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The study of the (α, α'f) reaction at 120 MeV on 232Th and 238U
Nuclear Physics A346 (1980) 349 - 370; @ ~or~~-H~~la~ P~~~hi~~ Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
THE STUDY OF THE (a, a’f) REACTION AT 120 MeV ON 232Th AND 238U (I). Fission probabilities and angular distributions in the region of the giant quadrupole resunances J. VAN DER PLIGHT, M. N. HARAKEH
and A. VAN DER WOUDE
Kernfbsisch Versneller Instituut, Groningen. The h’ethertands
and P. DAVID, J. DEBRUS, H. JANSZEN and J. SCHULZE Insfifut .fiir strQhie~- und Ke~nph~sik, Bonn, W. Germany
Received 20 May 1980 Abstract: The fission decay channel of 232Th and 23RUhas been investigated, using the (a,‘a’t) reaction at 120 MeV bombarding energy. The angular distributions of the fission fragments and the fission probabiiities up to around 15 MeV excitation have been measured. No evidence for the fission decay of the giant quadrupole resonance has been found, although for 23EU, a weakly excited structure is seen in the (a, ~‘f) spectrum at about 9.5 MeV excitation at backward angles with respect to the recoil axis. This effect is similar to what has been found in a (6Li, *Li’f) experiment reported recently. The over-all feature of the fission probability for excitation energies above the fission barrier are well reproduced by statistical calculations.
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NUCLEAR REACTIONS 232Th, 238U(a, a’f), E = 120 MeV; measured D (fragment, e) fission probabilities. Discussed fission decay modes in GQR region.
1. In~~uction One of the tools for the study of the fission process is fission induced by direct reactions. In these experiments one can measure the fission probability and the fission fragment angular distributions of the excited nucleus as a function of excitation energy. These experiments have been very important in,establishing the characteristics of the double-humid fission barrier, which originates from the effect of single-particle shell corrections on the smootd liquid-drop barrier [see e.g. ref. ‘), and references therein]. Most experimental work so far has been performed at excitation energies around the fission barrier, which is around 6 MeV. At higher excitation energies, around 11 MeV, another interesting possibility 349
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decay channel ofgiantresonances, and thus to learn about the interplay between the very different collective phenomena: fission and giant resonances. Up till now, the study of the isoscalar giant resonances has been mainly concentrated 2,J) on systematics of excitation energies E,, widths r and strength expressed as a fraction of the energy-weighted sum rules (EWSR). For 232Th, the giant quadrupole resonance (GQR) has been measured by means of inelastic scattering of a-particles at E, = 120 MeV. It was found to be located at 1l.OkO.3 Me?‘, has a width of r = 4.OkO.5 MeV and exhausts about 100 74 of the EWSR “). Similar results have been found earlier for 238TJ in inefastic proton scattering 5). In a recent (e, e’) experiment though, Pitthan et al. “) found GQR strength centered around 9.9 MeV. Recently, the main interest has shifted towards the decay properties of giant resonances. In these experiments one measures the inelastically scattered particle in coincidence with the decay products of the excited nucleus 7-9). The total resonance width f has two components: F = rt + Fi, Nere f T is the direct component or escape width, due to coupling of the resanance to the continuum, and fl is the spreading width due to coupling of the lplh states of the resonance to the more complicated 2p-2h, . . . ., Hp-nh states. There exists an extensive literature on theoretical calculations regarding the total width F, based on a macroscopic as well as a microscopic approach [see e.g. refs. I*, ’ “1-jrespectively. Ex~~mentally~ little is known on the partial widths f ’ and r”. ~eoreti~ally~ for the giant dipole resonance (GDR) in light nuclei as j60 it is calculated 12) that the total width is mainly due to the escape width; for heavy nuclei, however, the spreading width is dominant, about 90 % for ‘OaPb , For quadrupole excitations (the GQR) theoretical calculations indicate as well that the spreading width is mainly due to coupling to 2p-2h states, This suggests that the decay of the GQR in heavy nuclei will be mainly statistical. Experimentally, it has been found from (a, 01’c) studies, where c is a charged decaying particle (a or p) that in light nuclei (160, 24Mg, 28Si) direct emission is favoured, whereas in medium-weight nuclei (40Ca, 58,62Ni) the decay has been found to be mainly statistical ‘). The large a-decay of the GQR in I60 and other light sd shell nucIei can be understood in the framework of a SU(3) calculation including predominantly lp-i h excitations 13- ’ 5>. In agreement with the predictions, the GDR is known to have a fission probability, similar to the one of the compound nucleus 16). Also, the energy distribution of the decay neutrons of the GDR for “‘Bi indicates that the decay is mainly statistical i7). For the decay of the GQR in actinide nuclei one would also expect that the relative decay width of the fission channel would be similar to that for the compound nucleus. The assumptions underlying this expectation are: (i) the system does not regain its lpi h level (primary doorway) once it has reached the 2p2h level, and (ii) the escape width from the np-nh (n > 1) states before reaching complete equilibrium fprecompound emission) is negligible. isto study the fission
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The first experiments on the decay mode of giant resonances in the actinide region were inclusive electron-induced studies, mainly (e, a) and (e, f) reactions on 238U. An electron-induced cc-decay study on 238U indicated that the GQR decays predominantly (around 50 %) through the a-channel I*). The same group also found that the (e, n) reaction on 238U takes place mainly through El absorption; for E2 decay, an upper limit of only 8 % of the EWSR is exhausted which implies that alpha or fission decay should be dominant 19). However, the subsequent (e, g) experiments on 238U did not confirm these measurements 20-22). Also in electroninduced fission studies on 238U a considerable amount of E2 strength was located at 9 and 9.9 MeV by Shotter et al. 23) and Arruda Neto et al. 24), respectively. Later on, similar results on other uranium isotopes ( 234*236U)were also reported 25). Contrary to these results however, we have found by means of the (a, a’ f) reaction, no evidence for the fission of the GQR in 232Th and 238U which can be interpreted as implying that the GQR has an unexpectedly small fission probability ‘). This result is in agreement with the most recent electron-induced fission experiment, also on 232Th and 238U 26). In this paper on the (e, f) reaction, also the problems involved in extracting reliable estimates for E2 strength from inclusive (e, f) reactions are discussed. Very recently, the results from a (6Li, 6Li’f) experiment 27) on 238U showed the existence of a resonating structure around 9 MeV excitation in the ~ssion-coincident particle spectrum which, however, is difficult to interpret on the basis of the present knowledge concerning the GQR. We have performed a study of the (a, a’ f) reaction at 120 MeV on 232Th and 238U. For both targets, angular distributions of the fission fragments were measured as a function of excitation energy. In this paper, we present the results on the fission probability and fragment angular distribution for the excitation energy region of the GQR. The data are compared with statistical-model calculations. The experimental data in the region of the Iission barrier and the interpretation of the lission probability in terms of a double-humped barrier will be published in a subsequent paper. 2. Experimental procedure The (a, a’ f) experiments were performed in two stages. In both cases, a beam of momentum-analyzed 120 MeV a-particles was obtained from the AVF cyclotron of the Kernfysisch Versneller Instituut (KVI). In the first stage, the inelastically scattered a-particles were detected in a telescope consisting of a 2 mm dE and 5 mm E silicon surface barrier detector. The targets used in this experiment were “OTh (200 @g/cm2 on a carbon backing) and 232Th (650 pg/cm2, self-supporting). Later, we used the QMG/2 magnetic spectrograph 28) for the detection of the scattered a-particles. In this case, the targets used were 232Th(950 pg/cm’) and 238U (1 mg/ cm2). In both cases, the fission fragments were detected in 60 ,um thick silicon surface barrier detectors with active areas varying from 100 to 600 mm’.
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Fig. I. The basic experimental-(left) and electronic setup for the (a, a’f) experiments.
The basic experimental setup for the (a, U’ f) measurements performed with the magnetic spectrograph is shown schematically in fig. 1 together with a simplified block diagram of the electronic setup. For the measurements of angular distributions of the fission fragments, three fission detectors were used simultaneously. The detectors f, and f2 were mounted on a rotatable cover of the scattering chamber of the spectrograph. The angular distributions were measured with respect to the aixs of the recoiling target nucleus, which is 72” for an excitation energy of 11 I’vfeV (the GQR region). The angles in the range of 60-90” with respect to the recoil axis were measured with detector f3, which was mounted on the bottom of the scattering chamber. The distances from the detectors to the target center were about 40 mm for f, and fi, and about 100 m for f3; the solid angle was defined by means of rectangular slits and varied from 0.02 to 0.04 sr. The total opening angle of the fission detectors varied from 2 to 10 degrees. All fission detectors were cooled to a temperature of around -25 “C in order to reduce the noise. The spectrograph was set at an angle of efab = 18”, with a full opening of 6” which corresponds to a solid angle of 4526 = 10.3 msr. The inelastically scattered or-particles were detected in the focal plane of the spectrograph by means of a detection system which basically consists of 3 detectors: 2 position-sensitive devices (resistive wires) and a scintillator 29). The active length of the detection system is about 50 cm, which corresponds to an energy range of around 10 MeV for 120 MeV a-particles. The experimental energy resolution was about 75 keV. The excitation energy scale was calibrated by means of well-known excited states in ‘08Pb. Particle identification was performed by means of the energy signal of the scintillator. A spectrograph event signal was defined as the result of a triple coincidence requirement of both position-sensitive detectors and the scintillator of the focal plane detection system. A coincidence between any of the fission detectors fj(i = 1, 2, 3) and a spectrograph (n, a‘) event defined the final coincidence event (a, a’ fi). For each fission detector, a time signal was created by means of a time to pulse-height converter (tphc), which was started by a fission event and stopped by the scintillator of the focal
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CHANNEL Fig. 2. Time spectrum for the (a, a’f) experiments, showing prompt and random coincidences for both spectrograph detection systems.
plane detection system. Such a time spectrum is shown in fig. 2; the distance between the peaks corresponds to the cyclotron r-f. interval of about 100 ns. The peaks due to prompt and random events can be clearly distinguished so that the contribution of the random coincidence events to the prompt coincidence spectrum can be easily subtracted. One can also recognize the (~1,tff events in this time spectrum, the tritons being delayed by about 70 ns in time of flight through the spectrograph in comparison with the cr-particles. The two time spectra in fig. 2 correspond to the two detection systems beside each other in the focal plane in coincidence with one fission counter. In the experiments described in this paper, only one of the focal plane detection systems covering the excitation energy range from 4 to 14 MeV excitation was used. For each (a, a’ fi) event, a routing unit created a gate for the corresponding linear signals. These signals were handled by a PACE-multiplexed ADC system, which is connected to a PDP-15 computer. Angular correlations were measured by detecting in plane the fission fragments at angles of O*, lo*, 20*, 300, 40, W, 60” (not for 232Th) 7S” and 90” with respect to the recoil axis. The beam current during the measurements was limited to 50 nA, mainly because of the count rate ir, the fission detectors which was held below 10 kHz.
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3. Experimental results The results of the experiment, in which the fission-coincident a-particles scattered from targets of 230Th and 232Th were detected in a AE-E telescope, are shown in fig. 3. The fission-coincident cl-particle spectra show a peak around 6 MeV which
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Fig. 3. Spectra of inelastically scattered a-particles from rJ”Th and ‘9% in coincidence fragments: a-particles were measured with a BE-E telescope.
with fission
is due to the fact that the fission threshold Bf is lower than the neutron binding energy B, for even-even nuclei. Above B,, the fission probability drops down to a nearly constant value because of the competition between fission and neutron decay of the excited nucleus. It rises again to about double its value at an excitation energy slightly higher than Bnf, which is the barrier for second chance fission. Above the third chance fission threshold Bznf at about E, = 18.3 MeV, the spectrum of 232Th shows a bump which is presumably due to the deexcitation of the target nucleus 232Th by two successive neutron emissions, in such a way that the remaining (A - 2) nucleus 230Th is excited above its fission threshold and below or close to the neutron binding energy. The excitation energy difference between the maxima in the fission probabilities and the corresponding thresholds 30*3’) indicates that the average energy of the emitted neutrons must be close to 0.7 MeV. For 230Th, such structures are not so apparent but this might be due to the poor statistics. The structure at 21 MeV in the 232Th spectrum cannot be due to the (a, ‘Li) or (a, ‘He) breakup reaction since this channel opens at about 25 MeV. Of course such a bump might also be due to the decay of some as yet unknown resonance excited in the (a, a’) reaction. The statistics in this experiment were not good enough to make any statement about the decay of the GQR into the fission channel. Therefore, the experiment was repeated using the QMG/2 magnetic spectrograph for detection of the a-particles. The result of the fission fragment angular distribution measurements performed
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Fig. 4. Spectra of fission-coincident a-particles, inelastically at Olsb = l8O and E, = 120 MeV for several angles
355
scattered from 232Th (left) and 23sU (right) with respect to the recoil axis (e_,,).
with the spectrograph are shown in fig. 4. Here the angles, denoted as O,,,,,, (recoil centre of mass), are the angles of the detected fission fragments, relative to the recoil axis of the target nucleus which is - 72” for 11 MeV excitation energy when the cl-particles are detected at Olab= 18O. Some features of these spectra are: (i) the strong anisotropy of the peak between B, and I?,,, which was also found in similar experiments at lower beam energies 32*33); (ii) the absence of a bump between B,
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and B,, which would correspond to the decay of the GQR into fission; (iii) in addition there is evidence for z38U for a broad and rather weakly excited bump at EX L 9.5 MeV and at angles 0, c m, around 50°. The last two points are stressed in fig. 5 in which squeezed spectra at several angles have been added so that gross features are emphasized. The spectrum for angles around the recoil axis (top of fig. 5) is flat and structureless in the region between the neutron binding energy (B, = 6.15 MeV) and the second chance fission threshold (B,,, = 12.5 MeV). For both nuclei, 238U and 232Th [see also ref. ‘)I there is no evidence for a bump originating from excitation of the GQR in the fission-coincident a-particle spectra measured around the recoil axis, although
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Fig. 5. Fission-coincident a-particle spectra, squeezed and summed around the recoil axis (0-20°) and backwards with respect to the recoil axis (5CH0°). Also shown as a dashed curve are the results from the (6Li, “Li’f) experiment, normalized to the (a, a’f) data at 6 MeV. The dotted curve in the lower part of the figure indicates a lower limit for the contribution of the continuum.
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this bump can be clearly seen in the singles spectra as is shown in fig. 6. These singles (a, a’) spectra for 232Th and 238U were taken at Olab= 18” and under the same conditions as the coincident (a, a’ f) spectra, except for the fact that the spectro-
r 232Th(a,a’) 8 LAB=18”
238ub,d) 8LA8=I8* 3000
A
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Fig. 6. Singles spectra of inelastically scattered a-particles at Olab= IF for 23zTh (top) and 238U (bottom). Insert on the right-hand side of the top spectrum: singles spectrum of 232Th at @,,, = 17”, measured with a A!?- E counter telescope. In the bottom spectrum, the shape of the f6Li, ‘Li’) spectrum from ref. *?) normalized to the (a, a’) spectrum at E, = 7.5 MeV is shown (dashed lines).
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graph was focussed on the peaks due to “C and ’ 6O contaminants in the target. In spite of the relatively small excitation energy region selected by the focal plane detector, the bump due to the excitation of the GQR is clearly visible in both cases. The top part of fig. 6 shows the spectrum for 232Th while in the insert a part of a spectrum at elab = 17O,which was measured with a AE- E telescope system 4, is shown. The background and shape of the GQR in the spectrograph spectrum is drawn in a similar manner to the telescope spectrum. As for 238U, the same background as for 232Th has been assumed as indicated in the lower part of fig. 6. Also shown here as dashed lines is the (“Li, (jLi’) spectrum of Shotter et al. 27) with the corresponding background. In this reaction, the peaks due to ’ 2C and l 6O contaminants have been subtracted and the data have been smoothened 27). The (6Li, ‘Li’) spectrum is normalized to (a, a’) at 7.5 MeV excitation energy. For the GQR, both (a, a’) and (6Li, 6Li’) reactions agree with respect to the shape of the bump but for the continuum, the shape seems to be different, a phenomenon which has been observed before [see e.g. ref. ‘)I. The coincidence spectrum measured at backward angles with respect to the recoil axis, which is shown in the bottom part of fig. 5, for 238U shows evidence for a bump centered around E, = 9.5 MeV. It is rather similar to the results from the (6Li, 6Li’f) reaction on 238U, which is also shown. The latter spectrum is measured at an average angle of 65” with respect to the recoil axis, to which also an out-ofplane spectrum (measured at 90”) is added 27). We have normalized the 6Li spectrum to the a-spectrum at the barrier (6 MeV). Thus, for 238U, in both reactions a bump at 9.5 MeV excitation with a width of 2 MeV is found at backward angles with respect to the recoil axis. For 232Th, such a bump is not observed in our (a, a’ f) spectrum but this might be due to the poorer statistics; for 232Th the fission probability is a factor of 4 lower in this excitation energy region compared to 238U. The excitation energy of this bump at 9.5 MeV is definitely below the excitation energy where the GQR has been observed in inelastic scattering 4, 5, and also below the value which one would obtain from the systematic behaviour E, = 65A-* MeV [ref. “)I. This implies that if this bump would be due to fission of a GQR component, it would have to be due to the K = 0 component of the GQR of which it is expected that it will be shifted downward in excitation energy in deformed nucfei [see e.g. ref. j4)]. This would contradict fission angular correlation theory where ifwe assume that Kremains a good quantum number during the fission process, then a K = 0 component of the GQR would be expected to show up strongly in the spectra around the recoil axis ‘). Thus we conclude that with our present knowledge of the behaviour of the GQR in deformed nuclei, and assuming K-conservation during the fission, the bump cannot be due to the fission of the GQR or any of its components. The angular distributions of the fission fragments for a representative excitation energy region around the barrier and for the GQR region are shown in fig. 7. Since the recoil axis changes as a function of excitation energy, different excitation energy
J. van der Plicht et al. 1 (a, aIf) reaction (I)
Fig. 7. Angular
distributions
of the fission fragments observed in the (a, a’f) reaction and 238U (right) for two excitation energy bins.
on 232Th (left)
parts of the spectra are measured in fact at different angles with respect to the recoil axis. In the analysis of the angular distributions, this effect is taken into account. The errors are partly due to statistics, and partly to systematic errors such as in the solid angles of the fission detectors which are around 5 %. The data points (full dots in fig. 7) are obtained at both sides of the recoil axis which in PWBA should be the axis of axial symmetry. As can be seen from fig. 7, the recoil axis is found to be the real symmetry axis indeed within the uncertainty due to the opening angle of the fission detectors which are indicated by the horizontal bars. Similar results have also been found before in (a, a’ f) experiments at 43 MeV [ref. 32)]. Thus all points may be plotted in one quadrant. In fig. 7, the mirror points are indicated by triangles. We have also performed a-fission angular correlation ‘calculations with the program ANGCOR 35), which uses m-state population amplitudes obtained from DWUCK 36). The result is shown in fig. 8 for two azimuthal angles: 4 = 0” (in plane) and 4 = 90” (out of plane). The results for 3 possible L-transfers, and 3 K-values are indicated. This calculation was performed for the (a, a’ f) reaction on 238U at a scattering angle elab = 18” and at an excitation energy of 6 MeV. The kinematical recoil axis is 76O in this case; the angular distributions W(0, 4) are calculated with respect to this axis. The DWBA calculations were performed using the optical-model potential obtained from elastic scattering on *O*Pb at Em = 135 MeV [ref. 37)]. Both plane wave (PWBA, smooth lines) and distorted wave (DWBA, dashed lines) results are shown. In the case of PWBA, the angular distribution yields an expression in Legendre polynomials lP,” = L(cos 8)1* [see e.g. ref. ‘), p.
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Fig. 8. Calculationsof angularcorrelationsfor the (u, a’f) reactionon t38Uat ES = 120MeV,in plane (# = 00)and out of plane (tp = 900).
1701. The DWBA curves are quite similar to those calculated in PWBA; the difference, caused by contributions of substates with M # 0 manifests itself in a shift of about 6O. On basis of these calculations, we conclude that the recoil axis is to a good approximation the axis of rotational symmetry. Thus, from the (a, a’) singles and (a, a’ f) coincidence data, the fission probability Pf can be calculated using the formula P, =
1 2QJGlgles
2n
* N,,,(e)
Sin
8de,
s0
where the factor of 2 in the denominator results from the possibility of detecting either of the two fission fragments [see e.g. ref. 38)]. Using this formula, the fission probability was obtained as a function of excitation energy from the angular correlations of excitation energy bins of about 0.5 MeV or smaller for the barrier region. In these calculations the peaks due to contaminations in the singles (a, a’) spectra were subtracted. The resulting fission probability as a function of excitation energy is shown in fig. 9, together with fission probabilities known from other reactions. For 232Th, the present results concerning the fission probability are somewhat
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Fig. 9. Fission probability spectra as a function of excitation energy for (a, a’f), compared with results from other reactions.
lower than the one published in our first report ‘). At the barrier, our fission probability values can be compared directly with the (t, pf) results from ref. 38). For z38U, the fission probability measured in both reactions are in agreement with each other. For 232Th, the (a, a’ 0 fission probability value is lower than the one for (t, pf) but agrees within the quoted uncertainty for the absohrte accuracy of 20 % of the measured fission probability in the (t. pf) measurement ‘*). For our (a, a‘ f) results, typical error bars are indicated. Also in fig. 9 results from photofission reactions 16, 39), and for 238U the fission probability obtained in the (6Li, 6Li’ f) reaction are included. This probability spectrum has been normalized to the (t, pf) results at the barrier *‘). 4. Discussion of the fission probability of the GQR The fission probability as shown in fig. 9 has been calculated by taking into account the total (a, a’) singles spectrum, thus including the GQR. From these Pt spectra it is difficult to extract definite conclusions concerning the fission decay of the GQR. Although for both nuclei, 232Th and 238U our experimental P,-data points are somewhat below the photofission values as one might expect if the GQR
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would be inhibited to fission, the effect is not very pronounced. Also one should realize that the P, values derived from photofission data are somewhat uncertain although the quoted P, values at around 10 MeV are in agreement with systematics of r,/r, branching ratios [see e.g. ref. ‘)I. Moreover it is not clear that the (y, I) and (a, ~1’f) fission probabilities should be the same although calculations based on the non-resonance version of the model of Back et al. 3*) indicate this to be approximately true 39).
excitation
energy
(MeVl
Fig. 10. Schematical dependence of the fission probability spectrum for *38U (c(, a’f) on the shape of the singles spectra.
Several other assumptions with respect to the fissioning part of the singles spectra can be made though. In fig. IO this is illustrated for 238U in a schematical way. In fig. lOa, the total inelastic (a, cr’) spectrum is used to calculate the fission probability; this plot is thus a schematical representation of fig. 9. The fission probability at an excitation energy of about 11 MeV obtained in this way is somewhat below 20 %, and also below the photofission data. Our results are clearly in contradiction with the results from recent inclusive electron-induced fission studies for the even uranium isotopes 24*25), in which it has been claimed that for instance for 238U there is a concentration of 2+ strength locatedat9.9+0.4MeV,with awidth of r = 6.8f0.4MeVand exhausting (71+7) %
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of the E2-EWSR. If we assume that the 2+ strength found has AT = 0, it would imply, in strong contradiction with our results, that the GQR would have a fission probability of 70 %. This is illustrated in fig. lob, in which it is assumed that the continuum is not fissioning at all and that all the observed fission events would be due to the fission of the GQR. Even in this unrealistic case, the fission probability obtained from our data would only be about 50 %. Recently, Aschenbach et al. 26) have performed a similar inclusive (e, f) experiment. Their data are in agreement with the electro-fission cross sections from Arruda Neto et al. 24). They show though that it is possible to lit their data and thus also the ones from ref. 24) by taking into account only the El virtual photon spectrum, but assuming a different extrapolation of the photo~ssion cross sections to higher excitation energies. Another possible situation is illustrated in fig. 10~. Here it is assumed that only the continuum as indicated in the (M,c(‘) singles spectra is fissioning. The resulting fission probability at E, z 11 MeV is then somewhat higher than the values of Pf = 0.22 deduced from the photo~ssion results. Good agreement with the photofission results is obtained for the case illustrated in fig. 10d. Here the continuum below the GQR in the singles spectrum is drawn slightly higher than before. In this case, an approximately flat fission probability spectrum with Ff. z 0.22 is obtained. Also, the slight bump at about 8 MeV in the fission probability spectrum for ‘j2Th (see fig. 9) disappears for this choice of the continuum underlying the GQR. Thus our results for the fission probability for the continuum can be made consistent with the value deduced from photofission data, by assuming that the continuum underlying the GQR has a shape as indicated in fig. 10d and that the GQR itself does not fission at all. For such a choice of the continuum the cross section of the GQR would be decreased by only 15 %, which is well within the usual uncertainties assigned to such an analysis of (cr, 0~‘)studies 3). The continuum part of the spectrum underlying the GQR excited in (~1,or’) and (‘jLi, 6Li’) is known to be different. This can be explained on the basis of quasielastic processes : inelastic scattering of 6Li produces a negligible amount of direct nucleon knock-out whereas inelastic a-scattering gives rise to such quasielastic processes 9). The quasielastic part of the continuum in the (a, a’) spectra in the excitation energy range E, < B,, z 12.5 MeV cannot contribute to the (a, a’ f) spectrum and thus, if it were present, the fission probability for (a, a’ f) would be lower than for (6Li, 6Li’ f). The data as shown in fig. 9 indicate a different trend: the (a, a’ f) fission probability is higher than the one for (6Li, “Li’ f), even taking into account the uncertainty around 50 y< for the latter reaction 27). Thus from this comparison, it is not possible to estimate the effect of direct nucleon knock-out in (ct, a’) scattering for excitation energies E, < 12.5 MeV. In fact, if we assume that also in the (6Li, 6Li’ f) reaction the GQR as observed in the singles spectrum does not tission, then the fission probability for the continuum in the (6Li, 6Li’ f) reaction becomes PI z 0.2, very similar to the results obtained from the (y, f) and (a, a’ f) reactions.
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With respect to the bump observed in both the (OT,CL’f) and (6Li, ‘Li’ f) reactions at large angles to the recoil axis (see fig. 5) it was ragued in sect. 3 that it is not likely to be due to a fissioning component of the GQR. In order to obtain an angular distribution for this bump which might give. an indication on its nature one has to assume a certain shape and magnitude of the underlying continuum in the (a, 01’f) spectrum. One possible choice for the background was obtained in the following way. The (CI,~1’f) spectra for 8 i Ex S 13 MeV at 00 and 90” with respect to the recoil axis were approximated by a straight line at a constant value indicated in fig. 4 by arrows. For the other angles we assumed that the shape of the continuum is similar to the shape at O”while the magnitude is found from the O”and 90” values using a statistical model caiculation according to Halpern and Strutinsky ‘O) {see next section and fig 13). The counts above the calculated continuum are then integrated, The resulting angular distribution is plotted in fig. 11 and clearly shows the peaking of the effect
238u (n,a’f 1 7,5-12.5MeV
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Pi+ P:
---P:
8fcm Fig. I I. Angular distribution of the resonating bump at 9.5 MeV in 238U (E, a’i) after background subtraction. Calculated curves result fram expansion in Legendre polynomials as indicated.
at angles around 45”, as is already apparent from an inspection of fig. 4. From this angular distribution we can estimate that if this bump originates from a bump in the singles spectrum with the normal fission probability Pf = 0.2, the corresponding bump in the singles spectrum would have a cross section of only 17 % of the GQR bump as shown in figs. 6 and 10. If, on the other hand, this bump results from the fission of the total GQR bump this would correspond to a fission probability of the GQR of 0.034 which is much less than the normalfission probability of 0.2. Here we again assume that the angular distribution pattern is rotationally symmetric around the recoil axis.
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Using an expansion in Legendre polynomials P:(6), this angular distribution can be reasonably well described as IPi I2 or a {lP: 1’+ IPi I”>combination as shown in fig. 11. While the former might be ascribed to a K = 1 component of the GQR, we have argued against that possibility in sect. 3 on account of the fact that it seems to be located lower in excitation energy than what would be expected 34) from the splitting of the GQR in a deformed nucleus. If we, nevertheless, still assume that it would be due to this K = 1 component of the GQR, this would correspond to a fission probability of this component of PC = 0.08, since this component is expected to exhaust 44 % of the total GQR strength for a defo~ation of 6 - 0.3 [see ref. 34)]. combination could be due to a part of the low-energy giant octupole A W:12+ IP:12) resonance (LEOR), of which the K > 0 parts might be shifted to a higher excitation energy than the systematically observed value of 32A-* = 5.2 MeV [see e.g. ref. 3)]. If we assume that the LEOR exhausts 30 % of the EWSR and has a fission probability of P, = 0.2, the bump would then correspond to 25 % of the LEOR (i.e. z 8 ok of the isoscalar E3, EWSR). In this discussion it is assumed that K remains a good quantum number. One obviously can make other choices for the continuum in the coincident spectra. For example, in order to obtain an upper limit for the fission probability for the GQR in our (a, a‘ f) data, one can draw in the (a, a’ f) spectrum of fig. 5 a lower limit background as indicated by the dotted line. With such a choice one obtains an upper limit on the decay of the GQR in 238U of 0.11, assuming a background as shown in fig. 6. This upper limit would become about 0.13, if one assumes that the continuum in the singles spectrum is as indicated in fig. 10d. This number is not in disagreement with the (6Li, 6Li’ f) results where the authors claim 27) that Pf (GQR) > 5 %. It is still considerably lower than the number of 0.22 observed for the GDR though. If the same procedure is applied to the 232Th spectra, an upper limit of 0.025 on the fission probability of the GQR in 232Th is obtained. This number is more realistic than the value published in our first report ‘) and estimated from the a-fission coincident spectrum taken at the recoil axis. One also might assume that the continuum has an angular distribution which is more or less similar in shape to that slightly above the barrier, a more backward peaked angular distribution would result for the observed bump. This would require lP:l2 or IPz/’ or a combination of both to fit the resulting angular distribution. While other possibilities such as lPg12 or IPi12 might as well do, the corresponding giant resonance components are not expected to be present at such low excitation energies with enough strength. A lPi12 or lP~12 distribution could result though from the fission of the K = 1 or the K = 3 component of the isoscalar dipole 41) or isoscalar octupole 3, resonances, respectively, shifted up in energy because of deformation. All of this, however, is speculative; the only rather certain conclusion to be drawn from this analysis is that the bump at 9.5 MeV is due to the fission of an excited state with a spin projection quantum number R > 0.
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5.Statistical calculations It can be seen from fig. 8 that as soon as the neutron channel opens the fission probability as a function of excitation energy drops down exponentially and then levels out after about 8 MeV. It is tempting to try to reproduce this behaviour by calculating the branching ratio m/r, on the basis of a statistical model. Following Vandenbosch and Huizenga ‘), the branching ratio r,/r, is given in the Fermi-gas approximation by the expression
where E is the excitation energy and a,, and 4 are the Fermi gas level density parameters for the residual nucleus after neutron evaporation and for the fissioning nucleus at the saddle point, respectively; B; is an effective fission barrier. The fission probability P, = r&T,+ m) is calculated using the formula given above and thus neglecting the y-decay width rY. The shape of Pfas a function of excitation energy is very sensitive to the ratio +/a,,, but not so much to the absolute values of a, and a,. We have used a, = 25 MeV- ’ x $4, which is a reasonable approximation in the near-barrier region according to ref. 42). The quantities a,/~,, B; and C /-r---T
I
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0
I-.+-u-_-
i___+1
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energy(MeV)
Fii. 12. Fission probability spectra as a function of excitation energy, fitted in the region above the barrier with calculations of the branching ratio FJF,. The insert shows the dependence on the parameters.
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were adjusted to get a best overall fit. The results of the calculations are shown in fig. 12. The effective fission barriers are B; = 6.4 and 6.1 MeV for 232Th and 238U, respectively. These values are close to the barriers known from other reactions and systematics 1’ ‘O), especially for 238U. For both nuclei, 232Th and 238U a level density parameter ratio @,/an = 1.1 gives the best fit. The dependence of the fission probability on the parameters a,/a, and B; is shown in the insert of fig. 12. Although the ratio Z’,/r, is very sensitive to the ratio a,/a,, the fission probability throughout the whole excitation energy interval 7 < E, < 13 MeV can be fitted with one value of a,/a,, indicating that this value is nearly independent of the excitation energy. It is somewhat surprising that the value obtained for a,/a, is close to 1.13, which was found in the analysis of the 23sU(p, xn) reaction results 43). For this reaction, the level density parameters were calculated in the Fermi gas model, and in this model it was found that the ratio a,/a, is nearly independent of excitation energy in the range of 7-17 MeV. For the calculation of the angular distribution as observed for E, > 7 MeV, another statistical model can be used which was developed by Halpern and Strutinsky 40*“). On basis of simple geometrical considerations, they calculated the angular distribution of the fission fragments for a specific nuclear spin Z, assuming that the projection of Z on the z-axis M, = 0 and by averaging over an assumed gaussian K-distribution. The shape of the angular distribution for a specific Z-value and a given average K-value equal to K. is then: W(Z,K,) -
ex,i-
[~~)Jo(i[~~),
where Jo is the zeroth-order Bessel function. This distribution can be integrated from Z = 0 to a maximum value Z,, and is then characterized in terms of a parameter p = (Z~/2~o)2. The underlying assumption M = 0 which in PWBA is the case if the recoil axis is taken to be the z-axis. The (a, a’ f) angular distributions in I
I
I
I
I
I
I
I
23%J(a,a’f I 9-13MeV
Fig. 13. Angular distributions
for the excitation energy region of Y-l 3 MeV, fitted with a statistical calculation for K and I.
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the excitation energy region of 9-13 MeV are shown in fig. 13, together with curves calculated for various parameter values p. For both nuclei 232Th and 238U the data can be well reproduced forp = +, which implies I,,, 2 = 6K$ Thus both, the excitation energy dependence and the angular distribution of the fission probability can be well reproduced by simple statistical calculations. 6. Summa~ and conclusions From the analysis of our (CL,a’f) data on 232Th and 238U, we conclude that the fission probability of the isoscalar giant quadrupole resonance as observed in our inelastic a-scattering data for these nuclei, should be considerably smaller than the fission probability of the GDR as observed from photofission measurements or than the fission probability of the compound nucleus obtained from systematics. On the other hand, a reasonable interpretation of our data indicates that for the continuum underlying the GQR, the fission probability is very close to the value observed in other reactions. Also we have argued that the bump which is observed in the (a, a’ f, spectrum of 238U at an excitation energy of about 9.5 MeV at fission angles large with respect to the recoil axis, and which is similar to the one observed previously in the c6Li, 6Li’ f) experiment 27), is unlikely to be due to a GQR component. If it would though, it would originate from only a fraction of the total observed GQR cross section. Its angular distribution indicates that it originates from an excited state which has a K # 0 component; for instance a state with J = 3 and with a mixture of K = 1 and K = 2 would produce an angular distribution in reasonable agreement with the experimentally observed distribution for this bump. The strongest indication that the fission probability of the GQR in 232Th and 238U is smaller than expected stems from the (a, a’ f) spectrum as observed at around the recoil axis. In both the (6Li, 6Li’ f) data 27) and in our (a, a’ f) data as presented here, these spectra are flat and structureless in the region 7 MeV < E, < B,r, while the corresponding (a, a’) and (6Li, 6Li’) spectra show clearly the bump due to GQR excitation. Of course it is possible that the continuum underlying the GQR in the (a, a’) spectrum has a fission probability strongly dependent on excitation energy and that the combined result of this dependence and the GQR-bump fissioning normally, would produce a flat (a, a’ f) spectrum. We have no way of excluding this possibility, but it would be rather accidental. The difference in behaviour with respect to fission of the GDR and the GQR is perhaps the most surprising conclusion to be drawn from our data. The larger fission probability of the GDR with respect to the GQR may well be due to a special mechanism. It is for instance known that the excitation energy of the K = 0 part of the GDR decreases more rapidly as a function of deformation than the GQR 34). Thus during the defo~ation path leading towards fission it could be that the K = 0 GDR component remains at approximately the same total energy which would
J. van der Piicht et al. f, (a, a’f) reaction (I)
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facilitate direct fission. More detailed calculations, however will be necessary to explain the unexpected behaviour of the decay properties of the GQR in the actinide nuclei as they are presented in this paper. We would like to thank Dr. H. P. Morsch and Dr. A. G. Drentje for their contributions in the early stages of the experiments described and Dr. H. C. Britt for critically reading the manuscript. This work was performed as part of the research program of the “Stichting voor Fundamenteel Onderzoek der Materie” (FOM) with financial support of the “Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek” (ZWO) and was also partially supported by the Bundesministerium fur Forschung und Technologie der Bundesrepublik Deutschland.
References 1) R. Vandenbosch and J. R. Huizenga, Nuclear fission (Academic, New York, 1973) 2) F. E. Bertrand, Ann. Rev. Nucl. Sci. 26 (1976) 457 3) A. van der Woude, Proc. giant multipole Topical Conf., Oak Ridge, USA, 1979, to be published 4) M. N. Harakeh, K van der Weg, A. van der Woude, H. P. Morsch and F. E. Bertrand, Phys. Rev. C2t (1980) 768 5) M. B. Lewis and D. .I. Horen, Phys. Rev. Cl0 (1974) 1099 6) R. Pitthan, F. R. Buskirk, W. A. Houk and R. W. Moore, Phys. Rev. C21 (1980) 28 7) J. van der Plicht, M. N. Harakeh, A. van der Woude, P. David and J. Debrus, Phys. Rev. Lett. 42 (1979) 1121 8) G. J. Wagner, Proc. giant multipole Topical Conf., Oak Ridge, USA, 1979, to be published 9) K. T. Knopfle, Int. Conf. on nuclear physics with electromagnetic interactions, Mainz, Germany, 1979. IO) J. R. Nix and A. J. Sierk, Phys. Rev. C21 (1980) 396 II) G. F. Bertsch, P. F. Bortignon, R. A. Broglia and C. H. Dasso, Phys. Lett. 808 (1979) 161 12) C. Dover, R. Lemmer and F. Hahne, Ann. of Phys. 70 (1972) 458 13) A. Faessler, D. J. Millener, P. Paul and D. Strottman, Nucl. Phys. A330 (1979) 333 14) K. T. Hecht and D. Braunschweig, Nucl. Phys. A295 (1978) 34 15) 0. van Roosmalen and A. E. L. Dieperink, private communication 16) A. Veyssiere, H. Beil, R. Berg&e, P. Carlos, A. Lepretre and K. Kembath, Nucl. Phys, Al99 (1973) 45 17) F. T. Kuchnir, P. Axel, L. Criegee, D. M. Drake, A. 0. Hanson and D. C. Sutton, Phys. Rev. 161(1967) 1236 18) E. Wolynec, M. N. Martins and G. Moscati, Phys. Rev. Lett. 37 (1976) 585 19) M. N. Martins, E. Wolynec and G. Moscati, Phys. Rev. Cl6 (1977) 613 20) D. H. Dowell, P. Axel and L. S. Cardman, Phys. Rev. Cl8 (1978) 1550 21) W. R. Dodge, E. Hayward, G. Moscati and E. Wolynec, Phys. Rev. Cl8 (1978) 2435 22) J. C. McGeorge, A. G. Flowers, A. C. Shotter and C. H. Zimmerman, J. Phys. 64 (1978) Ll45 23) A. C. Shotter, J. C. McGeorge, D. Branford and J. M. Reid, Nucl. Phys. A290 (1977) 55 24) J. D. T. Arruda Neto, S. B. Herdade, B. S. Bhandari and I. C. Nascimento, Phys. Rev. Cl8 (1978) 863 25) J. D. T. Arruda Neto, S. B. Herdade, B. L. Berman and I. C. Nascimento, Int. Conf. on nuclear physics with electromagnetic interactions, Maims, Germany, 1979. 26) J. Aschenbach, R. Haag and H. Krieger, Z. Phys. A292 (1979) 285 27) A. C. Shotter, C. K. Gelbke, T. C. Awes, B. B. Back, J. Mahoney, T. J. M. Symons and D. K. Scott, Phys. Rev. Lett. 43 (1979) 569 28) A. G. Drentje, H. A. Enge and S. 8. Kowalski, Nucl. Instr. 122 (1974) 485 29) J. van der Plicht and J. C. Vermeulen, Nucl. Instr. 156 (1978) 103 30) H. C. Britt, Int. Symp. on physics and chemistry of fission, Jiilich, Germany, 1979, to be published
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31) A. H. Wapstra and K. Bos, Nucl. Data Tables 1913 (1977) 175 32) B. D. Wilkins, J. P. Unik and J. R. Huizenga, Phys. Lett. 12 (1964) 243 33) H. C. Britt and F. Plasil, Phys. Rev. 144 (1966) 1046 34) T. Suzuki and D. J. Rowe, Nucl. Phys. AZ@ (1977) 461 35) M. N. Harakeh and L. W. Put, program ANGCOR, KVI report no. 67, unpublished 34) P. D. Kunz, program DWUCK, University of Colorado, unpublished 37) D. A. Goldberg, S. M. Smith, H. G. Pugh, P. G. Rossand N. S. Wall, Phys. Rev. C7(1976) 1938 38) B. B. Back, 0. Hansen, H. C. Britt and J. D. Garrett. Phys. Rev. C9 (1974) I924 39) A. Gavron, H. C. B&t, P. D. Goldstone, J. B. Wilhelmyand S. E. Larsson, Phys. Rev. L&t. 38(1977) 1457 40) I. Halpern and V. M. Strutinsky, Proc. 2nd Int. Conf. on peaceful uses of atomic energy, 15,p. 408, United Nations, New York (1958) 41) M. N. Harakeh, Phys. Lett. 9oB (1980) 13 42) A. Gilbert and A. G. W. Cameron, Can. J. Phys. 43 (1965) 1446 43) C. J. Bishop, 1. Halpern, R. W. Shaw, Jr. and R. Vandenbosch, Nuci. Phys. A198 (1972) 161
THE STUDY OF THE (a, a’f) REACTION AT 120 MeV ON 232Th AND 238U (I). Fission probabilities and angular distributions in the region of the giant quadrupole resunances J. VAN DER PLIGHT, M. N. HARAKEH
and A. VAN DER WOUDE
Kernfbsisch Versneller Instituut, Groningen. The h’ethertands
and P. DAVID, J. DEBRUS, H. JANSZEN and J. SCHULZE Insfifut .fiir strQhie~- und Ke~nph~sik, Bonn, W. Germany
Received 20 May 1980 Abstract: The fission decay channel of 232Th and 23RUhas been investigated, using the (a,‘a’t) reaction at 120 MeV bombarding energy. The angular distributions of the fission fragments and the fission probabiiities up to around 15 MeV excitation have been measured. No evidence for the fission decay of the giant quadrupole resonance has been found, although for 23EU, a weakly excited structure is seen in the (a, ~‘f) spectrum at about 9.5 MeV excitation at backward angles with respect to the recoil axis. This effect is similar to what has been found in a (6Li, *Li’f) experiment reported recently. The over-all feature of the fission probability for excitation energies above the fission barrier are well reproduced by statistical calculations.
E
I
NUCLEAR REACTIONS 232Th, 238U(a, a’f), E = 120 MeV; measured D (fragment, e) fission probabilities. Discussed fission decay modes in GQR region.
1. In~~uction One of the tools for the study of the fission process is fission induced by direct reactions. In these experiments one can measure the fission probability and the fission fragment angular distributions of the excited nucleus as a function of excitation energy. These experiments have been very important in,establishing the characteristics of the double-humid fission barrier, which originates from the effect of single-particle shell corrections on the smootd liquid-drop barrier [see e.g. ref. ‘), and references therein]. Most experimental work so far has been performed at excitation energies around the fission barrier, which is around 6 MeV. At higher excitation energies, around 11 MeV, another interesting possibility 349
3.50
.I. mm d-rP&&t 6%al.i iu,tvtyi ?‘eaClkm frj
decay channel ofgiantresonances, and thus to learn about the interplay between the very different collective phenomena: fission and giant resonances. Up till now, the study of the isoscalar giant resonances has been mainly concentrated 2,J) on systematics of excitation energies E,, widths r and strength expressed as a fraction of the energy-weighted sum rules (EWSR). For 232Th, the giant quadrupole resonance (GQR) has been measured by means of inelastic scattering of a-particles at E, = 120 MeV. It was found to be located at 1l.OkO.3 Me?‘, has a width of r = 4.OkO.5 MeV and exhausts about 100 74 of the EWSR “). Similar results have been found earlier for 238TJ in inefastic proton scattering 5). In a recent (e, e’) experiment though, Pitthan et al. “) found GQR strength centered around 9.9 MeV. Recently, the main interest has shifted towards the decay properties of giant resonances. In these experiments one measures the inelastically scattered particle in coincidence with the decay products of the excited nucleus 7-9). The total resonance width f has two components: F = rt + Fi, Nere f T is the direct component or escape width, due to coupling of the resanance to the continuum, and fl is the spreading width due to coupling of the lplh states of the resonance to the more complicated 2p-2h, . . . ., Hp-nh states. There exists an extensive literature on theoretical calculations regarding the total width F, based on a macroscopic as well as a microscopic approach [see e.g. refs. I*, ’ “1-jrespectively. Ex~~mentally~ little is known on the partial widths f ’ and r”. ~eoreti~ally~ for the giant dipole resonance (GDR) in light nuclei as j60 it is calculated 12) that the total width is mainly due to the escape width; for heavy nuclei, however, the spreading width is dominant, about 90 % for ‘OaPb , For quadrupole excitations (the GQR) theoretical calculations indicate as well that the spreading width is mainly due to coupling to 2p-2h states, This suggests that the decay of the GQR in heavy nuclei will be mainly statistical. Experimentally, it has been found from (a, 01’c) studies, where c is a charged decaying particle (a or p) that in light nuclei (160, 24Mg, 28Si) direct emission is favoured, whereas in medium-weight nuclei (40Ca, 58,62Ni) the decay has been found to be mainly statistical ‘). The large a-decay of the GQR in I60 and other light sd shell nucIei can be understood in the framework of a SU(3) calculation including predominantly lp-i h excitations 13- ’ 5>. In agreement with the predictions, the GDR is known to have a fission probability, similar to the one of the compound nucleus 16). Also, the energy distribution of the decay neutrons of the GDR for “‘Bi indicates that the decay is mainly statistical i7). For the decay of the GQR in actinide nuclei one would also expect that the relative decay width of the fission channel would be similar to that for the compound nucleus. The assumptions underlying this expectation are: (i) the system does not regain its lpi h level (primary doorway) once it has reached the 2p2h level, and (ii) the escape width from the np-nh (n > 1) states before reaching complete equilibrium fprecompound emission) is negligible. isto study the fission
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The first experiments on the decay mode of giant resonances in the actinide region were inclusive electron-induced studies, mainly (e, a) and (e, f) reactions on 238U. An electron-induced cc-decay study on 238U indicated that the GQR decays predominantly (around 50 %) through the a-channel I*). The same group also found that the (e, n) reaction on 238U takes place mainly through El absorption; for E2 decay, an upper limit of only 8 % of the EWSR is exhausted which implies that alpha or fission decay should be dominant 19). However, the subsequent (e, g) experiments on 238U did not confirm these measurements 20-22). Also in electroninduced fission studies on 238U a considerable amount of E2 strength was located at 9 and 9.9 MeV by Shotter et al. 23) and Arruda Neto et al. 24), respectively. Later on, similar results on other uranium isotopes ( 234*236U)were also reported 25). Contrary to these results however, we have found by means of the (a, a’ f) reaction, no evidence for the fission of the GQR in 232Th and 238U which can be interpreted as implying that the GQR has an unexpectedly small fission probability ‘). This result is in agreement with the most recent electron-induced fission experiment, also on 232Th and 238U 26). In this paper on the (e, f) reaction, also the problems involved in extracting reliable estimates for E2 strength from inclusive (e, f) reactions are discussed. Very recently, the results from a (6Li, 6Li’f) experiment 27) on 238U showed the existence of a resonating structure around 9 MeV excitation in the ~ssion-coincident particle spectrum which, however, is difficult to interpret on the basis of the present knowledge concerning the GQR. We have performed a study of the (a, a’ f) reaction at 120 MeV on 232Th and 238U. For both targets, angular distributions of the fission fragments were measured as a function of excitation energy. In this paper, we present the results on the fission probability and fragment angular distribution for the excitation energy region of the GQR. The data are compared with statistical-model calculations. The experimental data in the region of the Iission barrier and the interpretation of the lission probability in terms of a double-humped barrier will be published in a subsequent paper. 2. Experimental procedure The (a, a’ f) experiments were performed in two stages. In both cases, a beam of momentum-analyzed 120 MeV a-particles was obtained from the AVF cyclotron of the Kernfysisch Versneller Instituut (KVI). In the first stage, the inelastically scattered a-particles were detected in a telescope consisting of a 2 mm dE and 5 mm E silicon surface barrier detector. The targets used in this experiment were “OTh (200 @g/cm2 on a carbon backing) and 232Th (650 pg/cm2, self-supporting). Later, we used the QMG/2 magnetic spectrograph 28) for the detection of the scattered a-particles. In this case, the targets used were 232Th(950 pg/cm’) and 238U (1 mg/ cm2). In both cases, the fission fragments were detected in 60 ,um thick silicon surface barrier detectors with active areas varying from 100 to 600 mm’.
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Fig. I. The basic experimental-(left) and electronic setup for the (a, a’f) experiments.
The basic experimental setup for the (a, U’ f) measurements performed with the magnetic spectrograph is shown schematically in fig. 1 together with a simplified block diagram of the electronic setup. For the measurements of angular distributions of the fission fragments, three fission detectors were used simultaneously. The detectors f, and f2 were mounted on a rotatable cover of the scattering chamber of the spectrograph. The angular distributions were measured with respect to the aixs of the recoiling target nucleus, which is 72” for an excitation energy of 11 I’vfeV (the GQR region). The angles in the range of 60-90” with respect to the recoil axis were measured with detector f3, which was mounted on the bottom of the scattering chamber. The distances from the detectors to the target center were about 40 mm for f, and fi, and about 100 m for f3; the solid angle was defined by means of rectangular slits and varied from 0.02 to 0.04 sr. The total opening angle of the fission detectors varied from 2 to 10 degrees. All fission detectors were cooled to a temperature of around -25 “C in order to reduce the noise. The spectrograph was set at an angle of efab = 18”, with a full opening of 6” which corresponds to a solid angle of 4526 = 10.3 msr. The inelastically scattered or-particles were detected in the focal plane of the spectrograph by means of a detection system which basically consists of 3 detectors: 2 position-sensitive devices (resistive wires) and a scintillator 29). The active length of the detection system is about 50 cm, which corresponds to an energy range of around 10 MeV for 120 MeV a-particles. The experimental energy resolution was about 75 keV. The excitation energy scale was calibrated by means of well-known excited states in ‘08Pb. Particle identification was performed by means of the energy signal of the scintillator. A spectrograph event signal was defined as the result of a triple coincidence requirement of both position-sensitive detectors and the scintillator of the focal plane detection system. A coincidence between any of the fission detectors fj(i = 1, 2, 3) and a spectrograph (n, a‘) event defined the final coincidence event (a, a’ fi). For each fission detector, a time signal was created by means of a time to pulse-height converter (tphc), which was started by a fission event and stopped by the scintillator of the focal
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(a,af 1 IOOns i-7 6000
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f
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CHANNEL Fig. 2. Time spectrum for the (a, a’f) experiments, showing prompt and random coincidences for both spectrograph detection systems.
plane detection system. Such a time spectrum is shown in fig. 2; the distance between the peaks corresponds to the cyclotron r-f. interval of about 100 ns. The peaks due to prompt and random events can be clearly distinguished so that the contribution of the random coincidence events to the prompt coincidence spectrum can be easily subtracted. One can also recognize the (~1,tff events in this time spectrum, the tritons being delayed by about 70 ns in time of flight through the spectrograph in comparison with the cr-particles. The two time spectra in fig. 2 correspond to the two detection systems beside each other in the focal plane in coincidence with one fission counter. In the experiments described in this paper, only one of the focal plane detection systems covering the excitation energy range from 4 to 14 MeV excitation was used. For each (a, a’ fi) event, a routing unit created a gate for the corresponding linear signals. These signals were handled by a PACE-multiplexed ADC system, which is connected to a PDP-15 computer. Angular correlations were measured by detecting in plane the fission fragments at angles of O*, lo*, 20*, 300, 40, W, 60” (not for 232Th) 7S” and 90” with respect to the recoil axis. The beam current during the measurements was limited to 50 nA, mainly because of the count rate ir, the fission detectors which was held below 10 kHz.
J. van der Plicht et al. / {a,
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3. Experimental results The results of the experiment, in which the fission-coincident a-particles scattered from targets of 230Th and 232Th were detected in a AE-E telescope, are shown in fig. 3. The fission-coincident cl-particle spectra show a peak around 6 MeV which
-iiiiii
60
excit?Ytion e6Lgy e&v,
Fig. 3. Spectra of inelastically scattered a-particles from rJ”Th and ‘9% in coincidence fragments: a-particles were measured with a BE-E telescope.
with fission
is due to the fact that the fission threshold Bf is lower than the neutron binding energy B, for even-even nuclei. Above B,, the fission probability drops down to a nearly constant value because of the competition between fission and neutron decay of the excited nucleus. It rises again to about double its value at an excitation energy slightly higher than Bnf, which is the barrier for second chance fission. Above the third chance fission threshold Bznf at about E, = 18.3 MeV, the spectrum of 232Th shows a bump which is presumably due to the deexcitation of the target nucleus 232Th by two successive neutron emissions, in such a way that the remaining (A - 2) nucleus 230Th is excited above its fission threshold and below or close to the neutron binding energy. The excitation energy difference between the maxima in the fission probabilities and the corresponding thresholds 30*3’) indicates that the average energy of the emitted neutrons must be close to 0.7 MeV. For 230Th, such structures are not so apparent but this might be due to the poor statistics. The structure at 21 MeV in the 232Th spectrum cannot be due to the (a, ‘Li) or (a, ‘He) breakup reaction since this channel opens at about 25 MeV. Of course such a bump might also be due to the decay of some as yet unknown resonance excited in the (a, a’) reaction. The statistics in this experiment were not good enough to make any statement about the decay of the GQR into the fission channel. Therefore, the experiment was repeated using the QMG/2 magnetic spectrograph for detection of the a-particles. The result of the fission fragment angular distribution measurements performed
J. can der Plicht et al. / (2, aIf) reaction (I)
Fig. 4. Spectra of fission-coincident a-particles, inelastically at Olsb = l8O and E, = 120 MeV for several angles
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scattered from 232Th (left) and 23sU (right) with respect to the recoil axis (e_,,).
with the spectrograph are shown in fig. 4. Here the angles, denoted as O,,,,,, (recoil centre of mass), are the angles of the detected fission fragments, relative to the recoil axis of the target nucleus which is - 72” for 11 MeV excitation energy when the cl-particles are detected at Olab= 18O. Some features of these spectra are: (i) the strong anisotropy of the peak between B, and I?,,, which was also found in similar experiments at lower beam energies 32*33); (ii) the absence of a bump between B,
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and B,, which would correspond to the decay of the GQR into fission; (iii) in addition there is evidence for z38U for a broad and rather weakly excited bump at EX L 9.5 MeV and at angles 0, c m, around 50°. The last two points are stressed in fig. 5 in which squeezed spectra at several angles have been added so that gross features are emphasized. The spectrum for angles around the recoil axis (top of fig. 5) is flat and structureless in the region between the neutron binding energy (B, = 6.15 MeV) and the second chance fission threshold (B,,, = 12.5 MeV). For both nuclei, 238U and 232Th [see also ref. ‘)I there is no evidence for a bump originating from excitation of the GQR in the fission-coincident a-particle spectra measured around the recoil axis, although
II
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Ill
i
4000 A!? s 00 2000
0 2000 3 8_ xl ii u 1000
0L
6
14 exci+o+ikOn energy (MeV)
Fig. 5. Fission-coincident a-particle spectra, squeezed and summed around the recoil axis (0-20°) and backwards with respect to the recoil axis (5CH0°). Also shown as a dashed curve are the results from the (6Li, “Li’f) experiment, normalized to the (a, a’f) data at 6 MeV. The dotted curve in the lower part of the figure indicates a lower limit for the contribution of the continuum.
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this bump can be clearly seen in the singles spectra as is shown in fig. 6. These singles (a, a’) spectra for 232Th and 238U were taken at Olab= 18” and under the same conditions as the coincident (a, a’ f) spectra, except for the fact that the spectro-
r 232Th(a,a’) 8 LAB=18”
238ub,d) 8LA8=I8* 3000
A
.i excitatm mwgy (MeVJ
Fig. 6. Singles spectra of inelastically scattered a-particles at Olab= IF for 23zTh (top) and 238U (bottom). Insert on the right-hand side of the top spectrum: singles spectrum of 232Th at @,,, = 17”, measured with a A!?- E counter telescope. In the bottom spectrum, the shape of the f6Li, ‘Li’) spectrum from ref. *?) normalized to the (a, a’) spectrum at E, = 7.5 MeV is shown (dashed lines).
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graph was focussed on the peaks due to “C and ’ 6O contaminants in the target. In spite of the relatively small excitation energy region selected by the focal plane detector, the bump due to the excitation of the GQR is clearly visible in both cases. The top part of fig. 6 shows the spectrum for 232Th while in the insert a part of a spectrum at elab = 17O,which was measured with a AE- E telescope system 4, is shown. The background and shape of the GQR in the spectrograph spectrum is drawn in a similar manner to the telescope spectrum. As for 238U, the same background as for 232Th has been assumed as indicated in the lower part of fig. 6. Also shown here as dashed lines is the (“Li, (jLi’) spectrum of Shotter et al. 27) with the corresponding background. In this reaction, the peaks due to ’ 2C and l 6O contaminants have been subtracted and the data have been smoothened 27). The (6Li, ‘Li’) spectrum is normalized to (a, a’) at 7.5 MeV excitation energy. For the GQR, both (a, a’) and (6Li, 6Li’) reactions agree with respect to the shape of the bump but for the continuum, the shape seems to be different, a phenomenon which has been observed before [see e.g. ref. ‘)I. The coincidence spectrum measured at backward angles with respect to the recoil axis, which is shown in the bottom part of fig. 5, for 238U shows evidence for a bump centered around E, = 9.5 MeV. It is rather similar to the results from the (6Li, 6Li’f) reaction on 238U, which is also shown. The latter spectrum is measured at an average angle of 65” with respect to the recoil axis, to which also an out-ofplane spectrum (measured at 90”) is added 27). We have normalized the 6Li spectrum to the a-spectrum at the barrier (6 MeV). Thus, for 238U, in both reactions a bump at 9.5 MeV excitation with a width of 2 MeV is found at backward angles with respect to the recoil axis. For 232Th, such a bump is not observed in our (a, a’ f) spectrum but this might be due to the poorer statistics; for 232Th the fission probability is a factor of 4 lower in this excitation energy region compared to 238U. The excitation energy of this bump at 9.5 MeV is definitely below the excitation energy where the GQR has been observed in inelastic scattering 4, 5, and also below the value which one would obtain from the systematic behaviour E, = 65A-* MeV [ref. “)I. This implies that if this bump would be due to fission of a GQR component, it would have to be due to the K = 0 component of the GQR of which it is expected that it will be shifted downward in excitation energy in deformed nucfei [see e.g. ref. j4)]. This would contradict fission angular correlation theory where ifwe assume that Kremains a good quantum number during the fission process, then a K = 0 component of the GQR would be expected to show up strongly in the spectra around the recoil axis ‘). Thus we conclude that with our present knowledge of the behaviour of the GQR in deformed nuclei, and assuming K-conservation during the fission, the bump cannot be due to the fission of the GQR or any of its components. The angular distributions of the fission fragments for a representative excitation energy region around the barrier and for the GQR region are shown in fig. 7. Since the recoil axis changes as a function of excitation energy, different excitation energy
J. van der Plicht et al. 1 (a, aIf) reaction (I)
Fig. 7. Angular
distributions
of the fission fragments observed in the (a, a’f) reaction and 238U (right) for two excitation energy bins.
on 232Th (left)
parts of the spectra are measured in fact at different angles with respect to the recoil axis. In the analysis of the angular distributions, this effect is taken into account. The errors are partly due to statistics, and partly to systematic errors such as in the solid angles of the fission detectors which are around 5 %. The data points (full dots in fig. 7) are obtained at both sides of the recoil axis which in PWBA should be the axis of axial symmetry. As can be seen from fig. 7, the recoil axis is found to be the real symmetry axis indeed within the uncertainty due to the opening angle of the fission detectors which are indicated by the horizontal bars. Similar results have also been found before in (a, a’ f) experiments at 43 MeV [ref. 32)]. Thus all points may be plotted in one quadrant. In fig. 7, the mirror points are indicated by triangles. We have also performed a-fission angular correlation ‘calculations with the program ANGCOR 35), which uses m-state population amplitudes obtained from DWUCK 36). The result is shown in fig. 8 for two azimuthal angles: 4 = 0” (in plane) and 4 = 90” (out of plane). The results for 3 possible L-transfers, and 3 K-values are indicated. This calculation was performed for the (a, a’ f) reaction on 238U at a scattering angle elab = 18” and at an excitation energy of 6 MeV. The kinematical recoil axis is 76O in this case; the angular distributions W(0, 4) are calculated with respect to this axis. The DWBA calculations were performed using the optical-model potential obtained from elastic scattering on *O*Pb at Em = 135 MeV [ref. 37)]. Both plane wave (PWBA, smooth lines) and distorted wave (DWBA, dashed lines) results are shown. In the case of PWBA, the angular distribution yields an expression in Legendre polynomials lP,” = L(cos 8)1* [see e.g. ref. ‘), p.
I
0
.1_ 0
0
e
180
0
e
IS0
0
0
e
e
IS0
Fig. 8. Calculationsof angularcorrelationsfor the (u, a’f) reactionon t38Uat ES = 120MeV,in plane (# = 00)and out of plane (tp = 900).
1701. The DWBA curves are quite similar to those calculated in PWBA; the difference, caused by contributions of substates with M # 0 manifests itself in a shift of about 6O. On basis of these calculations, we conclude that the recoil axis is to a good approximation the axis of rotational symmetry. Thus, from the (a, a’) singles and (a, a’ f) coincidence data, the fission probability Pf can be calculated using the formula P, =
1 2QJGlgles
2n
* N,,,(e)
Sin
8de,
s0
where the factor of 2 in the denominator results from the possibility of detecting either of the two fission fragments [see e.g. ref. 38)]. Using this formula, the fission probability was obtained as a function of excitation energy from the angular correlations of excitation energy bins of about 0.5 MeV or smaller for the barrier region. In these calculations the peaks due to contaminations in the singles (a, a’) spectra were subtracted. The resulting fission probability as a function of excitation energy is shown in fig. 9, together with fission probabilities known from other reactions. For 232Th, the present results concerning the fission probability are somewhat
J. ran der Plicht er at. 1 fct, alf) reaction (1) II
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I
Fig. 9. Fission probability spectra as a function of excitation energy for (a, a’f), compared with results from other reactions.
lower than the one published in our first report ‘). At the barrier, our fission probability values can be compared directly with the (t, pf) results from ref. 38). For z38U, the fission probability measured in both reactions are in agreement with each other. For 232Th, the (a, a’ 0 fission probability value is lower than the one for (t, pf) but agrees within the quoted uncertainty for the absohrte accuracy of 20 % of the measured fission probability in the (t. pf) measurement ‘*). For our (a, a‘ f) results, typical error bars are indicated. Also in fig. 9 results from photofission reactions 16, 39), and for 238U the fission probability obtained in the (6Li, 6Li’ f) reaction are included. This probability spectrum has been normalized to the (t, pf) results at the barrier *‘). 4. Discussion of the fission probability of the GQR The fission probability as shown in fig. 9 has been calculated by taking into account the total (a, a’) singles spectrum, thus including the GQR. From these Pt spectra it is difficult to extract definite conclusions concerning the fission decay of the GQR. Although for both nuclei, 232Th and 238U our experimental P,-data points are somewhat below the photofission values as one might expect if the GQR
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would be inhibited to fission, the effect is not very pronounced. Also one should realize that the P, values derived from photofission data are somewhat uncertain although the quoted P, values at around 10 MeV are in agreement with systematics of r,/r, branching ratios [see e.g. ref. ‘)I. Moreover it is not clear that the (y, I) and (a, ~1’f) fission probabilities should be the same although calculations based on the non-resonance version of the model of Back et al. 3*) indicate this to be approximately true 39).
excitation
energy
(MeVl
Fig. 10. Schematical dependence of the fission probability spectrum for *38U (c(, a’f) on the shape of the singles spectra.
Several other assumptions with respect to the fissioning part of the singles spectra can be made though. In fig. IO this is illustrated for 238U in a schematical way. In fig. lOa, the total inelastic (a, cr’) spectrum is used to calculate the fission probability; this plot is thus a schematical representation of fig. 9. The fission probability at an excitation energy of about 11 MeV obtained in this way is somewhat below 20 %, and also below the photofission data. Our results are clearly in contradiction with the results from recent inclusive electron-induced fission studies for the even uranium isotopes 24*25), in which it has been claimed that for instance for 238U there is a concentration of 2+ strength locatedat9.9+0.4MeV,with awidth of r = 6.8f0.4MeVand exhausting (71+7) %
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of the E2-EWSR. If we assume that the 2+ strength found has AT = 0, it would imply, in strong contradiction with our results, that the GQR would have a fission probability of 70 %. This is illustrated in fig. lob, in which it is assumed that the continuum is not fissioning at all and that all the observed fission events would be due to the fission of the GQR. Even in this unrealistic case, the fission probability obtained from our data would only be about 50 %. Recently, Aschenbach et al. 26) have performed a similar inclusive (e, f) experiment. Their data are in agreement with the electro-fission cross sections from Arruda Neto et al. 24). They show though that it is possible to lit their data and thus also the ones from ref. 24) by taking into account only the El virtual photon spectrum, but assuming a different extrapolation of the photo~ssion cross sections to higher excitation energies. Another possible situation is illustrated in fig. 10~. Here it is assumed that only the continuum as indicated in the (M,c(‘) singles spectra is fissioning. The resulting fission probability at E, z 11 MeV is then somewhat higher than the values of Pf = 0.22 deduced from the photo~ssion results. Good agreement with the photofission results is obtained for the case illustrated in fig. 10d. Here the continuum below the GQR in the singles spectrum is drawn slightly higher than before. In this case, an approximately flat fission probability spectrum with Ff. z 0.22 is obtained. Also, the slight bump at about 8 MeV in the fission probability spectrum for ‘j2Th (see fig. 9) disappears for this choice of the continuum underlying the GQR. Thus our results for the fission probability for the continuum can be made consistent with the value deduced from photofission data, by assuming that the continuum underlying the GQR has a shape as indicated in fig. 10d and that the GQR itself does not fission at all. For such a choice of the continuum the cross section of the GQR would be decreased by only 15 %, which is well within the usual uncertainties assigned to such an analysis of (cr, 0~‘)studies 3). The continuum part of the spectrum underlying the GQR excited in (~1,or’) and (‘jLi, 6Li’) is known to be different. This can be explained on the basis of quasielastic processes : inelastic scattering of 6Li produces a negligible amount of direct nucleon knock-out whereas inelastic a-scattering gives rise to such quasielastic processes 9). The quasielastic part of the continuum in the (a, a’) spectra in the excitation energy range E, < B,, z 12.5 MeV cannot contribute to the (a, a’ f) spectrum and thus, if it were present, the fission probability for (a, a’ f) would be lower than for (6Li, 6Li’ f). The data as shown in fig. 9 indicate a different trend: the (a, a’ f) fission probability is higher than the one for (6Li, “Li’ f), even taking into account the uncertainty around 50 y< for the latter reaction 27). Thus from this comparison, it is not possible to estimate the effect of direct nucleon knock-out in (ct, a’) scattering for excitation energies E, < 12.5 MeV. In fact, if we assume that also in the (6Li, 6Li’ f) reaction the GQR as observed in the singles spectrum does not tission, then the fission probability for the continuum in the (6Li, 6Li’ f) reaction becomes PI z 0.2, very similar to the results obtained from the (y, f) and (a, a’ f) reactions.
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With respect to the bump observed in both the (OT,CL’f) and (6Li, ‘Li’ f) reactions at large angles to the recoil axis (see fig. 5) it was ragued in sect. 3 that it is not likely to be due to a fissioning component of the GQR. In order to obtain an angular distribution for this bump which might give. an indication on its nature one has to assume a certain shape and magnitude of the underlying continuum in the (a, 01’f) spectrum. One possible choice for the background was obtained in the following way. The (CI,~1’f) spectra for 8 i Ex S 13 MeV at 00 and 90” with respect to the recoil axis were approximated by a straight line at a constant value indicated in fig. 4 by arrows. For the other angles we assumed that the shape of the continuum is similar to the shape at O”while the magnitude is found from the O”and 90” values using a statistical model caiculation according to Halpern and Strutinsky ‘O) {see next section and fig 13). The counts above the calculated continuum are then integrated, The resulting angular distribution is plotted in fig. 11 and clearly shows the peaking of the effect
238u (n,a’f 1 7,5-12.5MeV
-
Pi+ P:
---P:
8fcm Fig. I I. Angular distribution of the resonating bump at 9.5 MeV in 238U (E, a’i) after background subtraction. Calculated curves result fram expansion in Legendre polynomials as indicated.
at angles around 45”, as is already apparent from an inspection of fig. 4. From this angular distribution we can estimate that if this bump originates from a bump in the singles spectrum with the normal fission probability Pf = 0.2, the corresponding bump in the singles spectrum would have a cross section of only 17 % of the GQR bump as shown in figs. 6 and 10. If, on the other hand, this bump results from the fission of the total GQR bump this would correspond to a fission probability of the GQR of 0.034 which is much less than the normalfission probability of 0.2. Here we again assume that the angular distribution pattern is rotationally symmetric around the recoil axis.
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Using an expansion in Legendre polynomials P:(6), this angular distribution can be reasonably well described as IPi I2 or a {lP: 1’+ IPi I”>combination as shown in fig. 11. While the former might be ascribed to a K = 1 component of the GQR, we have argued against that possibility in sect. 3 on account of the fact that it seems to be located lower in excitation energy than what would be expected 34) from the splitting of the GQR in a deformed nucleus. If we, nevertheless, still assume that it would be due to this K = 1 component of the GQR, this would correspond to a fission probability of this component of PC = 0.08, since this component is expected to exhaust 44 % of the total GQR strength for a defo~ation of 6 - 0.3 [see ref. 34)]. combination could be due to a part of the low-energy giant octupole A W:12+ IP:12) resonance (LEOR), of which the K > 0 parts might be shifted to a higher excitation energy than the systematically observed value of 32A-* = 5.2 MeV [see e.g. ref. 3)]. If we assume that the LEOR exhausts 30 % of the EWSR and has a fission probability of P, = 0.2, the bump would then correspond to 25 % of the LEOR (i.e. z 8 ok of the isoscalar E3, EWSR). In this discussion it is assumed that K remains a good quantum number. One obviously can make other choices for the continuum in the coincident spectra. For example, in order to obtain an upper limit for the fission probability for the GQR in our (a, a‘ f) data, one can draw in the (a, a’ f) spectrum of fig. 5 a lower limit background as indicated by the dotted line. With such a choice one obtains an upper limit on the decay of the GQR in 238U of 0.11, assuming a background as shown in fig. 6. This upper limit would become about 0.13, if one assumes that the continuum in the singles spectrum is as indicated in fig. 10d. This number is not in disagreement with the (6Li, 6Li’ f) results where the authors claim 27) that Pf (GQR) > 5 %. It is still considerably lower than the number of 0.22 observed for the GDR though. If the same procedure is applied to the 232Th spectra, an upper limit of 0.025 on the fission probability of the GQR in 232Th is obtained. This number is more realistic than the value published in our first report ‘) and estimated from the a-fission coincident spectrum taken at the recoil axis. One also might assume that the continuum has an angular distribution which is more or less similar in shape to that slightly above the barrier, a more backward peaked angular distribution would result for the observed bump. This would require lP:l2 or IPz/’ or a combination of both to fit the resulting angular distribution. While other possibilities such as lPg12 or IPi12 might as well do, the corresponding giant resonance components are not expected to be present at such low excitation energies with enough strength. A lPi12 or lP~12 distribution could result though from the fission of the K = 1 or the K = 3 component of the isoscalar dipole 41) or isoscalar octupole 3, resonances, respectively, shifted up in energy because of deformation. All of this, however, is speculative; the only rather certain conclusion to be drawn from this analysis is that the bump at 9.5 MeV is due to the fission of an excited state with a spin projection quantum number R > 0.
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5.Statistical calculations It can be seen from fig. 8 that as soon as the neutron channel opens the fission probability as a function of excitation energy drops down exponentially and then levels out after about 8 MeV. It is tempting to try to reproduce this behaviour by calculating the branching ratio m/r, on the basis of a statistical model. Following Vandenbosch and Huizenga ‘), the branching ratio r,/r, is given in the Fermi-gas approximation by the expression
where E is the excitation energy and a,, and 4 are the Fermi gas level density parameters for the residual nucleus after neutron evaporation and for the fissioning nucleus at the saddle point, respectively; B; is an effective fission barrier. The fission probability P, = r&T,+ m) is calculated using the formula given above and thus neglecting the y-decay width rY. The shape of Pfas a function of excitation energy is very sensitive to the ratio +/a,,, but not so much to the absolute values of a, and a,. We have used a, = 25 MeV- ’ x $4, which is a reasonable approximation in the near-barrier region according to ref. 42). The quantities a,/~,, B; and C /-r---T
I
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0
I-.+-u-_-
i___+1
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% I
I
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5
excitation
energy(MeV)
Fii. 12. Fission probability spectra as a function of excitation energy, fitted in the region above the barrier with calculations of the branching ratio FJF,. The insert shows the dependence on the parameters.
_I. van der Plichi et al. ] (a, a’fi reaction
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were adjusted to get a best overall fit. The results of the calculations are shown in fig. 12. The effective fission barriers are B; = 6.4 and 6.1 MeV for 232Th and 238U, respectively. These values are close to the barriers known from other reactions and systematics 1’ ‘O), especially for 238U. For both nuclei, 232Th and 238U a level density parameter ratio @,/an = 1.1 gives the best fit. The dependence of the fission probability on the parameters a,/a, and B; is shown in the insert of fig. 12. Although the ratio Z’,/r, is very sensitive to the ratio a,/a,, the fission probability throughout the whole excitation energy interval 7 < E, < 13 MeV can be fitted with one value of a,/a,, indicating that this value is nearly independent of the excitation energy. It is somewhat surprising that the value obtained for a,/a, is close to 1.13, which was found in the analysis of the 23sU(p, xn) reaction results 43). For this reaction, the level density parameters were calculated in the Fermi gas model, and in this model it was found that the ratio a,/a, is nearly independent of excitation energy in the range of 7-17 MeV. For the calculation of the angular distribution as observed for E, > 7 MeV, another statistical model can be used which was developed by Halpern and Strutinsky 40*“). On basis of simple geometrical considerations, they calculated the angular distribution of the fission fragments for a specific nuclear spin Z, assuming that the projection of Z on the z-axis M, = 0 and by averaging over an assumed gaussian K-distribution. The shape of the angular distribution for a specific Z-value and a given average K-value equal to K. is then: W(Z,K,) -
ex,i-
[~~)Jo(i[~~),
where Jo is the zeroth-order Bessel function. This distribution can be integrated from Z = 0 to a maximum value Z,, and is then characterized in terms of a parameter p = (Z~/2~o)2. The underlying assumption M = 0 which in PWBA is the case if the recoil axis is taken to be the z-axis. The (a, a’ f) angular distributions in I
I
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23%J(a,a’f I 9-13MeV
Fig. 13. Angular distributions
for the excitation energy region of Y-l 3 MeV, fitted with a statistical calculation for K and I.
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the excitation energy region of 9-13 MeV are shown in fig. 13, together with curves calculated for various parameter values p. For both nuclei 232Th and 238U the data can be well reproduced forp = +, which implies I,,, 2 = 6K$ Thus both, the excitation energy dependence and the angular distribution of the fission probability can be well reproduced by simple statistical calculations. 6. Summa~ and conclusions From the analysis of our (CL,a’f) data on 232Th and 238U, we conclude that the fission probability of the isoscalar giant quadrupole resonance as observed in our inelastic a-scattering data for these nuclei, should be considerably smaller than the fission probability of the GDR as observed from photofission measurements or than the fission probability of the compound nucleus obtained from systematics. On the other hand, a reasonable interpretation of our data indicates that for the continuum underlying the GQR, the fission probability is very close to the value observed in other reactions. Also we have argued that the bump which is observed in the (a, a’ f, spectrum of 238U at an excitation energy of about 9.5 MeV at fission angles large with respect to the recoil axis, and which is similar to the one observed previously in the c6Li, 6Li’ f) experiment 27), is unlikely to be due to a GQR component. If it would though, it would originate from only a fraction of the total observed GQR cross section. Its angular distribution indicates that it originates from an excited state which has a K # 0 component; for instance a state with J = 3 and with a mixture of K = 1 and K = 2 would produce an angular distribution in reasonable agreement with the experimentally observed distribution for this bump. The strongest indication that the fission probability of the GQR in 232Th and 238U is smaller than expected stems from the (a, a’ f) spectrum as observed at around the recoil axis. In both the (6Li, 6Li’ f) data 27) and in our (a, a’ f) data as presented here, these spectra are flat and structureless in the region 7 MeV < E, < B,r, while the corresponding (a, a’) and (6Li, 6Li’) spectra show clearly the bump due to GQR excitation. Of course it is possible that the continuum underlying the GQR in the (a, a’) spectrum has a fission probability strongly dependent on excitation energy and that the combined result of this dependence and the GQR-bump fissioning normally, would produce a flat (a, a’ f) spectrum. We have no way of excluding this possibility, but it would be rather accidental. The difference in behaviour with respect to fission of the GDR and the GQR is perhaps the most surprising conclusion to be drawn from our data. The larger fission probability of the GDR with respect to the GQR may well be due to a special mechanism. It is for instance known that the excitation energy of the K = 0 part of the GDR decreases more rapidly as a function of deformation than the GQR 34). Thus during the defo~ation path leading towards fission it could be that the K = 0 GDR component remains at approximately the same total energy which would
J. van der Piicht et al. f, (a, a’f) reaction (I)
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facilitate direct fission. More detailed calculations, however will be necessary to explain the unexpected behaviour of the decay properties of the GQR in the actinide nuclei as they are presented in this paper. We would like to thank Dr. H. P. Morsch and Dr. A. G. Drentje for their contributions in the early stages of the experiments described and Dr. H. C. Britt for critically reading the manuscript. This work was performed as part of the research program of the “Stichting voor Fundamenteel Onderzoek der Materie” (FOM) with financial support of the “Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek” (ZWO) and was also partially supported by the Bundesministerium fur Forschung und Technologie der Bundesrepublik Deutschland.
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