3 6 610-4 4 10-4 4 2 210-5 5 10 15 20 25 10-5 5 10 15E (MeV) E (MeV 2)0 2510-6 10-681Rb 80Zr10-7 data 10-7dataCASCADE no mixing CASCADE no mixingCASCADE Γ↓ =10 keV CASCADE Γ↓ =10 keV10-8 10-8 CASCADE large mixing 5 10 15 20 25 30 5 10 15 20 25 30E (MeV) E (MeV)Fig. 2. The high energy γ-ray spectra measured in the reaction 37Cl+44Ca→ 81Rbat E? = 83 MeV (left panel) and in the 40Ca+40Ca→ 80Zr (E? = 83 MeV) reaction(right panel). In the insets, the linearised spectra are shown. The statistical modelcalculations (see text) are displayed with continuous line [21, 22].The analysis of the data was done using a recursive fitting procedurebased on a χ2 minimization technique. The analysis of the reference 81Rbsystem allowed to fix GDR and statistical model parameters which werethen used for the system 80Zr. In this second step, the Coulomb spreadingwidth Γ ↓, that is a free parameter, has been tuned to have the best fittingmγa.u.mγa.u.626 A. Corsi et al.curve in the decay of 80Zr (see Table I). Finally, it was verified that the setof best fitting parameters listed in Table I and a Coulomb spreading widthΓ ↓ of 10 keV still reproduce the γ-decay spectrum of 81Rb. The index “<”used in Table I, in accordance with the notation of Ref. [6, 31, 32], refers tothe I = 0→ I = 1 mixing which is directly probed in our measurement.TABLE IBest fitting parameters obtained from the statistical model analysis [21, 22] to-gether with their statistical error. In the first three columns the GDR centroidEGDR (MeV), width ΓGDR and EWSR strength are reported. These parameterswere obtained from 81Rb γ-ray spectra analysis. In the last two columns theCoulomb spreading width (Γ ↓>) and the isospin mixing parameter (α2<), obtainedfrom 80Zr analysis, are listed [21, 22].EGDR (MeV) ΓGDR (MeV) EWSR Γ↓> (keV) α2< %16.2± 0.15 10.8± 0.3 0.90± 0.03 10± 3 5± 1This analysis has shown that the hindrance of GDR decay in the self-conjugate nucleus 80Zr makes possible the evaluation of the degree of isospinmixing present in a highly excited compound nucleus. The value of theCoulomb spreading width extracted from the statistical model analysis Γ ↓>[6, 31, 32] is comparable to the width of the isobaric analogue state Γ ↓IAR =9.9 keV measured in 80Se [33], a nucleus with a similar mass and deformationas 80Zr. As stated in Ref. [7], the value of Γ ↓↓ IARis equivalent to zero tempera-ture Γ , this means that the mixing mechanism, as Wilkinson proposed [30],is the same independently of the excitation energy. The measured value ofthe isospin mixing coefficient at T ' 2 MeV α2<, extrapolated to T = 0 usingthe technique described in [5, 6, 32, 33], has given a value of 5± 1% whichis consistent with the one calculated in Ref. [34] of 4.5% for 80Zr at zerotemperature.5. ConclusionsIn this work high energy γ-ray emission from hot nuclei has been used forthe measurement of the total yield of the Dynamical Dipole in the reaction16O+116Sn at 8.1, 12 and 15.6 MeV/u and of the isospin mixing in 80Zr atE? = 83 MeV. In both the experiments it has been necessary to measure, asa reference, the high energy spectra emitted in a fusion–evaporation reactionwhich produces a similar compound nucleus (132Ce in DD physics case and81Rb in the isospin mixing case) at the same excitation energy and angularmomentum but where DD was not present and E1 decay not hindered. Thepreliminary results of the data analysis have shown that: (i) there is thePrompt High Energy Dipole γ Emission 627same “rise and fall” trend of the total DD γ-ray yield as was observed inRef. [27] and that preliminary theoretical calculations do not manage toreproduce the experimental trend; (ii) A Coulomb spreading width in 80Zrat T ' 2 MeV of 10±3 keV was extracted from data. Following the analysisprocedure discussed in Ref. [31, 32] a mixing coefficient α2< = 5 ± 1 % wasextracted. Both results are consistent with previous data (the Γ ↓ in 80IAR Sewas measured to be 9.9 keV [33]) and very recent theoretical calculations [34].Even though data analysis is not concluded yet these preliminary resultscall for new measurements and theoretical calculations. In fact, it is notyet present a simple technique to compare the α2< values measured at highexcitation energies with theoretical values calculated at zero temperature.The work has been supported by the Italian National Institute of NuclearPhysics (INFN), by the Polish Ministry of Science and Higher EducationGrants No. N N202 486339 and No. N N202 309135.REFERENCES[1] F. Pulhofer, Nucl. Phys. A280, 267 (1977).[2] V. Baran et al., Nucl. Phys. A679, 373 (2001).[3] V. Baran et al., Phys. Rev. Lett. 87, 182501 (2001).[4] V. Baran et al., Phys. Rev. C79, 021603 (2009).[5] M.N. Harakeh et al., Phys. Lett. B176, 297 (1986).[6] J.A. Behr et al., Phys. Rev. Lett. 70, 3201 (1993) and PhD thesis.[7] H.L. Harney et al., Rev. Mod. 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Corsi et al., Proceedings of the International School of PhysicsEnricoFermi” Summer Courses 2010 Villa MonasteroVarenna, Lake Como,19–24 July, 2010.[22] A. Corsi, PhD thesis.[23] S. Flibotte et al., Phys. Rev. Lett. 77, 1448 (1996).[24] M. Cinausero et al., Il Nuovo Cimento A111, 613 (1998).[25] D. Pierroutsakou et al., Phys. Rev. C71, 054605 (2005).[26] B. Martin et al., Phys. Lett. B664, 47 (2008).[27] D. Pierroutsakou et al., Phys. Rev. C80, 024612 (2009).[28] A. Di Pietro et al., Nucl. Phys. A689, 668 (2001).[29] V. Baran et al., Phys. Rep. 464, 113 (2008).[30] D.H. Wilkinson, Phil. Mag. 1, 379 (1956).[31] E. Wójcik et al., Acta Phys. Pol. B 37, 207 (2006).[32] M. Papa et al., Eur. Phys. J. A4, 69 (1999).[33] S. Kailas et al., Nucl. Phys. A315, 157 (1979).[34] W. Satula et al., Phys. Rev. Lett. 103, 012502 (2009) Acta Phys. Pol. B 42,415 (2011), this issue.
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