Photon-induced nuclear reactions above 1 GeV

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Nuclear PhysicsA197 (1972) 81--87; ~ ) North-HollandPublishing Co., Amsterdam Not to be reproduced by photoprint or microfilmwithout written permissionfrom the publisher

PHOTON-INDUCED

NUCLEAR

REACTIONS

ABOVE

1 GeV

(HI). Fission in gold and lead I. KROON and B. FORKMAN Department of Nuclear Physics, Lund Institute of Technology

and Department of Physics, University of Lund, Professorsgatan 3, S-223 63 Lurid, Sweden Received 16 May 1972 Abstract: The photofission cross section per equivalent quantum and the forward-to-backward ratios of gold anti lead have been measured in the bremsstrahlung energy range 1.0-7.4 GeV using glass detectors. The experimental data are analysed using data from an earlier lowerenergy experiment done at Lund with the same experimental technique. It is verified that the fission cross sections for the two target elements are almost constant above 1 GeV. From the moderate dependence of the forward-to-backward ratio on photon energy it is concluded that the excitation energy of the fissioning nucleus and the momentum transferred to it are rather independent of photon energy. The forward momentum deposited at the instant of fission is shown to increase only slowly, decreasing from 40 % to 10 70 of the compound-nucleus value in the energy interval studied.

1. Introduction T h e i n t e r m e d i a t e a n d high-energy p h o t o fission cross sections f r o m the heaviest nuclides, such as u r a n i u m a n d t h o r i u m , to elements as light as nickel have been m e a sured in several l a b o r a t o r i e s using different experimental techniques. I n spite o f the large fission p r o b a b i l i t y for the heaviest elements, e x p e r i m e n t a l values for i n t e r m e d i a t e p h o t o n energies n e a r a n d a b o v e the first m e s o n resonance at 0.3 G e V are u n e x p e c t e d l y scattered. This is due to the use o f b r e m s s t r a h l u n g b e a m s as p h o t o n sources, which gives large c o n t r i b u t i o n s to fission f r o m giant-resonance energy p h o t o n s . T h e general feature o f the cross sections o b s e r v e d experimentally is a b r o a d m e s o n r e s o n a n c e reflecting the b e h a v i o u r o f the t o t a l p h o t o p i o n - p r o d u c t i o n cross-section curve 1) a n d a m o r e o r less p r o n o u n c e d decrease in cross sections for higher p h o t o n energies z - 5 ) . F o r lighter elements, Z < 83, the g i a n t - r e s o n a n c e fission c o n t r i b u t i o n is u n i m p o r t a n t because o f higher fission t h r e s h o l d s a n d smaller values o f the fission p a r a m e t e r Z 2 / A . The fission cross section reaches a c o n s t a n t value at o r s o m e w h a t a b o v e the m e s o n resonance with no o b v i o u s decrease at higher energies 2 . 6 - 9). I n the w o r k o f V a r t a p e t y a n et aL 5) it is shown t h a t the p h o t o f i s s i o n yields agree satisfactorily with the yields calculated o n the basis o f the p h o t o m e s o n i c m o d e l o f the fission process. This indicates t h a t the p h o t o m e s o n m e c h a n i s m is o f the greatest i m p o r t a n c e in p r o d u c ing photofission in this energy region. 81

82

I. KROON AND B. FORKMAN

Proton- and photon-induced fission mechanisms are expected to show many similarities. Nevertheless some fundamental differences exist. The threshold energy for pion production is higher in the proton case for kinematical reasons. Photopion production becomes the dominating photo-interaction process inside the nucleus above the photomeson threshold whereas in the proton case pion processes never dominate in comparison to elastic nucleon-nucleon scattering. This explains the fact that the plateau value for the proton fission cross section in elements with Z < 83 is reached at about twice the corresponding photon energy 6). Consequently it is easiest to investigate meson effects in a photofission experiment using not-too-heavy target elements. Angular distributions of fission fragments in high- and intermediate-energy photofission have been studied in a few cases z, 4-6, 8,1 o). Within experimental errors isotropic angular distributions are reported in refs. 2, 6,1 o). Wakuta 4) observed a faint forward-backward peaking in the c.m. for intermediate-energy photofission of uranium, but isotropy for thorium. In our previous work 8), a small forward peaking in the lab system was obtained in tantalum, gold and lead for bremsstrahlung energies below 1 GeV. This was attributed to nuclear motion of the post-cascade nucleus. From measured fragment forward-to-backward ratios some conclusions concerning the absorption mechanism, the de-excitation stage and the fission process were also drawn. In the recent work of Vartapetyan et al. 5) this forward peaking is verified for elements with Z < 83 but the angular distributions of photo fission fragments for Z > 90 were shown to be isotropic. The present work is an extension to higher energies where experimental photofission data are very few. The same geometrical arrangements as before are used and the fission cross sections and forward-to-backward ratios are determined using glass detectors. The experimental details are described in part I of this work.

2. Calculations

In fig. 19 of I the ratio Nf/Nb (Emax) is given as a function of the logarithm of the bremsstrahlung end-point energy. The straight lines fitted to the two sets of experimental points are evidently adequate representations of the experimental data. Using the 1/E spectrum approximation and the extrapolated intersections of the two straight lines with the energy axis in fig. 17 of I as threshold photofission energies, the photon energy dependence of the ratio

p = Nf/Nb(E ) is easily derived. Fig. 1 shows the ratio p as a function of photon energy. The observed anisotropy in the lab angular distributions of photofission fragments from gold and lead could be explained by introducing a moving nuclear system. In this reference system the angular distributions of fission fragments are assumed to be

P H O T O N - I N D U C E D R E A C T I O N S (II[) '~'1

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I

t

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10

Fig. 1. The calculated photon-energy dependence o f the measured forward-to-backward ratios p for the two target elements A u and. Pb.

isotropic. According to Porile and Sugarman 11) and Sugarman et aL 12) the nuclear velocity ~ in the lab system should be added vectorially to the fragment velocity yielding the lab fission fragment velocity. If the component of ~ perpendicular to the photon beam direction is much less than the parallel component, Oll, the ratio r/i I •

VlI/V ~ v/V

could be calculated from the observed forward-to-backward ratios. In the lab system the number of fission fragments is integrated for incidence angles on the glass plates less than the maximum angle to produce visible tracks in them. The target thickness relative to the fission-fragment ranges in the target material and the insensitivity of the glass detector to low-energy fragments have been considered in the calculations. For actual target thicknesses, the value of t/LI is given by the expression

r/ll

p-1 (p+l)(1 + costp,)

where p is the forward-to-backward ratio defined above and qh is the maximum incidence angle to produce visible tracks in the etching procedure. The value qh = 53° has been used in the numerical calculations. In fig. 2 the dependence of/711 on photon

84

I. K R O O N

L

I

I

A N D B. F O R K M A N

t

I

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1

I

Au 0.101 l

Pb

0.05

0

0

I

!

t

1

2

3 4 Photon energy (GeV)

I

l

f

5

6

I

7

Fig. 2. T h e calculated r/i I values (see text) as a function o f p h o t o n energy E. J

-

I

Au

I

I

L

I

I

I I I

I

i

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Ta

~

Pb

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0

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1.0

Photonenergy(GeV)

_1

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I I

10

Fig. 3. T h e ratio ~711t17o as a function o f p h o t o n energy for A u a n d Pb. T h e d a s h e d curve for T a i.< calculated f r o m o u r previous work a).

PHOTON-INDUCED REACTIONS (III)

85

energy is given. This quantity is rather independent of energy for higher energies reflecting the general features in fission also observed in proton-induced fission 13 - 14). The compound-nucleus value of r/ll, r/o, which corresponds to no net momentum loss due to the cascade, was also calculated. It was taken into account that a number of nucleons are evaporated before fission occur. The kinetic energies of the fission fragments in the photofission of Au, Bi and U have been measured by K o m a r et al. 15). Although their values are considerably lower than those theoretically calculated by Nix and Swiatecki 16) using a liquid-drop model, the experimentally determined values are used in this work. In fig. 3 the ratio r/ll/r/0 is given as a function of photon energy. It should be particularly noted that this ratio is approximately equal to 1 around the first meson resonance and decreases rapidly for increasing photon energies. The dashed curve given for tantalum in fig. 3 refers to forward-to-backward measurements for tantalum from a previous lower-energy experiment a). 3. Discussion

The present investigation shows that the fission cross sections for elements near mass number 200 are rather constant in the energy region from 1 GeV to 7 GeV. A small and broad resonance peak correlated with the first photomeson resonance is however observed below 1 GeV. The general shape of the cross-section curve is the same as that obtained by Vartapetyan et al. 5), although their analysis, which is based on very few experimental points above 1.6 GeV, indicates a decrease in the fission cross section above 1 GeV. Except for these differences there is a general resemblance with other measurements reported in similar works 2, 6-9). The early work of Jungerman and Steiner 17) also indicates a meson resonance in the photofission of gold and bismuth. However, their experiment is restricted to photon energies up to 500 MeV and the decrease in their cross-section curves for the higher energies is uncertain as their experimental errors are rather large. The structure found in the cross-section curves in fig. 18 of I shows up first when an efficient unfolding method and a very good bremsstrahlung spectrum approximation are used. Due to the mathematical simplicity of the 1/E spectrum approximation it is widely used. According to table 3 of I the observed mean fission cross sections at different laboratories are in agreement, although the experimental arrangements and the detectors used are quite different. At energies above 1 GeV, the cross-section values in the table ought to be reduced by about 20 % in the light of the shape of the curves in fig. 18 of I. The experimentally obtained forward-to-backward ratios in the previous work and here could be considered as a kinematical effect of the reaction mechanism. Previously it was shown that the angular distributions of fission fragments were isotropic in the c.m. system within experimental errors. In straightforward calculations described above, the nuclear velocity component in the photon direction at the moment of fission break-up was obtained. In the two-step reaction model the de-excitation pro-

86

I. KROON AND B. FORKMAN

cess is interpreted as a very fast nuclear cascade followed by a competition between fission and particle evaporation. For nuclei with mass numbers near 200 the fission cross section is very small compared to the total photon-nucleus reaction cross section. Above 1 GeV the fission cross section amounts to about 5 ~o and 12 ~ of this latter cross section for gold and lead respectively. From fig. 3 it is evident that the momentum of the fissioning nucleus is rather close to the compound-nucleus value when produced with photon energies near the first meson resonance. This means that most of the energy of the photon is transferred to the nucleus. Consequently the pion and the recoil nucleon produced in the photon absorption process must be absorbed in the nucleus if fission shall occur. The pion kinetic energy for these photon energies is known to be correlated with the energy of the large resonance peaks in the pion-nucleon absorption and scattering cross-section curves 18, 19). A compilation of experimental cross-section data for elementaryparticle reactions is given by Giacomelli 20). From fig. 2 it is concluded that the momentum and energy deposited in the postcascade fissioning nucleus increase very slowly with increasing photon energy above the meson resonance. The nuclear cascade will carry away a rapidly increasing fraction of the photon energy and momentum according to fig. 3. Contrary to the proton case, no complete Monte Carlo calculations based upon experimental results combined with theoretical models yielding estimates of such quantities as post-cascade deposition energy and number of emitted particles have been published. On the whole the differences in these properties for photon- and proton-induced fission are expected to be small. The distribution of nuclear post-cascade energies for actual particle energies and nuclei is probably very broad with a mean value somewhere round 200 MeV. The post-cascade de-excitation stage in the fission process could be discussed in some detail. It is possible to imagine two quite different types of de-excitation, particularly for nuclei such as gold and lead which have low fission probabilities. In the first model it is assumed that the fission width in the neutron-fission competition chain is almost independent of excitation energy. The first part of the de-excitation thus consists nearly exclusively of neutron evaporation resulting in a slow increase in the ratio Z 2/A. Consequently the fission probability compared to the neutron emission probability increases and fission takes place at the end of a long evaporation chain at low excitation energies. Only a small fraction of the initial momentum is dissipated by the neutrons. Even fission at high bombarding energies reveals low-energy characteristics. In the second approach the fission width is considered to increase significantly with increasing excitation energy in such a way that fission takes place in the early stages of the de-excitation process. The fragments still possess excitation energy and neutron evaporation continues from nuclei with much higher velocities. Fission at high energies should be different from fission at low energies. From the experimental point of view the two models are very difficult to distinguish

PHOTON-INDUCED REACTIONS (11I)

87

between. T h e r a t h e r c o n s t a n t p h o t o f i s s i o n cross section a n d the slowly increasing postcascade excitation energy, shown for instance in the energy d e p e n d e n c e o f qLI in fig. 2, suggest t h a t the first m o d e l is a p p l i c a b l e in the present case. F r o m s p a l l a t i o n r e a c t i o n studies L i n d g r e n a n d J o n s s o n 21) have concluded t h a t photofission in g o l d occurs late in the d e - e x c i t a t i o n stage being p r e c e d e d by the e v a p o r a t i o n o f a b o u t l0 neutrons. The same general b e h a v i o u r has also been observed in a large n u m b e r o f chargedp a r t i c l e - i n d u c e d fission experiments. The r a t h e r c o n s t a n t value o f t/lI in fig. 2 a n d the r a p i d decrease in qll/t/o given in fig. 3 c o u l d be discussed further. F r o m M o n t e C a r l o calculations on p r o t o n - i n d u c e d reactions, it is shown t h a t t/i I a n d the p o s t - c a s c a d e d e p o s i t i o n energy E* are i n t i m a t e l y correlated. I n nuclei with very high d e p o s i t i o n energies, the cascade loss o f p r o t o n s a n d the p r o b a b i l i t y o f c h a r g e d - p a r t i c l e e v a p o r a t i o n are increased. Since the fissility is a sensitive function o f Z 2 / A Jt is r e d u c e d for such nuclei. F o r high b o m b a r d i n g p r o t o n a n d p h o t o n energies fission p r o b a b l y occurs in a n a r r o w range o f p o s t - c a s c a d e d e p o s i t i o n energies at a b o u t 200 MeV.

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21)

C. E. Roos and V. Z. Peterson, Phys. Rev. 124 (1961) 1610 L. G. Moretto et aL, Phys. Rev. 179 (1969) 1176 T. Methasiri, Nucl. Phys. A158 (1970) 433 Y. Wakuta, J. Phys. Soc. Jap. 31 (1971) 12 G. A. Vartapetyan et al., Soy. J. Nucl. Phys. 14 (1972) 37 A. V. Mitrofanova, Yu. N. Runyuk and P. V. Sorokin, Soy. J. Nucl. Phys. 6 (1968) 512 T. Methasiri and S. A. E. Johansson, Nucl. Phys. A167 (1971) 97 I. Kroon and B. Forkman, Nucl. Phys. A179 (1972) 141 V. Emma, S. Lo Nigro and C. Milone, Nuovo Cim. Lett. 2 (1971) 117, 271 Yu. N. Ranyuk and P. V. Sorokin, Sov. J. Nucl. Phys. 5 (1967) 26 N. T. Porile and N. Sugarman, Phys. Rev. 107 (1957) 1410 N. Sugarman etaL, Phys. Rev. 143 (1966) 952 L. P. Remsberg et al., Phys. Rev. C1 (1970) 265 J. A. Panontin and N. T. Porile, J. Inorg. Nucl. Chem. 33 (1971) 3211 A. P. Komar et al., Sov. J. Nucl. Phys. 10 (1970) 30 J. R. Nix and W. J. Swiatecki, Nucl. Phys. 71 (1965) 1 J. A. Jungerman and H. M. Steiner, Phys. Rev. 106 (1957) 585 N. Metropolis et aL, Phys. Rev. 110 (1958) 204 H. W. Bertini, Phys. Rev. 131 (1963) 1801 G. Giacomelli, Progress in nuclear physics, vol. 12 (Pergamon, Oxford, 1970) p. 77 K. Lindgren and G. G. Jonsson, Nucl. Phys. A166 (1971) 643