Total kinetic energies in the fission of 101Rh, 110Cd, 119I and 138Ba nuclei

Nuclear Physics A252 (1975) 163--172; ~ ) North.Holland Publishing Co., Amsterdam Not to be reproducedby photoprint or microfilmwithout written permissionfrom the publisher

TOTAL KINETIC ENERGIES IN THE FISSION O F l°lRh, tt°Cd, ttgl AND t28Ba N U C L E I M. N. NAMBOODIRI, J. B. NATOWITZ, E. T. CHULICKt, K. DAS tt and L. WEBB tt Cyclotron Institute, Texas A &M University, College Station, Texas 77843

Received 30 July 1975 Abstract: Singles and coincidence experiments with solid state detector telescopes have been used to determine the total fragment kinetic energies in the symmetric fissioh of l°lRh, tt°Cd, t~gI and 12SBa nuclei produced in reactions induced by 197 MeV ~aC projectiles. These kinetic energies are found to be in excellent agreement with the predictions of Davies et al. based upon a dynamic liquid drop model calculation. For the reactions of ~2Cwith Ag, the dependence of the kinetic energy release on angular momentum has been explored. The increase in kinetic energy with increasing angular momentum is found to be ~_ 0.7 keV/?~2. E{

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NUCLEAR REACTIONS measured fragment kinetic energies agy, 9SMo' Ag, lt6Sn(t2C, F), E = 107, 197 MoV; deduced (TKE) for symmetric fission.

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1. Introduction The total kinetic energies of fission fragments reflect primarily the nuclear shape and charge distribution at the time of scission. An additional contribution f r o m pre-scission motion of the nascent fragments is expected to be particularly significant in the fission of heavy nuclei. Measurements of the fragment kinetic energies may therefore be used to test theoretical calculations t) of the scission configuration and the dynamics of the fission process, as well as to explore the variation of those properties with collective parameters such as the excitation energy and angular m o m e n t u m o f the fissioning nucleus. A number of measurements of total kinetic energy release have been made for the fission of heavy elements. The empirical systematics of these data have been explored [ref. 2)] and comparisons with theoretical calculations have been used to obtain information on the viscosity of nuclear matter 3). Most of the data currently available indicate that the increase o f the total kinetic energy with increasing excitation energy is not greater than 0.07 MeV per MeV of excitation energy. It has in fact been suggested that the increase results plimarily from increases in the angular m o m e n t u m of the fissioning nucleus rather than the t Present address: Babcock & Wilcox Co., Lynchburg Research Center, Lynchburg, Virginia. tt Robert A. Welch Foundation Undergraduate Fellow. 163

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M.N. NAMBOODIRI et aL

increased excitation energy 4). Although larger variations have been reported s), a recent investigation of the variation of the total kinetic energy with angular momentum of the fissioning nucleus 20SAt has led to the conclusion 6) that the increase is < 1 keV/h 2. This result is consistent with estimates made by Sikkeland 4) based upon calculations of the saddle-point shapes of nuclei in that mass region. Measurements of the total kinetic energies in the fission of medium mass (~, 100 ainu) nuclei offer some particular opportunities to test theoretical calculations of the saddle-point shapes of the fissioning nuclei since the saddle-point and scission point shapes are expected to be very similar and prescission contributions to the kinetic energies should be small 1). In addition, the smaller moments of inertia of such nuclei at scission 7) are predicted to result in significantly larger (..~ 3 keV]h 2) variations of the fragment kinetic energy with angular momentum 4), making possible a more sensitive test of the coupling between the rotational energy of the fissioning nucleus and the fragment kinetic energies. However, because the cross sections for fission of the medium mass elements are small and the fragment kinetic energies are much lower than those observed in the fission of heavy nuclei, the systematics of the kinetic energy release in the fission of medium mass elements has not been extensively studied 8,9). As part of a study of fission and fission-like reactions of heavy ions with medium mass targets we have measured the kinetic energies of fragments resulting from the symmetric division of l°IRh, 11°Cd, 1191 and 128Ba nuclei. In addition, for the reactions of 12C with Ag we have measured the variation of the fragment kinetic energy with increasing projectile energy in order to explore the dependence of the total kinetic energy on excitation energy and/or angular momentum. 2. Experiments

Both singles and coincidence experiments were performed to determine the total kinetic energies of symmetric fission reported in this paper. In the singles experiments, semiconductor detector telescopes employing A E detectors of 4.3 pm or 8.4 pm thickness were used to detect and identify products of the reactions of 197 MeV 12C projectiles with s 9y, 9SMo ' Ag, and ~~6Sn target nuclei. The self-supporting target foils ranged in thickness from 200 ttg/cm 2 to 725/~g/cm 2. In the coincidence experiments, two detector telescopes were placed at the complementary angles for fragments arising from symmetric fission. These angles were calculated by assuming complete momentum transfer to the composite system and estimating the fragment kinetic energies from the systematics of previous energy measurements 2). Angles of 3 ° to 15° were subtended in various coincidence experiments in order to assure that the final reported values of the total kinetic energies of symmetric fission were not biased by the choice of angles. In each experiment the detectors were calibrated using 5.48 MeV u-particles from an 241Am source.

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165

TABLE 1 Average total kinetic energies of fission fragments produced in reactions with 12C projectiles Projectile energy (MeV) 197 197 197 107 197

Target

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Compound nucleus

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(TKE>

(ainu)

(MeV)

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a) Assumed average mass difference between primary symmetric fragment and detected fragment. b) Most abundant isotope.

During an irradiation, the detector telescope data were recorded event by event on magnetic tape for later processing off-line. Singles data were processed with the code BINIT 1o). Coincidence data were processed with the code TANTALUS which, in addition to the capabilities of BINIT, includes provisions for kinematic calculations of the masses and energies of the coincident primary fission fragments. In the mass calculation, the iterative technique described by Plasil et al. ~1) is employed. An important parameter of the calculation is the average mass change experienced by the primary fragment during the de-excitation step. Based on the results of the evaporation calculations performed using the code ALICE 12), we have used the average mass changes indicated in table 1. A table look up technique was used to identify the detected ions. The identification tables are based upon the semi-empirical range energy calculations of Northcliffe and Schilling t3) but have been modified to take into account pulse height defects and detector window effects. The data required to make these modifications were obtained by comparing the observed energies of 14N, 160, 2sSi, 4°Ar, 56Fe, and S4Kr accelerated in the TAMU variable energy cyclotron with the energies determined by magnetic analysis 14). Following the identification of an incident ion, the observed energy was corrected for pulse height defect using the formulation proposed by Kaufman et al. i s). The constant A appropriate to the correction equation [eq. (5) of ref. ~5)] was also determined from the pulse-height defect data. A value of 17.0 was used. The resultant energies were further corrected for energy loss in the target by the use of range energy information 13) with the assumption that the ions passed through an amount of target material equal to one-half the target thickness, corrected for the angle of observation. The possible variation of the total fission fragment kinetic energy with projectile energy was explored in a series of singles experiments in which the products of the reactions of Ag with ~2C projectiles of 107 MeV and 197 MeV were observed. Experiments at the two different projectile energies were performed consecutively

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et al.

using the same target, detector telescope, angle of observation and energy calibration. Several measurements were made at each projectile energy. The energy calibration was verified between each pair of measurements. 3. Results

In fig. 1 we present, for the reactions o f 12C with Ag, data obtained in a coincidence experiment. The data are in the form of a plot of total kinetic energy as a function o f the mass of one of the primary fragments. The most probable total kinetic energies for symmetric division have been determined from such correlations. It is also possible to determine the total kinetic energy for symmetric division from the singles experiments. In fig. 2, identified distributions o f reaction products observed at a laboratory angle of 40 ° arc presented. The details of these elemental yield distributions and the implications with regard to reaction mechanisms are discussed elsewhere z 6). Although individual elements are not resolved above atomic number ~, 16, each of the elemental yield distributions has a peak occurring at a PI value slightly below that corresponding to the value which would be observed for an ion with an atomic number equal to one-half that of the nucleus which would be formed by the fusion o f the target and projectile. Such a peak is consistent with the fission of that nucleus into two symmetric fragments which then de-excite to produce the observed products. I f such is the case, correction of the measured laboratory kinetic

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168

M.N. NAMBOODIRI et al.

energies of those products of peak yield for the mass change of the fragment during the de-excitation process should yield the kinetic energies of the primary symmetric fragments. These corrections have been made using the same average mass changes assumed in the kinematic calculations for the coincidence experiments. In table 1, the average total kinetic energies ( T K E ) determined both from coincidence and singles experiments are presented. The estimated errors (90 ~ confidence limit) are also indicated. The possible variation of total kinetic energy with projectile energy was explicitly studied for the reactions of 12C with Ag. Previous reports have indicated a significant variation of the total kinetic energy with increasing projectile energy and have attributed this increase primarily to the increased angular momentum of the fissioning nucleus *). The average rotational energy of the saddle point nucleus may be written [ref. s)]

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In this equation J is the nuclear angular momentum, I is the moment of inertia about an axis perpendicular to the nuclear symmetry axis and Tis the nuclear temperature. The fusion cross section for the reaction of 197 MeV 12C projectiles with Ag has been measured 16) and corresponds to a sharp cut-off limiting angular momentum for fusion of 73h. Since the nuclei of higher angular momenta are those for which fission is most probable and the total cross sections for fission are not large in these systems, the angular momenta of the fissioning I nuclei should be very close to the limiting angular momentum for fusion. No measurement has been made of the fusion cross section at 107 MeV projectile energy but, based on a previous comparison 17) of experimental limiting angular momenta with those calculated using the model proposed by Bass, we estimate the limiting angular momentum for fusion of 107 MeV 12C with Ag to be 49h. The moments of inertia I for saddle point nuclei have been calculated as a function of fissionibility parameter and angular momentum by Cohen, Plasil and Swiatecki 7). For t2°l nuclei, having angular momenta of 49h to 73h, I is 4.2/0, where lo is the rigid body moment of inertia of a sphere having the same mass. We have evaluated I using the parametez s of ref. 7). The nuclear temperature of the saddle point nucleus is related to E~, the excitation energy at the saddle point, = ar 2- r.

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169

tion, En is the energy of the rotating equilibrium ground state relative to the energy Rsprt, of a rotating sphere of the same mass. These latter three quantities have also been evaluated using the parameters of ref. 7). For the reactions of 12C with 1°SAg at 197 MeV we calculate an excitation energy at the saddle point of 111 MeV which corresponds to a nuclear temperature of 2.7 MeV. At 107 MeV projectile energy the nuclear temperature is 1.6 MeV. Using eq. (1) we calculate that (Ett) is 16.4 MeV for the fissioning I nuclei produced in the reactions induced by 197 MeV projectiles and is 7.4 MeV for the lower projectile energy of 107 MeV. Corresponding increases in the total fragment kinetic energies would be expected if, at the time of scission, the entire rotational energy were converted to kinetic energy. In fact, as is confirmed by various experiments, some of the rotational energy appears as rotational energy of the separated fragments is). For symmetric fission, the requirement of angular momentum conservation in a rigid rotation model leads to the expectation that < of the total angular momentum will appear as angular momentum of the fragments and >= ~ of the total as relative orbital angular momentum of the fragments 18,19). In such a case, the conversion of rotational energy to kinetic energy would result in an increase of the kinetic energy of ~ 9.1 MeV at 197 MeV projectile energy and 4.3 MeV at 107 MeV projectile energy. In table 1, the total kinetic energies measured for the reactions of 12C with Ag at two different projectile energies are presented. The total kinetic energy of 71.4 MeV measured at the higher projectile energy is 0.6 MeV higher than the value of 70.8 MeV measured at the lower projectile energy. While the absolute errors on these individual measurements are estimated to be + 3.0 MeV, the relative error should be less than 1.5 MeV because of the manner in which the experiments were carried out and the fact that the target thickness corrections and pulse height defect corrections are almost identical at the two different projectile energies. If the angular momentum of the fissioning I nucleus is taken to be equal to the limiting angular momentum for fusion and the entire increase in kinetic energy is attributed to angular momentum effects, the observed difference corresponds to an increase of 0.2 keV/h 2. The 2.1 MeV upper limit to the difference corresponds to a rate of increase ~ 0.7 keV/h 2. Even this latter value is lower than the 1.6 keV/h 2 suggested by the model in which ~ of the angular momentum appears as rotational energy of the individual fragments and is much lower than the ~ 3 keV/h 2 which would result from the complete conversion of the saddle point rotational energy to kinetic energy 4). The difference between the observed and calculated values is increased if part of the observed kinetic energy increase is ascribed to excitation energy effects. On the basis of this experimental result, we conclude that there is no large increase of the total kinetic energy resulting from the high angular momenta of the fissioning nuclei produced in the reactions of 197 MeV 12C ions with sgy, 9BMo' Ag and 116Sn nuclei. Since the apparent increase of ~ 0.2 keV/h 2 does not exceed the absolute errors assigned to the measured total kinetic energies, the measured energies are

170

M.N. NAMBOODIRI

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compared directly with the calculations o f Davies et al. 3) in fig. 3. The other experimental data in the figure c o m e from a number o f different studies which are listed in refs. z, 3, 6).

FISSION

171

The new data from this study extend the region for which measurements are now available to nuclei of much lower fissionability and, as is readily verified by fig. 3, the new measurements arc in excellent agreement with the theoretical values calculated using a dynamic liquid drop model. These calculations were carried out assuming zero angular momentum. The inclusion of angular momentum for nuclei in the mass region under consideration here leads to saddle point shapes slightly more compact 7) than those obtained in the case of zero angular momentum, but probably has very little effect on the scission configuration. The angular distributions reported in ref. ~6) indicate that the symmetric fissioning systems have existed for at least several rotations before dividing and the c.m. kinetic energies determined from singles experiments at two or more different laboratory angles are the same within experimental error, showing no systematic variation with laboratory angle. Wc take this as evidence that the shapes of the fissioning nuclei producing the fragments observed at the different angles are the same, as would be expected for a rotating equilibrium system. Even so, we cannot a priori rule out the possibility that the scission configurations of the fissioning nuclei produced in these high energy t2C reactions are more elongated than those which would arise from evolution of a compound nucleus passing through the saddle point. If such were the case, an increase of the kinetic energy due to rapid rotation of the fissioning nucleus might be partially masked by such an elongation of the scissioning nucleus.

4. Summary and conclusion Total kinetic energies have been measured for the 1oip,~, 1~0Cd ' I, and ~2SBa fissioning nuclei produced in reactions with 197 M e V 12C projectiles. A test of the possible variation of the total kinetic energy with excitation energy or angular m o m e n t u m has been made. N o significant difference in the total kinetic energy has been observed at the two differentprojectileenergies of 107 M e V and 197 M e V cvcn though the excitation energy of the fissioning saddle point nucleus increases by ~ 75 M e V and the rotational energy increases by 9 M c V as the projectile energy is increased. The total kinetic energies reported here are in excellent agreement with the values calculated using a dynamic liquid drop model formalism. W c appreciate helpful conversations with J. R. Nix and A. J. Sierk. Our thanks also to K. Geoffrey and to the operations crew of the Texas A & M Cyclotron Institute for their assistance in this work. This research was supported by the U S E R D A and the Robert A. Welch Foundation. References 1) J. R. Nix, Nucl. Phys. A130 (1969) 241 2) V. Viola, Nu¢l. Data A1 (1966) 391

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3) K. T. R. Davies, S. E. Koonin, J. R. Nix and A. J. Sierk, Prec. of the Int. Workshop on gross properties of nuclei and nuclear excitations III, Hirschegg, Kleinwalsertal, Austria, January, 1975 (Inst. ftir Kernphysik, Technische Hochschule, Darmstadt, 1975) 4) T. Sikkeland, Phys. Lett. 31B (1970) 451 5) J. Unik, G. Cuninghame and I. F. Croall, IAEA-SM-122/58, Prec. 2nd IAEA Syrup. on the physics and chemistry of fission, Vienna, July 1969, p. 717 6) C. Ngo, J. Peter and B. Tamain, Prec. of the Int. Conf. on reactions between complex nuclei. Nashville, Tennessee, 1974 (North-Holland, Amsterdam, 1974) voL 1, p. 114 7) S. Cohen, F. Plasil and W. J. Swiatecki, Ann. of Phys. 82 (1974.) 557 8) F. Plasil, R. L. Fergnson and F. Pleasonton, IAEASM-174/71, Prec. of The Third IAEA Syrup. on the physics and chemistry of fission, Rochester, New York, August 1973, (p. 319) 9) C. Cabot, C. Ngu, J. Peter and B. Tamain, Nucl. Phys. A244 (1975) 134 10) E. T. Chulick, M. N. Namboodiri, G. Smith, S. Munden, C. Schnatterly and J. B. Natowitz, Nucl. Instr. 114 (1974) 503 11) F. Plasil, R. L. Fergnson, F. Pleasonton and H. W. Schmitt, Phys. Rev. C7 (1973) 1186 12) M. Blann and F. Plasil, USAEC Report C00-3494-10, November 1, 1973, unpublished 13) L. C. Northcliffe and R. Schilling, Nucl. Data 7 (1970) 233 14) R. Kenefick, J. C. Hiebert and C. W. Lewis, NucL Instr. 88 (1970) 13 15) S. B. Kaufman, E. P. Steinberg, B. D. Wilkins, I. Unik, A. J. Groski and M. J. Fluss, NucL Instr. 115 (1974) 47 16) J. B. Natowitz, M. N. Namboodiri and E. T. Chulick, to be published 17) M. N. Namboodiri, E. T. Chulick, J. B. Natowitz and R. A. Kenefick, Phys. Rev. C l l (1975) 401 18) T. Sikkeland and G. R. Choppin, J. Inorg. Nuclear Chem. 27 (1965) 13 19) R. Bass, Nucl. Phys. A231 (1974) 45