Search for coulomb fission induced by 84Kr ions on 238U

Nuclear Physics A221 (1974) 37--44; (~) North-tlolland Publishin9 Co., Amsterdam N o t to be reproduced by photoprint or microfilm without written permission from the publisher

SEARCH FOR COULOMB FISSION

INDUCED BY $4Kr I O N S ON 238U C. NG0, J. PETER and B. TAMAIN t Chimie Nucldaire, lnstitut de Physique Nucldaire, BP 1, 91406 Orsay, France

Received 31 December 1973 Abstract: We have searched for Coulomb fission induced by a*Kr ions on a 23su target at energies ranging from the interaction barrier down to 37 MeV below (408--458 MeV lab). No event attributed to Coulomb fission was detected; it was deduced that the cross section for this reaction is lower than 0.3 mb/sr near the interaction barrier. This value was compared to theoretical predictions. However, fission events originating from transfer reactions at the interaction barrier have been detected. E[

COULOMB FISSION 23aU("Kr' a'Kr)F' E = 408-458 MeV; measured ~[E(a'Kr)' E(fragment)], compared to theoretical predictions.

I

1. Introduction When a heavy ion comes close to a heavy nucleus, the long range Coulomb interaction is able to induce th.e excitation of various collective nuclear modes. An effect of this interaction may be to distort the target nucleus up to a saddle-point after which the nucleus slides down to scission. If the experiment is performed sufficiently far below the interaction barrier, then only Coulomb forces are involved in inducing the process and there is no transfer of nuclear matter between the projectile and the nucleus. In this case, the induced fission is called Coulomb fission. The possibility of such a reaction was first outlined by Guth and Wilets ~) who pointed out that this process would provide direct indications on the difference of deformation between the ground state and the first saddle-point for fission. Up to now no Coulomb fission has been observed experimentally and the available information on this subject consists of only theoretical predictions concerning the cross sections for Coulomb fission and the angular distribution of the fragments. The probability of Coulomb excitation to a high level is a rapidly increasing function of the nuclear charges of the projectile and of the target. Obviously, the lower the fission barrier, the higher the probability of reaching it. Precise quantitative theoretical predictions for Coulomb fission cross sections are difficult and those published up to now differ by a factor of 1000. The first calculations were made by Guth and Wilets 1) and a short time later they were developed by Wilets et al. 2): a collective description of the fissioning nucleus was used, the nuclear t On leave from Universit~ de C l c r m o n t - F e r r a n d . 37

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shape was described only by the use of the quadrupole moment, the higher moments were estimated roughly, and only axially symmelric shapes were considered. The relative motion of the projectile and the target was calculated for point charges and not as coupled dynamical variables. All this was done for a zero impact parameter. Then the cross section should be similar to the elastic scattering cross section at 180 °. In inducing Coulomb fission, the process is certainly adiabatic with respect to intrinsic excitations 2), but it is not with respect to collective motion 2, a). As pointed out by Beyer and Winther 3), the strength of the excitation is such that the excitation of the vibrational states cannot be described by classical mechanics. On the other hand, the adiabaticity parameter for rotational motion is so small that the rotational motion can be treated in the sudden approximation. Beyer et al. a, 4) have calculated quantum mechanically the probability of excitation of high vibrational levels. This probability is rather low. These calculations are very sensitive to the magnitude of the damping of the surface vibrations. Riesenfeldt and Thomas 5), in a paper concerning the effect of nuclear deformability on the reaction cross sections, have obtained by a method similar to that of Beyer et al., much higher excitation probability for high vibrational states, but their oscillator potential was not as good as that of Beyer et al. Another important problem which arises is to know the exact location of the interaction barrier. The effect of deformability of the two nuclei, which tend to flatten into oblate shapes, was first pointed out by Beringer 6) who has done static calculations. In fact, static calculations overestimate the influence of deformability and further studies were done which took into account the shell effects 7) and the dynamics 5,8-1o). Holm and Greiner 11) have included the influence o f nuclear forces on Coulomb fission cross sections and have performed two kinds of calculations: first, using a classical model and second, using the method of semi-classical Coulomb excitation. Their calculations are more sophisticated than the calculations of Beyer et al. a, 4) and they obtained a rather good agreement between the crosssections obtained by application of the two methods. They have also shown that the range of energies able to induce Coulomb fission should extend to energies several tens of MeV below the interaction barrier and the maximum of the Coulomb fission excitation function should not be located just below the interaction barrier. The heaviest projectile available at the Orsay ALICE accelerator is 84Kr and the doubly even target with the lowest fission barrier is z38U. For this set of target and projectile, the predictions extend from 100 mb/sr [ref. z)] down to 10 -z mb/sr [ref. 4)] with intermediate values around 1 mb/sr [refs. 5, t~)]. We first determined the value of the interaction barrier. We measured the elastic scattering cross section at an angle close to 180 ° as a function of the bombarding energy lz). It appeared that the interaction barrier between heavy ion and target is much higher 13) than expected. It is not clear whether this increase is due to the increase in the Coulomb interaction or if a dynamical deformation of the nucleus occurs. If the latter is true, the probability of Coulomb fission could be enhanced.

COULOMB FISSION

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2. Experimental technique We want to detect the coincident fragments emitted in a Coulomb fission together with the scattered K r ion which induced this fission, and measure their energies with semiconductor detectors. 2.1. GEOMETRY OF THE EXPERIMENT I f the 84Kr with initial velocity v t is back-scattered at 180 °, the recoil velocity of the 238U target nucleus at 0 ° has the value Va = [2x 84/(84+238)]~ 1. At a bombarding energy of 452 MeV, VR is 1.67 cm/ns. The total kinetic energy released in the fission of 238U at low excitation energy is known to be 168 MeV on the average. The mass distribution is asymmetric, with two peaks around masses 95 and 143, the velocities of which are around 1.4 and 0.94 cm/ns in the c.m. of the fissioning nucleus. These values are lower than VR, so all the Coulomb fission fragments will be observed at laboratory angles lower than 90°: the maximum angle for a fragment with velocity Vf is given by 0fm"x = arc sin (uf/VR) , i.e. around 57 ° for the light masses and 33 ° for the heavy masses. The laboratory differential cross section will be more important by a factor of up to 10 than the corresponding c.m. value - and this will help for the detection of Coulomb fission events. For instance, fission at 90 ° c.m. will give coincident light and heavy fragments with energies of 236 and 273 MeV at 39 c and 29 ° with c.m. to laboratory cross section ratios 3.8 and 8.7. This angular correlation and also these energies are quite different from the ones which could be observed for the fission fragments of the compound nucleus 322128. Indeed, the recoil velocity of the compound nucleus is exactly one half of VR and the velocity of the fragments of this superheavy nucleus is expected to be slightly higher than that of 238U fission fragments; then the angular correlation for symmetric fission at 90 ° c.m. should be around 60°-60 '~ in the laboratory. But the angular correlation is not sufficient to identify a Coulomb fission event. Indeed, when the bombarding energy is slightly above the interaction barrier, inelastic nuclear scattering and transfer reactions of one or several nucleons may occur. The final heavy nucleus has a mass, recoil velocity and fission kinetic energy release very close to that of the target nucleus, and the fission probability is high when the excitation energy is above 6 MeV. It would be very difficult to distinguish such an event from a Coulomb fission event by looking only at the two fission fragyaents; to make this distinction, it is necessary to simultaneously measure the energy of the scattered projectile or transfer product. It should be noticed that the scattering angle for this ion can be chosen different from 180 °, since the energy corresponding to the interaction barrier slowly increases with the impact parameter to which a given scattering angle corresponds. But the recoil velocity of the nucleus is no longer at 0 ° and, if one wishes to be able to transform the energies of the fragments into the c.m. system, one is obliged to limit the angular acceptance of the projectile detector in the plane perpendicular to the plane

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of the fragments. On the contrary, at scattering angles close to 180 °, the recoil o f the target is always close to 0 ° a n d all the projectiles scattered at the same angle to the b e a m direction can be detected. This is the reason why we have chosen to detect the scattered p r o d u c t near 180 ° . 2.2. DETECTORS The b a c k - s c a t t e r e d K r ions have been detected by an a n n u l a r detector o f a r e a 600 m m 2 (Z in fig. 1) especially m a d e for heavy ion detection. The useful detection a r e a covers angles between 175 ° a n d 169 ° from the center o f the beam. The loss o f energy resolution due to this variation o f angle is 1 M e V for the elastically scattered Kr. The c o r r e s p o n d i n g angles for the elastically scattered U nucleus are only between 2 ° a n d 5 °. The size a n d emittance o f the beam increases these a n g u l a r widths by a b o u t 2 ~. The fission fragments were detected by surface barrier heavy ions detectors (X a n d Y). The a n g u l a r width o f the fixed detector X was 6 ° in the reaction plane a n d 15 ° in the direction n o r m a l to this plane. F o r Y, these values were I0 ° a n d 4 °. This r beam

coLLimators " \\x

Kr

Z

beam

(

.l d;,ro0,; Fo~s

Fig. I. Experimental arrangement (not to scale). Z is an annular detector and detects the backscattered Kr projectiles. The X detector is held fixed at 24 °, Y is moved from 26 ° to 56 °. Pulse heights (energies) from detectors X, Y, Z and the time-of-flight differences between particles X and Z and/or particles X and Y are recorded on tape. set-up is similar to the ones used in experiments on fission induced by h e a v y ions [refs. 14, 15)]: it allows to collect the fragments sent out o f the plane by neutron e v a p o r a t i o n after :fission, a n d to cover in a few m e a s u r e m e n t s the whole a n g u l a r correlation o f the coincident fragments by m o v i n g the Y detector by 10 ° steps.

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The background of each detector was reduced by the use of a magnetic field and a 80 pg/cm 2 nickel foil to stop the slow electrons and soft X-rays. 2.3. TARGET

The target was natural uranium tetrafluoride and its thickness 420 pg/cm 2 of U. The beam energy loss in this material is about 21 MeV per mg/cm 2 [calculated with the D E D X R code, kindly communicated by P. G. Steward 16)]. This thickness causes the kinetic energy spectrum of elastically scattered Kr ions to be wide: a difference of 10 MeV exists between a Kr ion scattered at the upstream surface of the target and a Kr ion scattered at the downstream surface, which has to go twice through the whole U F 4 laycr. Then a total energy width of 11 MeV is expected and is experimentally observed. The backing of the target was 200 pg/cm 2 of aluminium, which slowed the fragments going to the X and Y detectors (fig. 1). 2.4. ELECTRONIC SET-UP

The electronic diagram was similar to the one used in other experiments 15, 17) and will not be described here. The pulse heights (energies) from detectors X, Y and Z were recorded on magnetic tape for each event, and also the differences of time-offlight between X and Y on one side, and between X and Z on the other side, i.e. t x - t v and t x - t z (or only one of them if the coincidence is only XY or XZ). This gives a much more precise result than a fast coincidence circuit and allows to continuously monitor the rate of random events 17). The magnetic tapes were read after the experiment and for each XY or XYZ event the c.m. energies and masses of the fragments X and Y were calculated on the basis of kinematic relationships obtained by assuming fission of a z38U nucleus scattered at 0°; the Z energy was compared to the elastic scattering value. For an XZ event, one can only look at the Z energy and see whether or not the X energy is in agreement with a Coulomb fission event. In addition, the energy spectra of all the particles received by the three detectors were recorded: the elastic scattering peaks on X, Y and Z allow to check the energy calibration schemes, and the number of elastic events on Z allows to verify the rate o f elastically scattered particles as a function of the bombarding energy. 2.5. BEAM

The beam energy was 458 MeV (Kr of charge 23 + at the maximum field of the cyclotron), slightly over the measured interaction barrier ~3). It could be changed by varying the magnetic field and frequency of the cyclotron. In order to save time, we preferred to use degrader foils of aluminium which could be immediately put into place. We checked that an important loss of energy (more than 50 MeV) did not change the shape of the beam spot on the target. During the measurements, graphitc collimators were set between the degrader foils and the target (fig. 1).

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c. NG0 et aL 3. Results and discussion

We have made the measurements between 458 and 408 MeV, i.e. 338 to 300 MeV in the center of mass, in 5 steps separated by I0 MeV and of about 12 MeV width. The X detector was set at 24 °, whereas Y covered 26o-56 ° for the two highest energies and 260-36 ° for the three other ones. The beam intensity was less than 2 x l0 s particles/s and the experiment lasted 36 h. We have observed several random coincidences on XY and some on XZ. They are easily established to be random events, for they are equally present on the time-offlight spectrum at several places which are separated by a time equal to the period of the cyclotron t T); moreover, most of them have the energy of the elastically scattered particles, which are the particles most frequently received by the detectors. We have also observed non-random XY events. For some of them, present at any bombarding energy, the treatment has shown that they can be attributed to the fission of the compound nucleus 11 ~In formed by fusion of SaKr and a 27A1 nucleus of the target backing. After the energy loss in UF4, the energy of the K r ions in A1 was between 446 to 399 MeV, i.e. E = 108 to 97 MeV in the c.m. K r + A I . The interaction barrier between K r and AI is given by: Bi, ' = (13 × 27 e Z ) / [ r e ( 2 7 " + 8 4 ~ ) ] = 62 MeV if r e = 1.45 fm [this value was obtained for 4°Ar induced reactions on medium and heavy targets 18)]. The total reaction cross reaction a R calculated from a , = nre 2 (279 + 84~) 2(1 - 62/E),

is around 1400 m b at these bombarding energies. The measured fission cross section tbr xa q n is of the order of 10- ~mb/sr at 24 ° in the lab system, which corresponds to less than 10 -1 mb/sr at 90 ° in the c.m. system. The m a x i m u m angular m o m e n t u m varies from 52 to 62 h and then the fragment angular distribution must have a 1/sin 0 shape in the c.m. system. The fission cross section is about 0.2 rob. This value is in agreement with the measured fission cross section (0.5mb) for In formed by fusion of a 126 MeV ' 4 N projectile and a natMo target 12). These very low fission cross sections are compatible with a fission barrier of the order of 50 MeV [ref. 13)]. At the highest energies, 446-458 MeV and 436-448 MeV, most of the XY events are due to the fission of a nucleus which has a mass in the vicinity of the target mass and which recoil velocity is slightly lower than that of an elastically scattered uranium nucleus. None of them is in coincidence with a particle on the Z detector, so they are likely due to a nuclear interaction between the projectile and the target nucleus, such as a transfer reaction just at the interaction barrier (see subsect. 2.1). The resulting heavy nucleus has an excitation energy greater than its fission barrier (around 6 MeV). The observed cross section for fission after transfer is around 6 mb for EKr in the range 446-458 MeV. This observation shows that nuclear reactions effectively occur at the interaction barrier value which was determined by backward elastic scattering. The absence of X Y Z coincidence could be due to a wrong position of the Y detector, but the absence of X Z coincidence clearly shows that no possible Coulomb

COULOMB FISSION

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fission was detected. We have calculated the m a x i m u m C o u l o m b fission cross section for each range o f energy. One has to take into account a factor o f ~ 5 between the differential cross sections at 24 ° in the lab system and the corresponding c.m. angle (near 90°). It was predicted tb.at the angular distribution should have a m a x i m u m near 90 ° [ref. 2)]. However, in order to obtain an upper limit for the total cross section, we have calculated it by assuming an isotropic c.m. angular distribution for the fragments: the C o u l o m b fission cross section is less than 0.3 mb/sr between 438 a n d 458 MeV, a n d less than 0.9 mb/sr between 408 and 438 MeV. It must be kept in mind that the occurrence o f a coincidence X Y Z or X Z in our experiment would not necessarily be due to C o u l o m b fission: the target thickness and the angular width o f the Z detector were such that the energy o f the Z p r o d u c t could not be measured with a sufficient accuracy to distinguish a scattered K r ion f r o m a transfer p r o d u c t having lost or gained a few nucleons. In case o f detection o f coincident events, it would have been necessary to reduce the target thickness. It would also be very useful to measure the angular distribution of the fission fragments associated with a K r ion on Z since this distribution is expected to be different for C o u l o m b fission (maximum at 90 °) and for fission after transfer (isotropy or m a x i m u m at 0°). The cross-section limit we have obtained is m u c h lower than the first theoretical predictions j' z), but is very m u c h greater than the m o s t pessimistic one 3, 4) and o f the same order as the intermediate values s, 11). C o u l o m b fission cannot then be excluded and must be searched with a much more intense beam and preferably with heavier ions, such as Xe. The possibility o f using targets o f transuranium elements with a lower fission barrier would also be a great advantage. We thank Professors M. Lefort and Z. Fraenkel for their interest and helpful discussions on this work.

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13)

E. Guth and L. Wilets, Phys. Rev. Lett. 16 1 (1966) 30 L. Wilets, E. Guth and J. S. Tenn, Phys. Rev. 156 (1967) 1349 K. Beyer and A. Winther, Phys. Lett. 30B (1969) 296 K. Beyer, A. Winther and U. Srnilansy, Proc. Int. Conf. Heidelberg, 1969 (North-Holland, Amsterdam, 1970) p. 804 P. W. Riesenfeldt and T. D. Thomas, Phys. Rev. C2 (1970) 711 R. Beringer, Phys. Rev. Lett. 18 (1967) 1106 C. Y. Wong, Phys. Lett. 26B (1968) 120 J. Maly and J. R. Nix, J. Phys. Soc. Jap. Suppl. 24 (1968) 224 H. Holm, W. Scheid and W. Greiner, Phys. Lett. 29B (1969) 473 A. S. Jensen and C. Y. Wong, Phys. Rev. 4 (1970) 1321 H. Holm and W. Greiner, Nucl. Phys. A195 (1972) 333 B. Tamain, M. Lefort, C. Ng6 and J. Pdter, Proc. Conf. physique nucl6aire, Aix-en-Provence, 1972 M. Lefort, C. Ng6, J. P6ter and B. Tamain, Nucl. Phys. 197 (1972) 485

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14) F. Hanappe, C. Ng6, J. PEter and B. Tamain, Proc. IAEA Symp. on fission, Rochester, 1973, paper SM 174/42 15) B. Borderie, F. I-Ianappe, C. Ng6, J. P~ter and B. Tamain, Nucl. Phys. A220 (1974) 93 16) P. G. Steward, U C R L 17958 (1968) 17) C. Cabot, C. Ng6, J. P~ter and B. Tamain, Nucl. Inst. 114 (1974) 41 18) M. Lefort, Y. Le Beyec and J. P6ter, Riv. Nuovo Cim. 4 0974) I 19) C. Cabot, Th~se de 36me cycle, IPN Orsay, 1973