Fusion-ﬁssion and fusion-evaporation processes in Ne Tb and Ne … · 2014. 10. 17. · Fusion-ﬁssion and fusion-evaporation processes in20Ne¿159Tb and 20Ne¿169Tm interactions

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PHYSICAL REVIEW C 68, 034613 ~2003!

Fusion-fission and fusion-evaporation processes in20Ne¿159Tb and 20Ne¿169Tm interactionsbetweenEÕAÄ8 and 16 MeV

J. Cabrera, Th. Keutgen, Y. El Masri, Ch. Dufauquez, V. Roberfroid, I. Tilquin, and J. Van MolFNRS and Institute of Nuclear Physics, Universite´ catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium

R. RegimbartLaboratoire de Physique Corpusculaire, IN2P3, CNRS/ISMRA, F-14050 Caen Cedex, France

R. J. CharityDepartment of Chemistry, Washington University, St. Louis, Missouri 63130, USA

J. B. Natowitz, K. Hagel, and R. WadaCyclotron Institute, Texas A&M University, College Station, Texas 77845, USA

D. J. HindeDepartment of Nuclear Physics, Research School of Physical Sciences and Engineering, Australian National University, Canb

Australian Capital Territory 0200, Australia~Received 21 May 2003; published 30 September 2003!

Fission lifetime studies are performed using the ‘‘neutron-clock’’ technique associated with statistical anddynamical model calculations. In this framework we have undertaken, at the Louvain-la-Neuve cyclotronfacility, the study of20Ne1159Tb and20Ne1169Tm induced fission reactions betweenE/A58 and 16 MeV. Inthis work we have determined~a! fusion-evaporation and fusion-fission cross sections;~b! the prescission andpostscission multiplicities of evaporated light particle~neutron, proton, and alpha! and their energy and angulardistributions, and~c! the total energy balance of fission process after taking into account preequilibrium orincomplete-fusion processes. The comparison of the experimental data, multiplicities, and cross sections, withthe statistical-model calculations incorporating simple aspects of the dynamics have enabled us to determinethe ranges of fission lifetimes and the contribution of fast fission at different compound-nucleus excitationenergies.

DOI: 10.1103/PhysRevC.68.034613 PACS number~s!: 25.70.Jj, 25.85.Ge

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I. INTRODUCTION

The time scale of the fission process has been previoaddressed using a number of experimental techniques.largest number of studies have been performed with‘‘neutron-clock’’ technique@1# which comprises measurements of the multiplicity of neutrons evaporated by the dcaying nucleus before scission occurs. Such measuredtiplicities are usually coupled with statistical-modcalculations to give a time for fission. Other prescissemissions such as light charged particles and giant-dipresonanceg rays can be substituted for the neutrons. Allthese techniques rely on the accuracy of the statistical-mcalculations. The authors of such studies@1# typically presentthe results of their work in terms of some extra dynamitime which must be introduced into the statistical modelsreproduce the measured prescission neutron multipli(nn

pre). These studies suggest dynamical time scales of oof 10 zs (1 zs510221 s). This extra time can comprisecontribution from a presaddle fission delaytd and/or a con-tribution from the dynamical time required for the fissioninsystem to move from the saddle-point to the scission-pconfiguration. The fission delay is associated with a transfission decay rate which is initially suppressed due tononequilibration of the compound-nucleus shape degree

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freedom. The relationship of these extra dynamical timesthe total fission time, which also contains contributions frostochastical processes, is complex.

In principle, more direct time scale measurements canobtained with the crystal blocking technique using a sincrystal. The sensitivity of this technique is limited by thvelocity of the fissioning system. Early measurementsported a significant tail to the fission time distributiontimes greater than 30000 zs@2# for fission induced by the19F1181Ta fusion reaction. More recent measurement forE/A524 MeV238U128Si reaction found mean fission lifetimes to be greater than 100 zs for excitation energies u250 MeV @3#. The importance of fission events with lontime scales (.1000 zs) has also been confirmed usingKx rays to time the fission of target and projectilelike framents in the reactionE/A57.5 MeV238U1238U @4#.

In view of the large range of fission time scales obtainfrom the different techniques, one must understand exawhat time is being measured by each method and attempobtain a global picture of the fission time distribution froall techniques. To this end, this paper will concentrate onneutron-clock method using recent data obtained fromneutron multidetector DEMON@5#. As one applies theneutron-clock technique using the statistical model to trthe evaporation, it is important to determine the initial extation energy and spin distributions of the fissioning nuc

©2003 The American Physical Society13-1

J. CABRERAet al. PHYSICAL REVIEW C 68, 034613 ~2003!

FIG. 1. ~Color! Schematic view of the experimental apparatus showing the location of the detectors in the scattering chamber~see textfor details!.

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For bombarding energies aboveE/A510 MeV, preequilib-rium ~PE! emissions of light particles are expected to remoexcitation energy and angular momentum, making it imptant to perform extensive studies of the evaporation residand fission fragments to infer these initial quantities. Alsohigh bombarding energies, even for relatively asymmereactions, the maximum spin of the fused system canquite large, possibly larger than the valueJBF50 at which thefission barrier vanishes. For such cases, a compound nu~CN! will not be formed and the fast-fission mechanism wbe observed@6#. To determine the extent of CN fission, thmagnitude, if any, of fast fission in the reaction needs toestimated.

In this paper, we report the results of an extensive semeasurements on the properties of evaporation residuesfission fragments formed in fusionlike reactions of20Ne1159Tb and 20Ne1169Tm from E/A58 to 16 MeV. Themagnitude of the preequilibrium emission is inferred frothe fission-fragment folding angles and the evaporation rdue ~ER! velocity distributions. From the total fusion crossection, determined from the sum of the fission andyields, the maximum, waves contributing to fusionlike processes are estimated. With estimates of the angular momtum fraction removed by PE emissions, the intrinsic angumomentum of the composite system is determined and cpared to the value where the fission barrier is predictedvanish in order to explore the possible presence of fastsion.

Prescission and postscission multiplicities of neutronslight charged particles in coincidence with fission fragmeare extracted from the kinetic-energy spectra and their anlar distributions using simulations which assume contribtions from up to four moving sources. Statistical-modanalyses are performed to estimate the dynamical timesfission, both statistical and fast fission and the total fiss

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time scales. The details of the experimental apparatusdescribed in Sec. II while the results of the experimenmeasurements are presented in Sec. III. Section IV discuthe analysis of the data including the estimation of fisstime scales and the conclusion of this work is containedSec. V.

II. EXPERIMENTAL METHOD

Beams of20Ne projectiles, extracted from the CYCLONaccelerator at Louvain-la-Neuve, were used to bombard ssupporting 159Tb and 169Tm foils of thickness 25068 mg/cm2. Measurements were performed at the bombaing energies ofE/A58, 10, 13, and 16 MeV. A schematiview of the detection apparatus is shown in Fig. 1. The tarwas located in the center of a 4-mm-thick Al scatterichamber of 160 cm diameter. The target holder was setpotential of 118 kV to suppress secondary electron emsion. Evaporation residues and fission fragments weretected in two 300-mm, 600-mm2 Si counters~GJ1 and GJ2!.These were placed at forward angles on either side ofbeam axis and were moved during the experiment to samthe angular region 8°,u lab,20°. Secondary electrons liberated during the passage of incident particles through thesurface layer~500 Å! of each Si detector were accelerateda 4 kV potential into double-microchannel-plate assembmounted in the chevron configuration@7#. Timing signalsfrom these assemblies were used to measure the timflight of detected particles over their 57 cm flight path frothe target with a resolution of 700 ps full width half maxmum ~FWHM!. Energy calibrations of the Si counters weobtained from beams of20Ne anda particles elastically scattered off a Au target. For heavy fragments, the energy wcorrected for the pulse-height deficit using the formalismKaufman et al. @8# fitted to the measured spectra of252Cf

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FUSION-FISSION AND FUSION-EVAPORATION . . . PHYSICAL REVIEW C68, 034613 ~2003!

FIG. 2. ~Color! Plot of measured energy vs time of flight for heavy fragments detected in the GJ counters atu lab59° in 20Ne1169Tm reaction atE/A516 MeV. The locations of the evaporation residues~ER!, the fission fragments~Fission!, the elastically scattered20Ne projectiles~ES!, and the deep inelastic collisions~DIC! are indicated.

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fission fragments. Particle identification was achieved frenergy and time-of-flight information. An example of a bidmensional plot of these two quantities is displayed in FigThe evaporation residues and fission fragments areseparated from the other reaction products~elastic, quasielastic, and deep inelastic scattering!.

Coincident fission fragments were detected in two320 cm2, X andY position sensitive, multiwire proportionagas counters~MWPC1 and MWPC2!. The counters werefilled with a continuous flow of isobutane gas at a constpressure of 7.5 torr. The emission angles of detected fments were determined to60.4° in bothu and f, whileeach counter subtended620° in the two directions. Thetimes of flight of detected fragments were measured over29.5 cm flight path from the target with a resolution of 5ps FWHM. The two MWPCs were arranged symmetricaon either side of the beam axis. Their angular positions wadjusted for each beam energy to optimize the coinciderate and to cover the entire fission-fragment mass distrtion, i.e., their central angles varied from 70° to 60° wincreasing beam energy. Absolute cross sections were dmined from the beam charge collected in the Faradaywhich was held at a potential of21 kV to suppress secondary electron emission. Two 3-cm-thick CsI counters~CsI1and CsI2!, read by photodiodes, were mounted atu lab564.1° at 66 cm from the target to detect elastically sctered beam particles. They were used to continuously mtor the beam intensity and its alignment.

Neutrons emitted in coincidence with the fission framents were detected in the 96 DEMON counters@5#. Eachdetector, consisting of an active volume of 16 cm diame

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by 20 cm thickness, is filled with NE213 liquid scintillatoThe detectors were mounted outside the scattering chamat a distance of 185 cm from the target and were arrangea 4p geometry as shown in Fig. 3. To minimize the neutrbackground, the scattering chamber was located at a distof 5 m above the ground and the beam was stoppedheavily shielded Faraday cup positioned 6 m from the target.The DEMON detectors were supported by the light-weigAl structure shown in Fig. 3. Separation of detected neutrand g rays and the determination of the neutron detectefficiency as a function of energy and detector thresholddiscussed in great detail in Ref.@5#.

Light charged particles emitted in coincidence with tfission fragments were detected in six triple-Si telesco(T1 –T6). Each telescope consisted of a 85-mm-thick Sifront element followed by two 706-mm-thick Si elements.The telescopes were positioned at 19.5 cm from the targeangles of6115°, 6140°, and6165° from the beam axisExcellent particle identification was achieved from tenergy-deposition and the energy-loss measurements.tons, deuterons, tritons, anda particles were well resolvedOnly proton anda-particle data will be presented in the remainder of this report as there were very few deuteronstritons in coincidence with the fission fragments.

III. RESULTS

A. Evaporation residue and fission cross sections

Following Ref. @9#, the distribution of residue velocitieabout the CN recoil velocityVCN is assumed to be GaussiaIn the laboratory reference frame, the distribution is thus

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FIG. 3. ~Color! Arrangement of the DEMON neutron counters around the scattering chamber in the Louvain-la-Neuve cyclotrohall.

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wheresER is the total ER cross section,S is the width of thedistribution, andu is the recoil angle from the beam axiThe parameterssER, S, VCN were adjusted to obtain the befits to u lab58° data detected with the counters GJ1 and GExamples of these fits are shown in Fig. 4 for the four retions on the159Tb target. The fitted values ofsER andVCNare listed in Tables I and II, respectively. At the lowest bobarding energy,VCN is consistent with the reaction center-omass velocityVc.m. and thus with complete fusion, but thratio VCN/Vc.m. steadily decreases as the bombarding eneis raised, consistent with an increased contribution from

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complete fusion and/or preequilibrium emissions. Theseperimental velocities are in excellent agreement with the stematics of linear-momentum transfer compiled in Ref.@10#.

The massMF of a fission fragment detected in the foward counters GJ1 and GJ2 was determined from the msured velocity and kinetic energy. The mean masMF

exp~secondary after evaporation! of the measured distributions are listed in Table III. The reaction center-of-massgular distributions were fitted with the form@13,14#

dsF

dVc.m.5

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sinuc.m., ~2!

where sF is the total fission cross section anduc.m. is thecenter-of-mass emission angle of the fragment. This ang

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FIG. 4. Velocity distributions of evaporation residues emittedthe 20Ne1159Tb reactions atu lab58° for the indicated bombardingenergies. The data points show the experimental distributions inlaboratory frame. The vertical lines correspond to the upperlower limits of velocity considered in the fit. The smooth solcurves indicate the fits. The fitted mean CN velocityVCN and thecenter-of-mass velocityVc.m., which is the complete-fusion valuof VCN , are indicated by the arrows in each panel.

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distribution is appropriate for fission of compound nucwith large angular momentum withuc.m.@0° and uc.m.!180°. An example of one of the fits is shown in Fig. 5. Tfitted fission cross sectionssF and the sumssER1sF , giv-ing the total fusion cross sectionssFU , are listed in Table Ias a fuction of the complete-fusion excitation energyE* .The corresponding critical angular momenta have beenculated assuming the sharp cutoff approximation, i.e.,sFU5p|2(,crit11)2. These are listed in Table I and are diplayed in Fig. 6 where they are compared to predictionsthe complete-fusion models of Wilcke and co-workers@16#and Bass@17# and from theHICOL code of Feldmeier@18#. Atthe larger bombarding energies, the experimental value,crit are much larger than these complete-fusion estimasuggesting the possible presence of another reaction menism. The values of the ratiosER/sF are also listed in TableI.

Coincident fission fragments detected in the MWPwere only analyzed when the detected fragment inMWPC1 was located within65° ~both in and out of thereaction plane! of the central angle. With this constraint, thcomplementary fragment detected in MWPC2 is unbiasedthat counter’s angular acceptance. From the measured veity vectors of the two fragments, the mass of each fragmand the total kinetic energyTKE released in fission in thecenter-of-mass frame can be reconstructed with the assution that the total momentum in this frame is zero and wan assumed total massMsc at scission. This mass is estmated from the multiplicities of coincident neutrons, protonand a particles ~see Sec. IV B!. These assumed values oMsc and the mean total kinetic energiesTKE for symmetricmass partition (65 nucleons! are listed in Table III. TheseTKE values are primary, before postscission evaporatfrom the fission fragments. This is because the fragmentlocities are not affected, on average, by the recoil kicks frthese evaporated particles. The deducedTKE values are con-sistent with the systematics of Viola@15# (TKEViola in TableIII ! to within at most 9 MeV.

The distributions of fission-fragment folding anglesu125u11u2 ~sum of the polar angles of the two fragmentslaboratory frame! for uf12f2u5180°65° are shown inFigs. 7 and 8 for both targets. In Fig. 7 the experimendistributions are each fitted with a single Gaussian comnent indicated by the curves. The folding angle is relatedthe CN velocity@19# by

tanS u12

2 D5A2 TKE/Msc

VCN. ~3!

Compound-nucleus velocitiesVCN were determined fromthis equation using the fitted centroids of theu12 distributionsand the meanTKE values of Table III. The ratiosVCN/Vc.m.extracted from this analysis are listed in Table II and copared to the CN velocities obtained from the evaporatiresidue velocity distributions. TheVCN values obtained fromthe ER and fission data need not be identical as these rtion products are expected to be associated with differ

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TABLE I. Evolution of evaporation residuesER , fission sF , and total fusionsFU cross sections asfunctions of the complete-fusion excitation energyE* . Also shown are the evaporation and fission crosection ratios and corresponding critical angular momenta,crit derived from the fusion cross sections asuming the sharp cutoff approximation.

E* sER sF sFU ,crit

~MeV! ~mb! ~mb! ~mb! sER /sF (\)

20Ne1159Tb112 711646 641625 1352672 1.1160.08 7262148 743648 838638 1581686 0.8960.07 8762201 796645 804635 1600680 0.9960.07 10062254 924653 759638 1683691 1.2260.09 11463

20Ne1169Tm108 351659 1070641 14216100 0.3360.06 7463144 359631 1230654 1589685 0.2960.03 8862196 414625 1210649 1624674 0.3460.02 10162251 478620 1160654 1638674 0.4160.03 11363

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distributions of impact parameter and, wave. However, theyare consistent with each other, within the experimentalcertainties, for all the reactions studied in this work.

The distributions of fission-fragment folding angles wealso analyzed following the method of Ref.@20# where thefusionlike yield is composed of both complete-fusion aincomplete-fusion components, but the incomplete-fuscomponent is associated purely with a singlea -particle ejec-tile from the 20Ne projectile in the massive transfer descrtion. In this method, folding-angle distributions are fittedthe sum of two Gaussian components; one componentcomplete fusion with the centroid fixed at the value apppriate for complete fusionVCN5Vc.m. and the second Gaussian component with the same width, but a centroid approate for the complete fusion of an16O projectile at the sameE/A. Examples of such fits for the20Ne1169Tm reactionsare displayed in Fig. 8. The quality of the fits is inferior

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that obtained with a single Gaussian component in Figespecially in the intermediate region between the two ctroids where the fitted yield falls significantly below the eperimental data. This implies that incomplete fusion is mocomplex than a singlea-particle ejectile. Thus, there musalso be fusionlike reactions with one, two, and three nucons from the projectile that are missing from the final CIncluding these processes will allow for increased yieldthis intermediate region and a better agreement with theperimental data. Similar conclusions were also deduced fthe 20Ne1159Tb data.

Fission cross sections were also obtained fromMWPC. They are consistent with, but not considered ascurate as, those in Table I due to the uncertainties in eslishing the experimental MWPC intrinsic detection efciency (;80% on average! over the entire fission-fragmenmass distribution.

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TABLE II. For each complete-fusion excitation energyE* are listed the experimental mean velocityVCN of the compound nucleusextracted from the ER velocity distributions~ER! and from the fission-fragment folding-angle distributions~fission!. The velocity isexpressed relative to the reaction center-of-mass velocityVc.m. which is the corresponding complete-fusion value. Also listed are valuesthe quantityj from Ref.@11# giving the ratios of the mean velocity of PE particles to the projectile velocity. The initial CN massesMin

PE fromthe PE systematics are also listed. In the last two columns are listed the maximum intrinsic angular momentaJcrit

PE of CN and the angularmomentaJBF50 at which the fission barriers are predicted to vanish in the calculations of Sierk@12#.

E* VCN /Vc.m. VCN /Vc.m. JcritPE JBF50

~MeV! ER fission j MinPE (\) (\)

20Ne1159Tb112 1.0060.01 0.9760.03 0.2260.21 17860.3 72 78148 0.9760.02 0.9660.03 0.6160.14 17860.2 84 78201 0.9460.02 0.9260.02 0.7260.08 17760.1 93 78254 0.8960.02 0.8960.01 0.7760.05 17660.2 99 78

20Ne1169Tm108 1.0060.01 1.0060.03 0.1160.42 18860.3 74 77144 1.0060.02 0.9560.03 0.1660.29 18860.2 87 77197 0.9460.02 0.9160.02 0.6260.13 18760.1 95 77251 0.9060.02 0.8860.02 0.6960.09 18660.2 100 77

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B. Neutron multiplicities

Neutrons detected in coincidence with fission fragmeare assumed to originate from 4 moving sources. In temporder, first there are the preequilibrium neutrons with muplicity nn

PE, second are the prescission neutrons evaporfrom the compound system before scission (nn

pre), and lastare postscission neutrons evaporated from the two fisfragmentsnn

F1 andnnF2 . The energy spectra of each of the

sources are assumed to be thermal-like in their respecreference frames. Based on statistical-model simulati~Sec. IV D!, the first-chance emission spectra of neutrofrom a compound nucleus are well described by Maxwelldistributions:

d2nn

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FIG. 5. Measured~data points! and fitted ~curve! fission-fragment angular distribution in the reaction center-of-mass frafor the E/A513 MeV20Ne1159Tb reaction. The data were fittewith a 1/sinuc.m. dependence.

TABLE III. Mean fission-fragment massesMFexp ~in nucleons!

measured with the GJ1 and GJ2 counters are listed for each bbarding energyE/A and target. These masses are secondary athe evaporation from the fission fragments. Also listed are thesumed masses of fissioning nucleus,Msc , in nucleons and the meatotal kinetic energyTKE released in symmetric fission extractefrom coincident fission fragments. These are compared to the vafrom the Viola systematics@15#.

E/A TKE TKEViola

~MeV! MFexp Msc ~MeV! ~MeV!

20Ne1159Tb8 83.665 174.4 12560.1 12910 82.465 172.1 13660.1 12813 85.265 168.8 12660.1 12516 83.665 165.7 12160.1 123

20Ne1169Tm8 89.065 184.8 12960.1 13810 86.565 182.3 14660.1 13713 86.565 178.4 14260.1 13416 83.565 175.5 13860.1 132

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whereT is the effective nuclear temperature of the emittisource while the solid angleVs and neutron energyEs are inthe source reference frame. Emissions with this distributfunction are often called surface emission. Prescissevaporation from the compound nucleus involves emissifrom a number of evaporation steps, but does not containvery low energy neutrons associated from last-chance deof a CN just before the excitation energy is exhausted.statistical-model simulations, these distributions can alsowell reproduced by the surface-emission expression@Eq.~4!#. However, the spectra for neutrons emitted from thesion fragments do contain these low-energy last-chaemissions and cannot be fitted with Eq.~4!. From manysimulations, these spectra were found to be more consiswith a Watt distribution or volume emission spectrum;

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Rossneret al. @21# came to similar conclusions concerninthe shape of the prescission and postscission neutron spfor the 36Ar1169Tm reaction. Therefore as in Ref.@21#, theprescission source was assumed to be surface emission@Eq.~4!# and the fission-fragment sources were taken as voluemission@Eq. ~5!#. The preequilibrium source was also asumed to exhibit volume emission with a source velocityhalf the beam velocity as in Ref.@22#. Note, that in otherstudies there are a number of other assumptions concerthe shape of the prescission and postscission sources;@20,23,24# assumed both sources are volume emission, win Ref. @22# both sources are surface emission. Hindeet al.@25# have used sums of Maxwellian distributions for bosources to model the multiple-chance emissions and in R

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FIG. 6. ~Color! Experimental data points show the dependenof the critical angular momentum for fusionlike reactions,,crit , onthe complete-fusion excitation energy. These are compared topredictions of the complete-fusion models of Wilcke and cworkers @16# ~solid curves! and Bass@17# ~dashed curves!. Thecircular points indicate the critical angular momenta at which ais formed in the dynamical codeHICOL @18#.

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θ

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FIG. 7. Distributions of fission-fragment folding anglesu12

measured for the reactions on the Tb target using coincidencefrom the MWPCs. The experimental distributions are displayedthe data points, while the thin solid curves indicate singcomponent Gaussian fits to these distributions. The vertical lshow the centroids of the Gaussian fitsu12

exp and the expected meavalues for complete fusionu12

CF.
re
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FIG. 8. ~Color! Distributions of fission-fragment folding angleu12 measured for the reactions on the Tm target. The experimedistributions are displayed by the data points, while the thick socurves indicate fits to these distributions using the prescriptionRef. @20# consisting of the sum of two Gaussian components asciated with complete fusion and incomplete fusion with a sina-particle ejectile. The fixed centroids for each component aredicated asu12

CF and u12CF21a and the two Gaussian components a

plotted as the thin and dashed curves, respectively.

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FIG. 9. ~Color! Examples of some of the multiple-moving-source fits~curves! to experimental neutron kinetic-energy spectra in tlaboratory frame for theE/A513 MeV20Ne1159Tb reaction. The thick solid curves TOT indicate the total contributions from all sourThe contributions from each of the sources are indicated by the labeled curves; CN represents contribution from the prescission CF1 and F2 from the two fission fragments, and PE from preequilibrium emission.

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@26–28# an iterative procedure which does not rely on asumed shapes for the prescission and postscission spwas utilized.

To reduce the number of fitting parameters, only eveassociated with symmetric fission~symmetric mass partition65 nucleons! were fitted, and thusTF15TF25Tpost andnn

F15nnF25nn

post/2. The neutron multiplicities associated wiasymmetric fission have been analyzed@29–31# andnn

pre andnn

post5 (nnF11nn

F2)/2 were not found to have a significanasymmetry dependence, while the individualnn

F1 and nnF2

show approximately linear dependencies on the mass orespective fission fragment as in Ref.@22#.

The velocities of the two fission-fragment sources wfixed to the mean fission-fragment velocities measured wMWPC1 and MWPC2 for symmetric mass partition whthe CN prescission source was fixed to the valueVCN fromTable II obtained from the residue velocity distributions. Eamples of some of the many fitted spectra and angulartributions ~both in and out of the reaction plane definedfn50° and 180°) are shown in Figs. 9 and 10 for tE/A513 MeV reaction on the159Tb target. The spectra in

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Figs. 9~a! and 9~b! are for DEMON detectors directly behinMWPC1 and MWPC2, respectively. Due to the kinemafocusing of the postscission neutrons by the fission frments, these spectra are dominated by contributions fromrespective fission fragments~F1 and F2!. The preequilibriumcomponent is constrained mostly from the most forwaangle DEMON detectors at 12.5° in Fig. 9~c!, and the fittedPE multiplicitiesnn

PE are listed in Table IV. The spectra foDEMON detectors at backward angles, as in Fig. 9~d!, havethe largest contributions from the CN source. In Fig. 10,simultaneous fit to all of the experimental angular distribtions both in, and at a number off angles to, the reactionplane is extremely good, indicating the data are well dscribed by these four moving sources.

The fitted prescission and postscission multiplicities atemperatures from each source are listed in Table IVsymmetric mass partition. The extracted multiplicities do dpend on the assumed spectral shapes for the diffesources. For example, if volume emission is assumed forprescission and postscission sources, as in Refs.@20,23#, thefits to the kinetic-energy spectra and angular distributions

FIG. 10. ~Color! Examples of some of the multiple-moving-source fits~curves! to experimental neutronun distributions in the laboratoryframe for theE/A513 MeV20Ne1169Tb reaction. Distributions both in (fn50°,180°) and others at differentfn angles to the reactionplane are shown. The curves have the same meaning as in Fig. 9 and the fits correspond to the same set of fitted parameters (n i , Ti) as thosein Fig. 9.

3-9

ork. The


TABLE IV. The prescission and postscission neutron multiplicitiesnnpre andnn

post and corresponding nuclear temperaturesTpre andTpost

deduced from a multiple-moving-source–type analysis of symmetric fission data obtained from the two reactions studied in this wexperimentally extracted preequilibrium multiplicitiesnn

PE are also listed as a function of the complete-fusion excitation energiesE* andcompared~in the last column! to nn

PE(sys), the estimated PE multiplicities from the systematics of Refs.@20,22,32–34# ~see Sec. IV A!.

E* Tnpre Tn

post nnPE nn

PE~sys!~MeV! nn

pre nnpost/2 ~MeV! ~MeV!

20Ne1159Tb112 3.5360.17 1.9660.11 1.3860.07 1.3160.07 0.2360.15148 4.8360.09 1.8460.07 1.7560.02 1.3060.04 0.3460.03 0.3260.19201 5.9160.16 2.2960.12 2.0460.04 1.4160.06 0.4960.04 0.5860.23254 7.0860.22 2.5160.16 2.2560.07 1.3860.08 0.8860.07 0.9860.25

20Ne1169Tm108 3.2260.16 2.4360.10 1.3360.07 1.3560.03 0.2360.15144 4.6660.08 2.2260.06 1.6660.02 1.3460.03 0.3260.19197 6.2060.13 2.3460.09 1.9360.02 1.4460.05 0.6060.04 0.5860.23251 7.0860.15 2.5060.10 2.1160.03 1.4660.05 0.7860.04 0.9860.25

esarar

e

eic-cita-ite

lts

is-our

ci-trafor

rce,b-

ob-eresta-ere

t,forbar-x-thuceveddof

fengw.

of similar quality and the fitted values ofnnpre are increased

by approximately one neutron for all bombarding energiThe evolutions of the multiplicities and effective nucletemperatures with complete-fusion excitation energyshown in Fig. 11.

Also plotted in Fig. 11 are neutron multiplicities for thsimilar reactions19F1159Tb and 19F1169Tm obtained by

0

1

2

3

4

5

6

7

8

0.0

0.5

1.0

1.5

2.0

60 110 160 210 260 310

E* (MeV)

Tem

perature

(MeV

)

20 159Ne + Tb

19 159F + Tb

20 169Ne + Tm

19 169F + Tm

Multiplicity

npre

npost/ 2

20 169Ne + Tm20 159Ne + Tb

Tnpre

Tnpost

ν

ν

FIG. 11. Evolution with complete-fusion excitation energyE*of prescission and postscission neutron multiplicities and the eftive nuclear temperatures extracted from the multiple-movisource fits to the neutron data. Multiplicities are shown for the ttargets of this work and for the similar19F induced reactions of Ref@28#. Broken lines are to guide the eye.

03461

.

e

Newtonet al. @28# using the iterative technique to extract thprescission and postscission multiplicities from the kinetenergy spectra. These data are associated with lower extion energies than those of this work, but they match up quwell with the multiplicities we have measured. Our resuseem to agree quite well with the published data on20Ne1165Ho @20# and 20Ne1168Er @25# reactions, considering thedifferent methods of extracting the neutron multiplicities dcussed previously. This gives us further confidence indata and the extracted neutron multiplicities.

C. Charged-particle multiplicities

The a and proton prescission and postscission multiplities were extracted from fits to the kinetic-energy specassuming contributions from three moving sources: oneCN emission and two for the fission fragments. Each souin its respective moving frame, is described by a Coulomshifted Maxwellian spectrum:

d2n i

dVsdEs5

n i

4pT2~Es2Bi !expS 2

Es2Bi

T D , ~6!

where Bi is the effective Coulomb barrier. Preequilibriumcharged-particle emission could not be experimentallyserved in this work because the triple-Si telescopes wonly positioned at backward angles. Because of the poortistics of the data, the prescission nuclear temperatures wfixed to the maximum-allowed temperaturesTpre5AE* /a~with a5ACN/9 MeV21). For the postscission componenTpost was fixed to the experimental value determinedpostscission neutrons. Moreover, the effective emissionriers, initially taken from the systematics of Vaz and Aleander @35#, had to be decreased by 2–3 MeV, for boprescission and postscission emission, in order to reprodthe experimental data. Such modifications were obserpreviously@36,37# and were justified by the deformation anthe shape oscillations of the hot emitting nuclei. Examplesfitted spectra are shown in Fig. 12 for the169Tm target. The

c--o

3-10

eregion


FIG. 12. ~Color! Examples of multiple-moving-source fits to the experimental proton anda-particle kinetic-energy spectra in thlaboratory frame obtained for the20Ne1169Tm reaction. The labeling of the curves is the same as in Fig. 9. The arrows indicate theof the a-particle spectra which cannot be fitted with the three assumed moving sources~see text for details!.

lun

ofed

for

po-ey

fitted multiplicities are presented in Table V and the evotion of these multiplicities with complete-fusion excitatioenergyE* is displayed in Fig. 13. One notable failurethese fits is fora particles at energies near 10 MeV indicat

03461

-by the arrows in the Fig. 12. We suspect that the reasonthis discrepancy is due to the presence of scissiona particlesemitted during the snapping of the neck at scission or evarated from the neck region just before or after scission. Th

3-11

-s work.


TABLE V. Prescission and postscission multiplicities for protons anda particles extracted from multiplemoving-source fits to the measured kinetic-energy spectra are listed for the two reactions studied in thiThe complete-fusion excitation energiesE* are also listed.

E*~MeV! np

pre nppost/2 na

pre napost/2

20Ne1159Tb112 0.10260.055 0.04060.027 0.06560.031 0.02460.017148 0.21960.030 0.06160.015 0.20560.018 0.01060.006201 0.51460.055 0.16660.027 0.42260.041 0.03460.015254 0.63660.063 0.25760.032 0.55560.068 0.09160.028

20Ne1169Tm108 0.08060.009 0.03460.007 0.06060.008 0.02360.005144 0.18860.008 0.10560.004 0.20460.006 0.04960.003197 0.50860.018 0.19160.009 0.44960.015 0.09760.007251 0.64060.020 0.20060.009 0.59160.020 0.10360.009

fiio

insa

uer

fed

un-ionted

tedllerthefu-uiren-ofentaen-thePEnts,PEs.i-en

pro-theofter-l

hensem-

u-ci-

E-os of

e

have been observed in a number of detailed studiescharged particles accompanying fission@38,37# and are ex-pected to be emitted approximately perpendicular to thesion axis. Our sensitivity to the magnitude of the postscissa-particle multiplicity comes only from fitting the spectraa small range of kinetic energy below the region for thescission particles, and thus can be quite sensitive to thesumed shape for this spectral component in the fits. Thecertainties, listed in Table V, are only the statistical unctainties from the fitting process, for postscissiona particlesthe systematic uncertainties due to the assumed shape ospectra and the presence of scission particles are expect

0.0

0.2

0.4

0.6

0.0

0.2

0.4

0.6

60 110 160 210 260 310

20 169Ne + Tm

20 159Ne + Tb

Proton

ppre

ppost

/ 2

20 169Ne + Tm

20 159Ne + Tbpre

post

/ 2

E (MeV)*

Multiplicity

Multiplicity

ν

ν

ν

ν

α

α

α

FIG. 13. Evolution with complete-fusion excitation energyE*of the prescission and postscission proton anda-particle multiplici-ties obtained from fitting the kinetic-energy spectra. Broken linare to guide the eye.

03461

of

s-n

es-

n--

theto

be larger, but are difficult to estimate. These systematiccertainties are much less of a problem for prescissa-particle multiplicities as these particles dominate the fitspectra at the largera kinetic energies.

IV. DISCUSSION

A. Preequilibrium emission

For the three highest beam energies, the extraccompound-nucleus velocities in Table II are clearly smathan the corresponding complete-fusion values indicatingoccurrence of preequilibrium emission and/or incompletesion. As statistical-model analyses of the fission data reqa good knowledge of the spin and the initial excitation eergy of the CN, it is important to estimate the magnitudethese PE emissions and to determine the angular momand excitation energies removed by these particles. As mtioned before, our experimental setup was not adapted formeasurement of the charged-particle contributions toemission. To estimate the magnitude of these componewe have used a second-order polynomial interpolation ofmultiplicity systematics of light particles obtained from Ref@20,22,32–34#. To adjust these multiplicities to our expermental conditions, the reference multiplicities have bescaled by the ratio between our projectile mass and thejectile mass of the reference data. Figure 14 displaysevolution of these expected PE multiplicities as a functionthe beam energy per nucleon for neutrons, protons, deuons, tritons, anda particles. These multiplicities are identicafor the two 20Ne beam induced reactions. Table VI shows tresults of the polynomial interpolations for the reactiostudied in this work. Note that PE emissions in these systatics are not dominated bya particles. This is consistent withour analysis of the fission-fragment folding-angle distribtions in Sec. III A. One must compare the neutron multiplitiesnn

PE(sys) of Table VI with the experimental values (nnPE)

extracted from the multiple-moving-source fits of the DMON neutron spectra of Table IV in Sec. III B for the twstudied reactions. The agreement between the two set

s

3-12

s

ylvh

ectro

e-y

t-

otalofhis

erees

ifm-the

I

ofeFor

themeoxi-en-toor-ton-

ati-ata

-

s.hee

.


values is good. Total mass (Dm) and charge (Dz) losses byPE emission are then calculated as

Dm51nnPE11np

PE12ndPE13n t

PE14naPE, ~7!

Dz51npPE11nd

PE11n tPE12na

PE. ~8!

Dm andDz are listed in Table VI.The CN mass after PE emission was expressed asMin

PE

5MCNCF2Dm ~Table II!. The excitation energy of the CN i

estimated using the formalism of Cerrutiet al. @11#. The pa-rameterj5VPE/Vp , giving the ratio of the average velocitof PE emission to the projectile velocity, is obtained by soing Eq.~1! of Ref. @11#. The variation of this parameter witcomplete-fusion excitation energy is shown in Fig. 15. Whave assumed the PE emissions are solely from the proje(t50 in Ref. @11#! and the mean PE emission angle is zeThe CN excitation energies after PE emission,Ein*

PE, de-duced from this formalism will be plotted versus thcomplete-fusion valuesE* in Fig. 17. The difference betweenE* andEin*

PE is of course the energy carried away bPE emission.

The intrinsic angular momentum of the CN is assumedbe J5(,2D,), where D, is the angular momentum removed by PE emission. It has been assumed that

0.0

0.5

1.0

1.5

2.0

2.5

3.0

5 10 15 20 25 30 35

PEMultiplicity

E/A (MeV)

n

p

d

t

α

FIG. 14. Evolution of the preequilibrium multiplicities of neutrons @nn

PE(sys)# and light charged particles@nPE(sys)# for proton,deuteron, triton, anda, extracted from the systematics of Ref@20,22,32–34# as a function of beam energy per nucleon. Tcurves represent a second-order polynomial interpolation to thsystematics.

03461

-

ile.

o

D,5j,Dm

M p, ~9!

whereM p is the initial projectile mass. Ifj51 (VPE5Vp),the angular momentum removed by PE emission is the tinitial orbital angular momentum scaled by the fractionthe projectile mass which does not fuse with the target. Tis consistent with the simple incomplete-fusion picture whthe portion of the projectile, which does not fuse, continutraveling forward with the projectile velocity. However,this piece of the projectile is slowed down during the incoplete fusion process, its angular momentum is reduced byfactor j. The maximum intrinsic angular momentaJcrit

PE de-duced from the,crit values of Table I are listed in Table Iand compared to the angular momentaJBF50 for which thefission barriers are predicted to vanish in the calculationsSierk @12#. These values ofJBF50 are thus exceeded in thfusionlike reactions at the highest bombarding energies.those impact parameters which lead toJ.JBF50, a com-pound nucleus cannot be formed as there is no pocket inpotential energy surface into which the system can becotrapped. The composite system separates into two apprmately equal fragments and the reaction mechanism is gerally called ‘‘fast fission’’ as the scission time is expectedbe faster than that for statistical fission which has an imptant stochastic component. It is experimentally difficultdistinguish from conventional CN-fission reactions if the agular momentum cannot be inferred. Borderieet al. @39#have shown that fast-fission mass distributions are systemcally wider than those measured for CN fission. Our d

se

FIG. 15. Evolution with complete-fusion excitation energyE*of j ~the ratios of mean PE velocity to the projectile velocity! asdetermined for the two reactions studied in this work.j is definedfollowing the formalism of Ref.@11#. The lines are to guide the eye

TABLE VI. Preequilibrium multiplicities of light particles (n, p, d, t, anda) estimated from the systematics of Refs.@20,22,32–34# andthe total mass (Dm) and charge (Dz) losses from these emissions at each beam energy.

E/A nnPE(sys) np

PE(sys) ndPE(sys) n t

PE(sys) naPE(sys) Dm Dz

8 0.2360.15 0.0060.03 0.0060.02 0.0060.01 0.1160.02 0.6760.32 0.2260.1010 0.3260.19 0.0060.02 0.0060.02 0.0060.01 0.1860.02 1.0660.20 0.3660.0913 0.5860.23 0.1960.01 0.0760.01 0.0460.01 0.2860.01 2.0660.14 0.8660.0516 0.9860.25 0.4060.01 0.1760.01 0.1260.01 0.3560.01 3.3860.17 1.3960.05

3-13

on

io

thpf tnitiencie

firs

on

oi-de

ng.

.1asece isghta

s

m-

ntni-y

of

i-

re

th

n-ial


from both targets show increased widths for the fissifragment mass distributions atE/A513 and 16 MeV@29,30#, consistent with the systematics of Borderieet al.andthus supporting the presence of fast fission in these react

B. Mass, charge, and energy balance

Since the average energies and multiplicities of allimportant evaporated particles have been measured, it issible to reconstruct the excitation energies and masses osystems formed in different stages of the CN decay. Not odoes this allow us to observe the evolution of these quantwith beam energy, it also allows us to check the consisteof the data and see if the estimated initial excitation energEin*

PE from the PE systematics are accurate. Let us startwith the mass balance. Using the estimated initial CN masMin

PE in Sec. IV A, the total mass removed by the prescissin p, anda evaporations~determined from the multiplicitieslisted in Tables IV and V! are subtracted giving the massesthe systems at scission (Msc). The average mass of the prmary fission fragment is half of this value. The final, seconary massMF of a fragment is determined by removing thmass loss associated with postscission evaporation agaiing the multiplicities in Tables IV and V. The curves in Fi16 show the evolution of final, secondary massMF of the

Mass(nucleon)

E (MeV)*

75

80

85

90

95

75 125 175 225 275

MF

MFexp

20 159Ne+ Tb

Mass(nucleon)

MF

MFexp

20 169Ne+ Tm

80

85

90

95

100

FIG. 16. Evolution of the final, secondary massMF of the fis-sion fragments~for symmetric fission! with the complete-fusion ex-citation energyE* for the studied reactions. These quantities aderived from mass-balance considerations~Sec. IV B!. TheMF val-ues~dotted curves! are compared to the data~open squares!, which

are the mean valuesMFexp of the fission fragments measured wi

the counters GJ1 and GJ2 after postscission evaporation.

03461

-

ns.

eos-helysys

stes,

f

-

us-

fission fragments~for symmetric fission! with complete-fusion excitation energyE* for the two studied reactionsThe mean values ofMF were directly measured with the GJand GJ2 counters~see Table III! and are indicated by the datpoints (MF

exp) in this figure. The agreement between themeasured values and the curves inferred by mass balanextremely good. Using the experimental and predicted licharged particles multiplicites listed in Tables V and VI,similar procedure was applied to infer the atomic numberZof the fission fragments. For example, for the20Ne1159Tbexperiment, theseZF ~for symmetric fission! were, respec-tively, 37.560.2, 37.060.1, 36.560.2, and 36.060.2 forthe different excitation energiesE* . Unfortunately, ZF

exp

were not measured experimentally and could not be copared to their corresponding calculated values.

For energy balance, we proceed in a slightly differemanner. First, we start with some initial estimate of the itial CN excitation energyEin* and then remove the energassociated with prescission emission. This is comprisedtwo components; first is theQ-valueQ1 and the second is thetotal kinetic energyEk

pre of these particles. The average knetic energy for prescission neutrons is 2Tpre ~surface emis-

FIG. 17. ~Color! Plotted vs the complete-fusion excitation eergyE* and for the two studied reactions the evolution of the initCN excitation energyEin* , the excitation energy at scission,Esc* ,and the residual excitation energyEres* , all these quantities weredetermined from energy-balance consideration~Sec. IV B!. Eres* hasbeen set equal to the excitation energy removed byg-ray emissionin the systematics of Refs.@41,42#. CN excitation energy after PEemission calculated from energy-balanceEin* is also compared toEin*

PE calculated from PE systematics.

3-14

e-


TABLE VII. For each complete-fusion exitation energyE* are listed, for the two studied reactions, thestimated initial CN excitation energies after preequilibrium emissionEin*

PE from PE systematics, as discussed in Sec. IV A, and the results of the energy-balance calculations~see Sec. IV B for details!. The initialexcitation energyEin* gives, at the end of the calculations, a residual energyEres* equal to the energy carriedaway byg-ray emission,Eg . This latter energy was estimated from the systematics of Refs.@41,42#.

E* Ein*PE Ein* Ek

pre Q1 Esc* Ekpost Q2 Eres*

~MeV! ~MeV! ~MeV! ~MeV! ~MeV! ~MeV! ~MeV! ~MeV! ~MeV!

20Ne1159Tb112 10363 9768 12.2 228.960.8 56.162.4 8.9 87.764 10.467.8148 13361 13564 23.8 240.460.4 70.361.5 8.4 85.161 11.563.5201 17363 17068 40.3 249.861.9 80.164.2 12.8 71.163 12.868.0254 20766 20369 53.8 259.561.0 89.964.4 16.0 60.662 13.969.2

20Ne1169Tm108 9963 8968 10.8 226.960.8 51.762.4 11.0 98.764 10.467.8144 13261 13464 22.4 239.160.4 72.261.5 11.8 96.861 11.563.5197 17263 17468 42.1 250.461.9 82.164.2 15.6 87.963 12.868.0251 21166 20169 54.2 258.061.0 89.264.4 16.9 80.062 13.969.2

oefo

foc-se

apthta

ii

b

itainsenvio

ncnn

llse

-

omsst

N

h ahe

onntieso

dilyra-iclesal-the

nti-tion

er

nse-e-calefe-

sion!, while for protons anda particles it isBipre12Tpre.

TheQ-values were calculated using the mass-deficit tableRef. @40#, with shell and pairing corrections removed for thheavy CN-like systems and experimental mass deficitsthe light particles. This prescription was felt appropriatecalculating averageQ-values as the shell and pairing corretions will vary greatly for each particular event, but are leimportant for the average. At this point we have determinthe excitation energy at scission,Esc* . A secondQ-valueQ2,associated with symmetric fission and the subsequent evration of the postscission particles, is now removed as iskinetic energy of the particles including the average tokinetic energy release in fission,TKE ~Table III!, and thetotal kinetic energy of postscission particles,Ek

post. Note thatin this step, as the postscission neutrons were fitted wvolume-type emission, their average kinetic energy(3/2) Tpost. The residual energy is thusEres* 5Esc* 2Q2

2Ekpost. This residual energy is supposed to be removed

g ray emissions. The total energy of emittedg rays (Eg) wasestimated from the systematics of Refs.@41,42#. The initialexcitation energy is then adjusted so as to makeEres* 5Eg ina second iteration of the energy balance. The initial exction energiesEin* determined in this manner are comparedTable VII to the valuesEin*

PE estimated from PE systematicas discused in Sec. IV A. They are in excellent agreemThus both mass and energy balances are shown to proexcellent consistency with the data. The various excitatenergies are listed in Table VII andEin* , Esc* , Eres* , andEin*

PE are plotted against the complete-fusion valuesE* inFig. 17 for the studied reactions.

An uncertainty in determining mass and energy balacomes from the systematic uncertainties in the postscissioamultiplicities due to the difficulties in fitting the postscissiocomponent of thea-particle kinetic-energy spectra~Sec.III C !. However, asa-particle emission removes only a smafraction of the initial excitation energy, on average, theuncertainties inEin* are not too large. For example, if thpostscissiona-particle multiplicities forE/A516 MeV reac-

03461

f

rr

sd

o-el

ths

y

-

t.iden

e

e

tions are increased by a factor of 4,Ein* is only increased by12 MeV. This uncertainty is even smaller for the lower bombarding energies.

C. Target dependence

The most striking difference in the datasets obtained frthe two targets is the ER probability. The smaller ER crosections for the169Tm target shown in Table I reflect the facthat the CN is more fissile, having aJ50\ fission barrierBF

which is;4 MeV smaller than that for the159Tb target@12#.The ER yield is predominantly associated with the lower Cspins extending up to the value whereBF(J) is equal to theneutron separation energy. This condition is achieved witsmaller value ofJ for the more fissile system, and hence tsmaller value ofsER. However, practically all of the fissionyield is expected to come from interactions with low fissibarriers, i.e.,BF(J) is smaller than the neutron separatioenergy or zero in the case of fast fission. Thus the properof the fission fragments should be very similar for the twtargets as they are not that different in mass. This is reaseen in terms of the fitted multiplicities and nuclear tempetures for the prescission and postscission evaporated partdisplayed in Figs. 11 and 12. All these quantities showmost the same dependence on bombarding energy fortwo targets. Although we have assumed the PE to be idecal for the two targets, the deduced values of the excitaenergies at scission (Esc* ) in Fig. 17 are again similar for thetwo targets. Therefore in the following, we will only considthe interpretation of the20Ne1159Tb reaction.

D. Statistical-model simulations

As the excitation energy at scission (Esc* ) increases withbombarding energy~Fig. 17!, then the initial excitation en-ergy of the fission fragments must also increase, and coquently the initial CN lifetime of these fragments must dcrease. It is not unreasonable that the scission time sshould be commensurate with this fission-fragment CN li

3-15

dithui

ldiodic

dth

ncWdleioa

ri-s-

t

d

israin

nfi

-e

esrt

isebdlh

o-to

ehef tnu

erestotionde-toion.

is.

rac-is-

tionre-i-

sioneffi-

-n-the

s-the

er-tios

n ofere

not

tcis-are

s

ed-s-

d


time, thus suggesting that the time scale for scission iscreasing with increasing bombarding energy. However wout some modeling of the fission decay modes, it is difficto ascertain whether this decrease is simply due to thecreasing proportion of fast fission in the total fission yiewith beam energy and/or to changes in the statistical fisstime scale. To investigate these possibilities, statistical-mosimulations incorporating simplistic aspects of the dynamof fast fission and statistical fission have been performethis work. The Monte Carlo simulations were based onstatistical-model computer codeGEMINI @14,43#.

The simulations have to take into account the occurreof both the preequilibrium and fast-fission processes.have assumed that the preequilibrium probabilities are inpendent of impact parameter. This seems quite reasonabthe measured CN velocities determined form ER and fissdata, which probe different regions of impact parameter,consistent within their experimental uncertainties~see TableII !. The initial excitation energiesEin*

PE are taken from TableVII. We further assume, as in Eq.~9!, the angular momentumremoved by PE emission (D,) is proportional to,, the or-bital angular momentum of the collision. Thus an initial tangular distribution of, waves for fusionlike reactions mapto a triangular distributions ofJ. Figure 18 shows some examples of these distributions, the maximum spinsJcrit

PE aretaken from Table II. These distributions are subdivided intwo regions; the first is region~1! with J,JBF50 where con-ventional CN decay is considered to occur, and the seconregion ~2! whereJBF50,J,Jcrit

PE , which is associated withthe fast-fission process.

In region ~1!, a standard statistical decay of the CNmodeled. The partial decay width for light-particle evapotion is calculated with the Hauser-Feshbach formalism usstandard spherical transmission coefficients as in Ref.@44#.The fission decay width is calculated from the transitiostate formalism using the angular-momentum-dependentsion barriers from Sierk@12#. By treating fission purely statistically, it has generally been found difficult to explain thlarge experimental prescission multiplicities of light particlin CN decay @1#. Therefore in order to simulate largeprescission emissions, dynamics are often introduced intosimulations. This consists of either a fission delaytd

(1) , aninitial time period where evaporation is allowed but fissionhindered due to the entrance-channel dynamics and thtainment of a thermal distribution of CN shapes, and/orparticle evaporation during the transition from the sadpoint to the scission point. In these simulations we have csen to model only the first of these and obtaintd

(1) fromfitting the experimental data. However, the fitted valuestd

(1) may be interpreted as also including the saddlescission time. As a simplification in theGEMINI simulations,the fission decay width is set to zero up totd

(1) and thenpromptly assumes the transition-state value.

In region~2!, a full treatment of fast fission would requira dynamical model which considers the variation of tshape of the composite system from the amalgamation oprojectile and target nuclei to the subsequent separatiothe fission fragments. During these dynamics, one sho

03461

e--

ltn-

nelsine

eee-asn

re

o

is

-g

-s-

he

at-yeo-

f-

heofld

also allow for the evaporation of light particles. However, whave followed a simpler scheme which we believe captuthe most important aspects of fast fission, which relateprescission and postscission evaporation. The evaporafrom the composite system was treated as being from aformed system of constant deformation which is meantrepresent the mean shape of the system prior to scissBased on the dynamical codeHICOL @18#, this shape wastaken as prolate~with ratio of major to minor axes of 1.5!,rotating about an axis perpendicular to its symmetry axEvaporation was considered for a time period oftd

(2) , whichis meant to represent the duration of the fast-fission intetion. Deformation energies, rotational energies, and transmsion coefficients appropriate for the assumed deformawere used in the statistical-model simulations. For bothgion ~1! and ~2!, the excitation energy at scission is subdvided between the two fission fragments and the postscisevaporation is simulated using spherical transmission cocients.

As fast fission was not observed in theE/A58 MeV re-action data, the values oftd

(1) and the level-density parametersa0 and aF for the ground state and saddle-point cofigurations, respectively, were adjusted to reproduceprescission and postscission multiplicities ofn, p, anda par-ticles and the cross section ratiosER/sF ~Table I!. Thesefitted values of the level-density parameters area05A/9 MeV21 andaF /a051.05. These values were then asumed independent of excitation energy and used insimulations for the higher bombarding energies (E/A510,13, and 16 MeV!. The fitted value oftd

(1)54565 zs atE/A58 MeV, and its values at the higher bombarding engies were adjusted to fit the experimental cross-section rasER/sF . Note, that region~2! is also allowed to contributeto the sER . If after the timetd

(2) , the angular momentumremoved by the evaporated particles is such that the spithe system is now belowJBF50, then a CN is assumed to bformed and its statistical decay is followed. However, theis only a small yield of ER from such decays and it doeseffect sER significantly.

Oncetd(1) is adjusted, the fast-fission time periodtd

(2) isthen varied in order to fit the multiplicities of all the lighparticles at the higher bombarding energies. For both pression and postscission multiplicities, the simulated valuescalculated as a weighted average:

n i5n i

(1)~td(1)! s (1)1n i

(2)~td(2)! s (2)

s (1)1 s (2), ~10!

wheren i(1)(td

(1)) andn i(2)(td

(2)) are the simulated values fromregion ~1! and ~2!, respectively, each is a function of itcorresponding dynamical time ands (1) and s (2) are thecross sections associated with the two regions withsFU5s (1)1s (2) being taken from Table I.

Figures 19~a–c! compare the experimental and simulatmultiplicities of n, p, anda particles, respectively, as functions of E/A. A similar comparison is made for the crossection ratiossER/sF in Fig. 19~d!. Quite good reproduc-tions of all of the experimental multiplicities are obtaine

3-16

mumhe twoe value


�

��

��

�

�

� �

�

��

�

FIG. 18. ~Color! Examples of the, wave and the initial CN spin distributions used for the statistical-model simulations. The maxivalues,crit andJcrit

PE are from Tables I and II, respectively. The arrows indicate the angular momenta removed by PE emission. Tregions~1! and ~2! of the spin distributions, which are treated differently in the simulations, are indicated. They are separated at thJBF50 where the fission barrier is predicted to vanish in the calculations of Sierk@12#.

034613-17


α

α

α

FIG. 19. ~Color! For the 20Ne1159Tb reaction, a comparison, as a function of bombarding energy per nucleonE/A, of the experimentalprescission and postscission multiplicities with the simulated values for~a! neutrons,~b! protons, and~c! a particles. The comparison in~d!is for the cross-section ratiossER/sF . The broken curves are to guide the eye.

034613-18

vat

in

-

ar

rems-

iom

e

on

ie

stluapi

mtiob

adda

aleth-thee,ro-he21

ofc-

k-

ticver-hisisthe

itehei-

theweionthe

en


with the exception of the postscissiona particles where thesimulated values are much larger than the experimentalues. However, there are large systematic uncertainties inmeasured values~which are not included in the error barsthis figure! due to the difficulty in fitting the low-energyportions of thea-particle kinetic-energy spectra~Sec. III C!.Some of the predicted postscissiona particles may even account for some of the experimental scissiona particleswhich were inferred from the kinetic-energy spectra. Apfrom this difficulty with the postscissiona particles, all theother multiplicities and the cross section ratios are wellproduced by the adjustment of only the two dynamical tiscalestd

(1) and td(2) , giving us some confidence in the a

sumptions of the simulations.The evolutions of the extracted values oftd

(1) and td(2)

with bombarding energy are shown in Fig. 20. The fissdelay td

(1) associated with CN fission decreases with bobarding energy from;45 zs to approximately 1565 for thetwo highest bombarding energies. The value oftd

(1);45 zsfor the lowest two bombarding energies agrees quite wwith the systematics of Hindeet al. ~Fig. 3 in Ref.@22#! for16O induced fusion-fission reactions. The agreement is mremarkable because these systematics were based oanalysis of neutron multiplicities only, whiletd

(1) , in thiswork, is determined by fittingsER/sF andn, p, a multiplici-ties. The amount of fast fission is quite small atE/A510 MeV, and thus we should concentrate on thetd

(2) val-ues extracted from the two highest bombarding energThey are also approximately 15 zs, almost equal to thetd

(1)

values. The similarity of the two dynamical times suggethat they may have similar origins. For example, the evotion from a compact composite system to a dinuclear shmay be quite similar for conventional and fast fission, simlarly the initial entrance-channel dynamics may also be silar. On the other hand, the time scale for shape equilibrais not a consideration for fast fission, and thus it maysmall fraction of the total dynamical time for theE/A513and 16 MeV reactions. The larger values oftd

(1) for the lowertwo bombarding energies might therefore correspond toincreased importance of the shape equilibrium time or apendence of the dissipation of temperature. Clearly moretailed simulations of the dynamics are required to investigthese ideas further.

50

E/A (MeV)

0

10

20

30

40

7 9 11 13 15 17

d(1)

d(2)

d(zs)

τ

τ

τ

FIG. 20. Evolution of the dynamical timestd(1) and td

(2) ex-tracted from the statistical-model simulations with bombardingergy per nucleonE/A for the 20Ne1159Tb reaction~see text fordetails!.

03461

l-he

t

-e

n-

ll

rean

s.

s-e

-i-ne

ne-e-te

E. Fission time scales

In the case of fast fission, the fission or scission time scis justtd

(2) . However, for CN fission, one must consider bothe dynamical timetd

(1) and the statistical time. In the simulations, a time is obtained for each decay step based ontime for the previous steps including the dynamical timplus a time chosen from an exponential distribution apppriate for the calculated total decay width. An example of tsimulated distribution of scission times is plotted in Fig.for the E/A58 MeV 20Ne1159Tb reaction. The scissiontime distribution has a long tail extending over five ordersmagnitude. It is the tails of distributions like these that acount for the long fission times reported in ‘‘crystal blocing’’ @2,3# andK x-ray measurements@4#. Given such a widedistribution of times, there are a number of characteristimes that can be associated with the distribution. The aage time is very difficult to determine as it requires that ttail to high times should be known quite well. However, itorders of magnitude larger than the dynamical time. Onother hand, the median time or half lifetimetF

1/2, the time bywhich half of the scissions have already occurred, is quwell defined and much more similar in magnitude to tdynamical time. The variation of this time with initial exctation energyEin*

PE is plotted in Fig. 22. This time, like thedynamical time, decreases from 115 zs to 40 zs overrange of excitation energies studied. As a conclusionstress that there are major difficulties in comparing fisstime scales obtained from the different techniques due to

-

F

dSim

ulations

log(t (s))F

0

20

40

60

80

100

-21 -20 -19 -18 -17 -16 -15 -14


region (1)τ

τ1

2

FIG. 21. Distribution of scission timestF predicted byGEMINI

simulation for CN fission in theE/A58 MeV 20Ne1159Tb reac-tion. The dynamical timetd

(1) and the median scission timetF1/2 are

indicated.

FIG. 22. Variation of the simulated median scission timetF1/2

with the initial excitation energiesEin*PE ~see text for details!.

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ambiguity in defining a single time to represent a very wdistribution. However, by combining the different tecniques, the overall shape of the distribution should becobetter defined.

V. CONCLUSION

The properties of fission events have been extensivstudied in the20Ne1159Tb and 169Tm reactions at beam energies ofE/A58, 10, 13, 16 MeV. Measurements of evapration residues, fission fragments, and the properties ofaccompanying light particles have been made. Frevaporation-residue velocity distributions and fissiofragment folding angles, the compound-nucleus velociwere found to be less than the complete-fusion values athighest bombarding energies. This implies the emissionpreequilibrium particles, the magnitude of which was esmated from published systematics in a very self-consisway. The deduced excitation energies of the compoundtems ranged from about 100 to 210 MeV. From the measuresidue and fission cross sections, the maximum, wavesassociated with fusionlike events were determined and, aremoving reasonable estimates for the angular momenloss by preequilibrium emission, the maximum spins ofcomposite systems were also estimated. For the highest bbarding energies, these spin values are greater than thegular momenta in the calculations of Sierk@12# where thefission barrier vanishes, thus implying a significant contribtion of fast fission to the fission yield.

The measured kinetic-energy spectra and angular distrtions of neutrons, protons, anda particles were fitted to extract the prescission and postscission multiplicities and cresponding effective nuclear temperatures. Using thextracted values and the measured total kinetic-energylease in fission, the excitation energies and masses ofinitial compound systems were reconstructed by massenergy balance and found to be consistent with the estimfrom preequilibrium systematics. There is very little depedence of prescission and postscission emissions on tamass. However, this is not the case for the evaporatresidue cross sections. The small cross section for the hetarget shows the influence of the smallerJ50 fission barrierfor the heavier CN. However, the fission yield is expectedoriginate only from systems at high angular momenta, wh

ae

te

03461

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r-see-hendes-et

n-ier

ore

the fission barrier is smaller. Thus fission selects out systwith low fission barriers for both targets, and thus the proerties of the fragments should be similar.

The excitation energy of the fissioning system at scisswas found to increase with initial excitation energy, suggeing that the time scale for scission is decreasing. Statistimodel simulations incorporating dynamics in a simplisfashion were performed to investigate the dependence ofscission time scale with initial excitation energy. Statisticfission and fast fission were treated separately and the inence of dynamics on each was considered by introducinfission-delay time and fast-fission time scale, respectivThese time scales and the level-density parameters werejusted to fit the cross section and prescission and postscismultiplicity data. The level-density parametersa0 and aFwere constrained only by the data at the lowest bombardenergy where there was no fast-fission component. Suquently, the data at the higher bombarding energies weach fitted by adjusting just the two dynamical time scalFor E/A513 and 16 MeV, these extracted dynamical timscales for both statistical fission and fast fission were sim;1565 zs, suggesting a common origin. The dynamic timfor statistical fission was found to be larger at the lowenergies, with the value of 4565 zs at the lowest excitationenergy of;100 MeV. The total time scale for conventionCN fission can be much larger than the dynamical times,simulated distribution of scission times extends over maorders of magnitude. However, the median time, the timewhich half of the scission events have occurred, is of orsimilar to the dynamical times and was found to decrefrom 115 zs to 40 zs over the range of excitation energstudied.

ACKNOWLEDGMENTS

The authors are indebted to the crew of Louvain-la-NeuCyclotron for the excellent and efficient running of the mchine. We also thank P. Demaret for his important contribtions to the target preparation. We wish to thank Dr. H. Femeier for making his code HICOL available to us. Someus ~R.C., J.N., and D.H.! would like to acknowledge theUniversity of Louvain for its hospitality during their multiplestays in Belgium.

J.

.A.

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Fusion-ﬁssion and fusion-evaporation processes in Ne Tb and Ne … · 2014. 10. 17. · Fusion-ﬁssion and fusion-evaporation processes in20Ne¿159Tb and 20Ne¿169Tm interactions