PHYSICAL REVIEW C VOLUME 30, NUMBER 4 OCTOBER 1984

Mass and kinetic energy distribUtions in near-barrier fission of '82W

B.D. Wilkins, B.B.Back, J. E. Gindler, and B.G. Glagola*Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439

K. Kwiatkowski, S. H. Zhou, t and V. E. Viola, Jr.Department of Chemistry and Cyclotron Facility, Indiana University, Bloomington, Indiana 47405

(Received 23 April 1984)

Mass and kinetic energy distributions have been measured for the fission of "W at an excitation

energy above the fission barrier E —Ef=20 MeV. A primary motivation for these studies was tosearch for evidence of asymmetric mass division and anomalously low total kinetic energy release, as

predicted by scission-point model calculations which include deformed (Strutinsky) shell effects.Double kinetic energy measurements of coincident fission fragments were performed, from which

fragment mass distributions were derived. From the data it is concluded that at this excitation ener-

gy, liquid-drop behavior dominates the fission of ' W and any shell strength, if present, is less than

20 percent of full strength.

I. INTRODUCTION

Studies of nuclear fission at low excitation energieshave demonstrated the important role of shell effects indetermining fragment mass and kinetic energy distribu-tions. It has been known that mass distributions at near-barrier energies exhibit a continuous transition from dou-ble huinped for the fission of actinide nuclei to triplehumped for radiumlike nuclei to a single symmetric peakin the lead region. ' This behavior had been qualitativelyexplained in terms of the liquid-drop model, modified byspherical shell effects; i.e., the energy stabilization pro-vided by the N=82, Z=50 shell closures favors an asym-metric mass division for nuclei in the uranium region.

Subsequent models ' have attempted to account for thecharacteristics of the fission process more quantitativelyby the inclusion of deformed shell effects. The scission-point model, a static model which assumes statisticalequilibration among the collective degrees of freedom atthe scission point, has been successful in explaining manyof the observed fission phenomena. In this model the to-tal potential energy of the system at the scission point iscalculated as the sum of liquid-drop, shell, and pairingterms with Coulomb and nuclear potential terms describ-ing the interaction between the fragments. A key featureof this inodel is the inclusion of deformed shell effects inthe fragment potential-energy surface, following the Stru-tinsky prescription. This model has proven successful inproviding a much more comprehensive description of fis-sion mass and kinetic energy distributions and the depen-dence of these upon excitation energy. Particularly im-portant in these calculations is the influence of fragmentdeformation in determining the fragment kinetic energydistributions. An important early prediction of thismodel'was that the neutron-excess isotopes of fermium(Z=100) would exhibit symmetric mass division and ananomalously high total kinetic energy release due to theinfluence of closed spherical shells at Z=50 and N=82.

This behavior is observed in the spontaneous fission of258Fm and 259F 8, 9

The scission-point model of Ref. 6 also predicts the ex-istence of mass regions below 2 =200, where asymmetricmass division may be competitive with symmetric fission,which is predicted by the liquid-drop model. One such re-gion occurs in the vicinity of the nuclide 74 Wips For de-formations near P=0.55 strong minima in the potential-energy surface are calculated for N=64 and 44 and forZ=44 and 30. These minima present a very favorable sit-uation for asymmetric fission, for the complementaryfragments would have both N and Z shells at the samedeformation and N-to Zratios whi-ch are nearly the sameas the ratio in the fissioning nucleus, 1.46. Thus, on thebasis of the scission-point model, the fission of ' W withzero excitation energy is predicted to form a mass split ofAtt ——108 ( ZH ——44, NH ——64) and AL,

——74 ( ZL,——30,

NI. ——44) with a P deformation of -0.55 for both frag-ments. Because the total deformation (PL +PH -1.10) forthis mass split is larger than that predicted on the basis ofthe liquid-drop model, the total kinetic energy for thissplit is expected to be anomalously low.

A second asymmetric fission configuration is possiblefor ' W in which there are strong N and Z shell effectsat the same P deformation and the N-to-Z ratio in thetwo fragments is nearly the same as that of the fissioningnucleus. This configuration of AIt ——98 ( ZH ——40,Nlt 58, pH =0.4) and ——AL, =84 (ZL, ——34, Nl ——50,PL,

——0.1) would be expected to have a relatively high totalkinetic energy release, as the total deformation of thisconfiguration is much less than that expected fromliquid-drop forces. Therefore, observation of mass asym-metry and structure in the total kinetic energy release as afunction of fragment mass for the fission of nuclides inthe region of ' W would serve to further reinforce thepredictive power of the scission-point model. However, inorder to detect these effects, experiments must be per-formed at sufficiently low excitation energy for the shelleffects to be competitive with symmetric fission, which is

30 1228 1984 The American Physical Society

30

favored on the basis of liquid-drop forces. To date nosuch experiments have been performed because of the verylow cross sections in the near-barrier region for nucleiwell below the lead region.

In these studies the reaction

He+ ' Hf—+' W*—+fission

was studied with 49.2-MeV ~HC ions from the IndianaUniversity Cyclotron Facility (IUCF). Beam intensitieswere typically 200—400 nA. For the formation of ' W,Q= —1.7 MeV and the liquid-drop fission barrier' for

W at 1=0 is 26.3 MCV. Thus, the excitation energy ofthe fissioning nuclei prepared in this system isE —Ef &20 MCV, depending on angular momentum.Fission of nuclei with A &210 in this energy region isknown to be dominated by complete fusion processes, "and must be primarily first-chance fission because of thevery strong dependence of the fission cross section on ex-citation energy in the barrier region. The bombarding en-ergy of 49 MeV was chosen as a compromise between thedemands of low excitation energy in order to preserve sig-nificant shell strength in the fissioning nucleus and thoseimposed by cross section, measured' to be about 2 pb forthis system at 49 MCV.

An isotopically separated ' Hf target of thickness100 pg/cm was prepared 111 R11 Iso'tope scpalatol' 011 R

60-pg/cm carbon foil. Although actinide contaminationwas only about one part in 10, this was sufficient toIllakc R Iiotlccablc contribution to thc observed flssiollspectrum. Actillldc flssloII was paItlally cllmlnatlxl bymeans of procedures described in the following section.Fission coincidence events were detected with three pairsof silicon surface-barrier semiconductor detectors, each ofarea 400 mm and a nominal depletion depth =100 pm,placed lnsldc thc I62-clTl-d1am scat ter1ng chamber RtIUCF. Each dctcctol pa1r w'as mounted 1n R coplsnarconfiguration which included the beam axis and targetccntcI'. VAthin th1s plRnc thc angle bctwccn eacI1 dctcctoI'pair, 8&II, was defined by the constraints of completefusion kinematics leading to symmetric binary fission, i.e.,H~z ——170'. The three coincidence planes thus definedwcI'c arranged so that thc sz1IDUthsl Rnglc 4 between cach-plsnc wRs 4=0 RIld +30 with 1cspcct to thc horizontalplane of the scattering chamber. One detector of eachpair was placed 7.5 cm from the target and the otherdetector at 10.2 crn. This arrangement was a compromiseto provide a reasonably large solid angle, to ensure thatthe fragments which were counted in the more distantdetector would have thc1I' complcIQcnts coUntcd 1n thccloser detector (detector efficiency), and to give measur-able timing differences in the flight paths. The latter wereused in analyzing the data as described below.

Fragment energies were determined from coincidentevents, with fast-timing coincidence circuitry based onfast-timing pickoffs of the Sherman-Roddick-Metzdesign. Detectors were calibrated with a Cf sourceusing the calibration scheme of Kaufman et a/. ' Frag-

ment energy resolution was approximately +2 MCV.Masses were then determined according to the double-energy technique assuming (1) complete fusion kinemat-ics, (2) binary fission of "W only, and (3) neutron emis-sion from the fragments as calculated from the availableexcitation energy and (E„)=2T, where T ="t/E'/awith a =A/8 MeV '. Folding in the uncertainties infragment energies, kinematics (due to the large solid an-gles), and neutron evaporation energetics, we estimate a fi-nal mass resolution of +4 u. This resolution was con-sidered sufficiently accurate to distinguish between a sym-metric mass split and one with AII/Az ——108/74. Crudemasses were also calculated by means of the fast-timinginformation obtained in these measurements. Thesemasses were compared with those calculated from energymeasurements. Events which gave inconsistent resultswere discarded.

Approximately 2100 valid coincidence events were ob-served during the course of these experiments. Of these,about 12% were attributed to actinide fission. Of theremaining 1850 events, it was estimated that less than 3%of these could be due to heavy-element fission.

III. RESULTS

In Fig. 1 a two-dimensional contour plot of the center-of-mass El vs E2 distribution is shown for all valid coin-cidence events observed in these experiments. The contri-bution of higll-clicl'gy Rctlllldc flssioil fo thc total dlstrlbll-tion is apparent in the portion of the data with large Eland Ez values. In order to eliminate these spuriousevents, a window was set on the data (dashed hne in Fig.1) for which it was assumed that

, Zl Z~8'EE= i/3 I/3 =kALAH .

ro(AJ +ALII )

I'

I

l t 1 I l I 1 i

l2 56 60 84 l08Ez (MRV)

FIG. 1. Contour plot of center-of-mass, preneutron evapora-tion fragment kinetic energies, Ei vs E2, for the fission of ' %V.

Each solid line represents a contour representing a factor of' 2 inrelative cross section. The dashed line represents the ~indo~defined by Eq, (1) (see the text), above which all events wereeliminated from the data analysis.

1230 B. D. WII.KINS et al. 30

200—

(AI—& 20O

IO

9l 95 99 l03 l07 III

A„

I

II5

FIG. 2. Relative mass yield curve for fission of ' W atE Ef 20 MeV. Solid line is a Gaussian function fit to thesymmetric and far asymmetric regions of the distribution.

For symmetric fission E~ was taken to be 150 MeV andEq. (1) was solved for k. This value of k was then used todetermine the window shown in Fig. 1 for all fissionevents. Events with values in excess of this window( —12%) were eliminated from the data set in subsequentanalysis. It is estiinated that the remaining fission coin-cidences contain about a 3% contamination due to ac-tinide fission. This value was obtained by assuming

U( He,f) to be the contaminant and estimating fromEx(&) and oz (A) the percentage of fission events that

fall below the dashed line of Fig. 1. A similar percentageof valid coincidences from ' W fission is probably elim-inated by this method. All additional data (Figs. 2—5) in-clude only events which have passed the above-mentionedsoftware window.

In Fig. 2 the mass distribution determined for ' W fis-sion, corrected for neutron emission, is shown. Error barsinclude only statistics. The solid line in Fig. 2 representsa Gaussian function that has been constrained to fit thesymmetric and far-asymmetric regions of the mass distri-bution in order to accentuate any possible shoulder in the2 = 100—108 region of the curve. Although a weak devi-ation in the mass yield curve above the Gaussian fit is ob-served in this region, the evidence for a definitive massasymmetry effect is not compelling. From these data thestandard deviation of the mass distribution is determinedto be o.=9.0 u.

The experimental total kinetic energy release Ez andvariances in Ex are shown in Figs. 3(a) and (b), respective-ly, as a function of heavy fragment mass, AH. Fromthese data a most probable Ex value of (Ex) =128.6MeV is obtained with an estimated error of +2 MeV.This value is in good agreement with (Ex ) =125.6 MeV,based on systematics. ' The standard deviation for the

I

its —(&)

EK

(MeV}l24—

(b)

IG—

iiK

il

I l I ( I & I } I } I

93 97 IOI 105 IO9 I I3

A„

FIG. 3. Total kinetic energy release (a) and standard devia-tion in E& (b) as a function of heavy fragment mass, A~, forfission of" W.

Ex distribution is 9.4 MeV. The dashed curve in Fig. 3(a)is the liquid-drop expectation for the dependence of Exon fragment mass, as given by the scission-point model ofRef. 6 with all shell strengths set equal to zero. The necklength d in the calculations [Eq. (1}]has been adjusted tofit the Ex systematics of Ref. 15. The most probable to-tal kinetic energy release from the model is then obtainedby taking the calculated Ez at each mass split andweighting it with the experimental mass yield. In the re-gion A~ —102—108 [Fig. 3(a)) the value of Ex deviatesslightly above the Ex curve. Again, the effect is not dis-tinct, and furthermore, it should be noted that deviationsabove liquid-drop behavior indicate enhanced sphericityfor the fragments, rather than more deformed shapes.Hence, if the observed weak deviation is real, it would im-ply that the neutron shell at N=50 (P=0.1) and atN=58 (P=0.4) is responsible. However, it should beremembered that a few percent of the "valid" events maybe the result of actinide fission. Assuming that the ac-tinide contaminant is U, the most probable masssplits' for the reaction U+ He are AH ——138—142and AL ——104—100. If these most probable actinide fis-sion events are assumed incorrectly to be ' W fissionevents, the mass splits calculated will be AH ——104—107and AL ——78—75, just where the deviations appear in Fig.3. It is therefore possible that the observed deviations arecaused by spurious actinide fission events that have notbeen completely eliminated in analysis.

30 MASS AND KINETIC ENERGY DISTRIBUTIONS IN NEAR-. . . 123i

Figures 4 and 5 show the predictions of the scission-point model for fission of ' W for the relative mass yieldand Ez distributions for various shell strengths, using thesame assumptions concerning the neck length d and(Ex ) from systematics, ' as above. The data are best fitby the liquid-drop calculation (shell strength=0. 0) andcannot tolerate any shell strength greater than 0.2. On thebasis of this analysis we conclude that liquid-dropbehavior dominates the fission of ' ~W at this excitationenergy and that any shell strength, if present, is &20%full strength.

The fact that no definitive evidence for shell effects isobserved in the fission of ' W at E Ef —20 MeV mustbe examined in the context of evidence for shell effects inthe fission of thorium or uranium. at 20—30 MeV abovethe fission barrier. ' The mass distributions for theselatter fissioning systems are slightly asymmetric in char-acter, which is accounted for in the scission-point modelas due to the effect of shells. In fact, it was because ofthese distributions that the present experiment with ' Wwas attempted. There are, however, at least two majordifferences between the fission of a lower-Z nucleus, suchas 's~W, and a uranium or plutonium (Th+ He orU+ He) nucleus excited to 20 MeV above Ef. The ex-cited lower-Z nucleus has essentially only one chance tofission. That is, it either fissions or emits a neutron, afterwhich the excitation energy is so low ( —10 MeV & Ef )

that the probability for the resulting A-I nucleus (e.g. ,' 'W) to fission is negligible. This is not the case for the

I30—I I I i I 1 I

125

OXLLI

I20

I I5

9II I I ) I ) I ! I I I I I I

95 99 I 03 I07 I I I I I 5 I I9

AH

FIG. 5. Eg data as a function of heavy fragment mass, AH,for fission of ' W. Solid lines compare predictions of thescission-point model (Ref. 6) for various sheB strengths, as indi-cated in the figure.

loo

lo

lA

0)0~0K

ShellStrength

I.O

0.80.60.40.2LiquidDrop

O. l

O.OI 97 IO9I I

l2 I

FIG. 4. Relative mass yield curve (x) for fission of ' W.Solid lines compare predictions of the scission-point model (Ref.6) for various shell strengths, as indicated in the figure.

fission of an actinide system in which second- and third-chance fission are appreciable. Vandenbosch et al. 's haveestimated that the interaction of 32-MeV He ions with

U, which results in a Pu' nucleus with E' Ef=20-MeV (nearly the same as in the present case of 's~W),yields 78% first-chance, 16% second-chance, and 6%third-chance fission. It is therefore possible that thestructure observed in the mass distributions of the ac-tinides is caused entirely by contributions from second-and third-chance fission which occur at significantlylower excitation energy. An attempt by the present au-thors to extract a first-chance fission mass distribution forthe 32-MeV He-ion-induced fission of ~ 5U from the dataof Vandenbosch et al. ' gave results sufficiently crude asto preclude any definitive statement about the shape ofthe mass distribution.

The second major difference between 'siW fission andactinide fission concerns differences in shapes between thesaddle and scission points. For a high-Z system in the ac-tinide region the saddle configuration is relatively com-pact with a thick neck -between nascent fragments. Thedescent to the elongated, narrow-necked scission configu-ration not only involves a significant decrease in potentialenergy with the possible interplay of fission dynamics, butmust also require a relatively long time for the nucleus toadjust to these large changes in energy and shape. Thistime would allow the system to adjust to any microscopicshell effects. However, for a light-Z system, such as

W, the saddle and scission configurations are essentially

1232 B. D. WILKINS et al. 30

the same. Thus, very little time is needed to scission afterthe saddle point is achieved. For such a system excited to20 MeV above the fission barrier it is conceivable thatthere is insufficient time for any expected shell effects toexpress themselves at scission. It is noteworthy that justwhere the calculated saddle and scission points approacheach other (i.e., the Pb region), any shell. effects which canbe observed experimentally disappear.

In order to conduct a more conclusive test of the pre-diction of deformed-shell effects in the fission of ' W, orneighboring nuclides for which the effects may be moredominant, it would appear that fission at substantiallylower values of E' —Ef must be explored. This is a verydifficult and time-consuming experiment with present-dayaccelerator and detector technologies. Nonetheless, thesedata do constitute a test of liquid-drop mass and kineticenergy properties of A (200 nuclei at the lowest excita-tion energy yet studied. As such, they provide a useful

confirmation of the underlying liquid-drop properties ofnuclear matter.

ACKNOWLEDGMENTS

The authors wish to recognize the contribution of J.Lerner (deceased) of Argonne National Laboratory, whoprepared the ' Hf targets. The assistance of Terry Sloanof IUCF in constructing the detector mounts was also ap-preciated. In addition, we acknowledge Dennis Freiseland the IUCF machine operations crew for excellentbeams during these experiments. This work was per-forined under the auspices of the Office of High Energyand Nuclear Physics, Division of Nuclear Physics, U.S.Department of Energy under Contract Nos. W-31-109-ENG-38 and DE-AC02-81ER-40007, and the NationalScience Foundation.

'Present address: U.S. Naval Research Laboratory,Washington, D.C. 20375.

Present address: Institute of Atomic Energy, Academica Sini-ca, Beijing, People's Republic of China.

R. Vandenbosch and J. R. Huizenga, Nuclear Fission (Academ-ic, New York, 1973).

R. Vandenbosch, Nucl. Phys. 46, 129 (1963).J. Terrell, Phys. Rev. 127, 880 (1962).

4H. W. Schmitt, Proceedings of the 2nd International Symposium on Physics and Chemistry of Fission (IAEA, Vienna,1969), p. 69.

~U. Mosel and H. W. Schmitt, Phys. Rev. C 4, 2185 (1971).B. D. Wilkins, E. P. Steinberg, and R. R. Chasman, Phys. Rev.

C 14, 1832 (1976).7V. M. Strutinsky, Nucl. Phys. A95, 420 (1967).E. K. Hulet, R. W. Lougheed, J. H. Landrum, J. F. Wild, D.

C. Hoffman, J. Weber, and J. B. Wilhelmy, Phys. Rev. C 21,966 (1980).

D. C. Hoffman, J. B. Wilhelmy, J. Weber, W. R. Daniels, E.K. Hulet, R. W. Lougheed, J. H. Landrum, J. F. Wild, and R.

J. Dupzyk, Phys. Rev. C 21, 972 (1980).oW. D. Myers and W. J. Swiatecki, Nucl. Phys. 81, 1 (1966);

W. D. Myers and W. J. Swiatecki, Lawrence Berkeley Radia-tion Laboratory Report UCRL-11980, 1965.W. G. Meyer, V. E. Viola, Jr., R. G. Clark, and S. M. Read,Phys. Rev. C 20, 176 (1979).A. Khodai-Japoori, Lawrence Berkeley Radiation LaboratoryReport UCRL-16489, 1966.

~ I. S. Sherman, R. G. Roddick, and A. F. Metz, IEEE. Trans.Nucl. Sci. 15, 500 (1968).S. B. Kaufman, B. D. Wilkins, and E. P. Steinberg, Nucl. In-strum. Methods 115, 47 (1974).

~5V. E. Viola, Jr., At. Data Nucl. Data Tables 1, 391 (1966).J. P. Unik and J. R. Huizenga, Phys. Rev. 134, B90 (1964).

i7E. K. Hyde, The Nuclear Properties of the Heavy ElementsIII. Fission Phenomena (Prentice-Hall, Englewood Cliffs,N.J., 1964).

' R. Vandenbosch, T. D. Thomas, S. E. Vandenbosch, R. A.Glass, and G. T. Seaborg, Phys. Rev. 111, 1358 (1958).