Neutron spectra as a function of spin and the neutron multiplicity distribution have been measured for the reaction 233-MeV Ni64 + Zr92. The emission of two neutrons constitutes the strongest decay channel, in contrast to statistical-model calculations which predict the emission of three neutrons to be the strongest by more than one order of magnitude. This is possibly due to trapping in a superdeformed potential well, similar to that giving rise to fission isomers, as the compound nucleus relaxes from the highly distorted initial shape

Chowdhurj, P.

Haas, F.

Janssens, R.V.F.

Kasagi, J.

Khoo, T.L.

Kuhn, W.

Ronningen, R.M.

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Suppression of neutron emission after heavy-ion fusion: is shape relaxation affected by a superdeformed minimum ?

Kuehn, W.

Chowdhury, P.

Carolina Digital Repository

VOLUME 5 1, N UMBER 20 PHYSICAL REVIEW LETTERS 14 NOVEMBER 1985Suppression of Neutron Emission after Heavy-Ion Fusion: Is Shape Relaxation Affectedby a Superdeformed Minimum?W. Kuhn, "' P. Chowdhury, ' ' R. V. F. Janssens, and T. L. KhooArgonne National Laboratory, Argonne, Illinois 60439F. Haas, "' J. Kasagi, ' ' and B. M. BonningenNational Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824(Received 26 April 1983)Neutron spectra as a function of spin and the neutron multiplicity distributionhave been measured for the reaction 233-MeV 4Ni+ Zr. The emission of twoneutrons constitutes the strongest decay channel, in contrast to statistical-modelcalculations which predict the emission of three neutrons to be the strongest bymore than one order of magnitude. This is possibly due to trapping in a super-deformed potential well, similar to that giving rise to fission isomers, as thecompound nucleus relaxes from the highly distorted initial shape.PACS numbers: 25.70.Jj, 21.10.MaAn important facet of heavy-ion physics is thedynamics of ion-ion collisions. However, it isnot yet clear how collision properties and nuclear-structure aspects govern the division of the totalreaction cross section into the partial cross sec-tions for complete fusion, incomplete fusion,fast-fission, deep-inelastic, and quasielastic re-actions. To solve this problem it is importantfirst to understand the dynamics of complete fu™sion at low incident energies without the complica-tions introduced by the presence of other strong-ly competing reaction channels. In the initialstage of fusion, at the moment of contact betweenthe interacting ions, the composite system ishighly deformed. The relaxation of such a highlydistorted shape towards the ground-state defor-mation represents an interesting case study innuclear dynamics. Moreover, it may present anopportunity for exploring the structure of nucleiwith high spin and temperature, perhaps at high-er temperature than can be probed with conven-tional continuum y spectroscopy. Several ques-tions may be raised concerning, for example, therelaxation time for attaining the equilibriumshape, the nature of this equilibrium shape athigh excitation energy, the influence of shellstructure on the shape and relaxation time, andthe temperature at which shell effects diminish.A suitable compound system for study is onewhere the yrast line is known up to high spin andwhere there exists an appropriate entrance chan-nel for bringing in sufficient angular momentumat moderate excitation energies. These condi-tions can be met in the rare-earth region. Hereneutron evaporation is the predominant decaycha.nnel. Thus, neutron spectra and multiplicitydistributions may prove useful for probing theearly stages of the compound-nucleus deexcita-tion process, particularly when measured as afunction of spin to select specific impact param-eters.In this Letter, we present the results fromstudying the system ' ¹i+"Zr with a 238-MeV-Ni beam from the Argonne superconducting linac.The effective beam energy is 233 MeV, which isa weighted average with the weight given by anestimated fusion cross section at each of the en-ergies encountered within the 1-mg-cm ' target.At this effective energy the compound nucleus'"Er is formed at 46 MeV excitation energy andl „=37h (calculated with the Bass model' ). Wehave measured neutron and gamma spectra incoincidence with the total gamma-ray energy.The neutrons were detected at 0' with a 12.5 x5cm NE213 liquid scintillator located 71 cm fromthe target and the neutron energy was determinedby the time of flight with respect to the beammicrostructure. Gamma spectra were measuredwith a Ge(Li) detector and 25&30 cm NaI detec-tors (with 10-cm-diam central collimators) posi-tioned at 75 cm from the target at angles of 0and 90 . Singles spectra were also recorded withthe Ge detector. The sum energy was measuredin a NaI spectrometer described by Khoo. 'The y multiplicity as a function of sum energywas determined from the ratio of sum-energyspectra corresponding to threefold (sum-neutron-NaI) and twofold (sum-neutron) coincidences.The entry spin was determined by taking into ac-count the average spin removed by a prompt yQc 1983 The American Physical SocietyVOLUME 51, NUMBER 20 PHYSICAL REVIEW LETTERS 14 NOVEMBER 1983ray (1.215, determined from y yields at 0' and90') and corrections for feeding of isomers. Forevents populating an isomer of spin I;, one ob-tains I= 1.21(M» -4 -M;, )/1.06+I;,. The multi-plicity M„, measured at 90, is reduced by 4 toaccount for the typical number' of statisticaltransitions (which remove no angular momentum)and by M;„ the gamma multiplicity in the isomerdecay. The factor 1.06 represents a correctionfor angular distribution effects. As a result, weobtain neutron spectra for different sum-energyslices corresponding to different entry line spins.The neutron spectra have been corrected for theefficiency response of the neutron detector4 andhave been transformed into the center-of-masssystem. Measurements with an iron bar shadow-ing the neutron detector showed that neutronswhich are first scattered before impinging on thedetector constitute less than 15%%d of the total yield,are concentrated at low energy, and so have nosignificant contribution for energies above 2 MeV.Figure l(a) shows the neutron spectra for differ-ent sum-energy slices. The "temperatures, "IO~:. ';5lo p=.i,.4.r~IO=—'O3''o IO .-—',=~,LLjO~ IOLOW-I I-IOi & xIi i lERGY (a)4 6 8C.M. —ENERGY (MeV)10I[I I I I [ II I I[I I I I(b):cL 20—LLI10 20 50 40SPIN (h)FIG. 1. (a) Neutron spectra, measured at 0', forsix consecutive gamma-ray sum-energy slices. Thestraight lines represent fits with an exponential functionin the energy interval spanned by the lines. Deviationsfrom the exponential shape at high sum energy are dueto contamination from isomeric gamma rays. (b) "Tem-peratures, " derived from the fits in (a), as a functionof mean entry line spin corresponding to the differentsum slices. The solid line represents results fromsimilar fits to neutron spectra obtained in cARcADEcalculations, using the elevated (dashed) yrast line inFig. 3 and a level-density parameter & =&/16 (see text).IOO—50C)LdLLJ0 IO5LLIRI IIIII Il [I II II II I I2NEUTRON MULTIPLICITYFIG. 2. Comparison of experimental (circles) neutronmultiplicity distribution with those from statistical-model calculations using the normal (solid bars) andelevated (dashed bars) yrast lines of Fig. 3.obtained from fits to the exponential tails of thespectra, are shown in Fig. 1(b) as a function ofthe corresponding spine. (N.B. the temperaturederived in this manner is characteristic of ameasured spectrum and should not be equatedwith a nuclear temperature. ) The spectra exhibitfalling temperatures with rising spin. This isexpected qualitatively because the energy above'the yrast line is smaller at high spin. Similarresults have been obtained by Cabot et al. ' in thereaction "Cu +"Rb.Figure 2 shows the neutron multiplicity dis-tribution which was deduced from the yields of'" ")Er observed in the Ge spectra. Here x isthe number of neutrons emitted from the com-pound nucleus. The solid bars indicate predic-tions of the statistical-model code CASCADE;6The code has been modified to include enhance-ment of collective E2 transitions parallel to theyrast line' and EI deexcitation through the giantdipole resonance" (GDR). The E1 strength wasgiven by the energy-weighted sum rule, ' whichyielded agreement for I&observed in neutroncapture' and yielded a "GDR bump" in the yspectrum of similar strength to that observed'in ("Ar, xn) reactions. The yrast lines for even-A nuclei in our calculation follow that in '"Er,where states up to spin 36 are known'; in odd-A.nuclei the yrast line is 1 MeV lower at equivalentspin values larger than 105. It is obvious fromFig. 2 that the statistical model underestimatesthe ratio B of 2e to 3n emission by a factor of 20.In contrast, in the case of "0-induced reactionsleading to heavier Er compound nuclei, the mod-el predicts neutron multiplicity distributions inVOLUME 51, NUMBER 20 PHYSICAL REVIEW LETTERS 14 NovEMBER 1983excellent agreement with experiment. " In thefollowing we discuss possible reasons for thefailure of the model for "Ni-induced reactions.At the low beam energy used here (close to theCoulomb barrier) incomplete-fusion reactions orpreequilibrium processes should not contributeto the formation of the Er isotopes. This is con-firmed by the lack of any significant high-energytail in the neutron spectra. As a consequence,the failure of the statistical-model calculationmay be attributed to an inadequate choice of therelevant parameters. In an attempt to reproduceA we have performed calculations with enhancedE1 strengths and have found that it is necessaryto increase the strength -200 times over thatgiven by the energy-weighted sum rule. ' Besidesbeing unreasonable, such an enhancement leadsto a high-energy tail in the gamma spectrum wellin excess of that which is observed experimental-ly. ' We have also performed calculations withlevel-density parameters a between A/6 a,nd A/16, which is the range usually given in the litera-ture. (A more detailed discussion on the leveldensities used in the calculation is given by Pul-hofer. ') R was found to be rather insensitive tovariations in a. In contrast, the neutron tempera-tures do depend sensitively on the choice of aand can be reproduced with a =A/12; however,R is too low by a factor of 20 (Fig. 2). Calcula-tions with larger f values, l „=lg, =41K (Wilkeet al. ") and l „=478, underestimate R by factors10 and 6, respectively. (The latter f „value isalready larger than indicated by the experimentalspin distribution. ) Even combining the increasedl~„of 415 with an enhancement of the GDRE1strength by a factor of 10 still underestimates Rby a factor of 7.Thus, we conclude that any change of param-eters within reasonable limits is not able to re-produce consistently the neutron multiplicity dis-tribution and the shape of the neutron spectra atthe same time. The suppression of the third neu-tron suggests that the available free energy forneutron emission, i.e., the energy above thecompound-nucleus yrast line, is smaller thanexpected by roughly half of a neutron binding en-ergy. This is borne out by the measured aver-age y sum energy (16 MeV), which exceeds by 5MeV the value expected from the calculated rieu-tron multiplicity distribution and is consistentwith that expected from the measured distribu-tion. Experimental indications for large deforma-tions have been reported" in the Pd region, whileseveral calculations"'" have suggested that inI I I lI~ I 1 III I I III ~ I IIIv 00—0-cL. 30—LLJLLJ 20—Z0~ 10—oX0 IO 20 30 40sPI N (5)FIG. 3. Angular momentum distribution (top) andyrast lines used in cAscADE calculations. The yrastlines shown are for even-g nuclei; the solid one issimilar to that of '~4Er (Bef. 9), while the dashed oneapproximately follows the superdeformed minima cal-culated for Er by Aberg (Bef. 13) for I & 10. Theyrast excitation energies of odd-A isotopes are 1 MeVlower than those of even-4 isotopes for I & 10. Thethick horizontal bar indicates the initial compound-nucleus energy and the arrows illustrate the averageenergy and angular momenta removed by neutron emis-sion, demonstrating that there is easily sufficient ex-citation energy to emit three neutrons.the Er nuclei of interest there exists at high spina superdeformed well with e-0.6, which arisesfrom shell effects and which is related to thosewhich give rise to fission isomers. The existenceof a barrier between the domains of normal andsuperdeformed shapes may affect the shape re-laxation of the initially highly distorted compoundnucleus, possibly leading to trapping in the super-deformed minimum for an interval comparableto typical neutron emission times (10 "-10 "s).The available energy for neutron decay is thenmeasured with respect to this minimum and iscorrespondingly decreased from its nominal val-ue, In this event neutron emission will be sup-pressed, with the excitation energy being re-moved by y emission instead. To test this con-jecture we have performed a calculation employ-ing an elevated yrast line (dashed in Fig. 3) whichwas constructed to roughly follow (for I&10) thesuperdeformed minima in '"Er calculated byAberg. " Good agreement for both R (Fig. 2) andneutron temperatures (Fig. 1) was obtained. Toreproduce the neutron temperatures a value of a=A/16 was found necessary, a value similar tothat used" to account for y multiplicities observedin ('He, n) reactions.In all calculations the yield for one-neutronVOLUME 51, NUMBER 20 PHYSICAL REVIEW LETTERS 14 NOVEMBER 198)emission was significantly smaller than observed.On the other hand, the cross section for emis-sion of four neutrons can be reproduced if betteraccount is taken of the energy spread in the tar-get than through the use of an effective beam en-ergy. With the normal yrast line (Fig. 3) the sumof the partial cross sections in each of five slicesof the target gives 1-4 neutron yields of 0, 5g90% and 5 /p, With the elevated (dashed) yrastline of Fig. 3 a decrease in the four-neutronemission cross section would result; however,this yrast line is inappropriate for describingthis cross section since it originates primarilyfrom lower l values, for which the superdeformedminimum barely exists. "To summarize, we have measured neutron spec-tra for '"Er compound nuclei as a function ofangular momentum and have determined the neu-tron multiplicity distribution. The neutron tem-peratures provide sensitive information on leveldensities, and together with other available data(on the yrast line' and y-decay strength') providetight constraints on the parameters used in statis-tical-model calculations. Such calculations areunable to reproduce the measured neutron multi-plicity distribution unless an yrast line elevatedwith respect to the known one is employed. Thisraises the possibility of superdeformed shapes athigh spin and energy occurring for a time inter-val comparable to typical neutron emission times("deformation traps"). This suggestion is clearlyspeculative at this point, but it can be subject tomany further experimental tests. Since the ini-tial deformation of the fusing system may bevaried by choosing different entrance channels,the neutron multiplicity distribution for a givenspin interval should depend on the mass asym-metry of the entrance channel, in contrast to theBohr independence hypothesis. Another conse-quence of the existence of deformation traps maybe a strong enhancement of fusion-fission. Inaddition, both the entry line (locus of maximumpopulation in an E vs I plot prior to y decay) andthe y-decay spectrum should reflect an excessenergy release through y emission over the morenormal case. Finally, we hope to stimulate theo-retical calculations on the shape relaxation timeof the compound nucleus, particularly in thepresence of a superdeformed well.We thank the Argonne tandem linac crew forexcellent support and Professor F. Puhlhofer forproviding us with a copy of his program CASCADE.This research was supported by the U. S. Depart-ment of Energy under Contract No. W-31-109-Eng-38 and in part by the U. S. National ScienceFoundation through Grant No. PHY80-17605.~ &Present address: II. Physikalisches Institut, Uni-versitÃt Giessen, West Germany.~"&Present address: Niels-Bohr Institute, Copenhagen,Denmark.(~&Permanent address: Centre de Recherche NucleaireStrasbourg, France.&d&Present address: Tokyo Institute of Technology,Tokyo, Japan.'R. Bass, Nucl. Phys. A231, 45 (1974).T. L. Khoo et al. , Phys. Scr. 24, 283 (1981).R. M. Diamond and F, S. Stephens, in Annual Reviewof Nuclear and I'article Science, Vol. 30, edited byJ. D. Jackson, H. E. Gove, and R. F. Schwitters (Annu-al Reviews, Palo Alto, 1980).4L. Kurz, Lawrence Berkeley Laboratory Report No.UCRL-11359, 1965 (unpublished) .C. Cabot etal. , to be published.F. Puhlhofer, Nucl. Phys. A280, 267 (1977).YJ. O. Newton et al. , Phys. Rev. Lett. 46, 1383 (1981).8J. E. Lynn, Theory of Neutron Resonance Reactions(Clarendon, Oxford, 1968), pp. 315 and 322.C. Baktash etal. , Phys. Rev. Lett. 42, 637 (1979).R. Broda etal. , Nucl. Phys. A248, 356 (1975)."W. Wilke etal. , At. Data Nucl. Data Tables 25, 389(1980).' F. Folkmann etal. , Nucl. Phys. A361, 242 (1981).S. Aberg, Phys. Scr. 25, 23 (1982), and privatecommunication.J. Dudek etal. , Phys. Lett. 1128, 1 (1982).J. Rekstad etal. , Phys. I ett. 1178, 384 (1982).1861

Suppression of neutron emission after heavy-ion fusion: Is shape relaxation affected by a superdeformed minimum?

Suppression of neutron emission after heavy-ion fusion: is shape relaxation affected by a superdeformed minimum ?

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