Angular distributions in photofission of thorium and uranium

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Nuclear Physics 70 (1965) 209--218; (~) North-HollandPublishino Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

ANGULAR DISTRIBUTIONS IN P H O T O F I S S I O N OF T H O R I U M AND U R A N I U M E. ALBERTSSON and B. FORKMAN

Department of Physics, University of Lund, Lund, Sweden Received 19 February 1965 Abstract: The angular distributions in photofission of thorium and uranium have been measured. Both bremsstrahlung with a maximum energy of 6.5 MeV and mono-energetic gamma radiation of 6.1, 6.9 and 7.1 MeV were used as photon sources. The fission fragments were detected in soaked emulsions. Strong anisotropy in the angular distribution was observed. The increase of the isotropic term with excitation energy was compared to reported values. These were fitted to a penetration function and a channel fission analysis was performed. E

NUCLEAR REACTIONS, NUCLEAR FISSION ~3ZTh,23sU, (~, fission), E <: 6.5 MeV; [ measured a(E, 0). Natural targets. I 1. Introduction

Two features of the angular distribution of the photofission fragments from even nuclei are of special interest. The first is that the distribution is anisotropic with no or almost no isotropic term at energies close to the energy of the fission barrier height. This fact clearly shows that the nucleus passes slowly over the saddle point and thus is in a well-defined quantum state. It also shows that the projection K of the angular momentum on the symmetry axis is, to a good degree of approximation, a good quantum number when the nucleus passes over the saddle point towards the scission point. This means that the nucleus passes rapidly between the saddle and the seission points, as there would otherwise be a weakening in the anisotropy. This first property is one of the foundation-stones in the model of fission given by A. Bohr ~). The second feature is that the anisotropic distribution quickly disappears as the excitation energy is increased above the fission barrier height. According to Bohr, new fission channels with different K values will be opened, corresponding to intrinsic excitation of the nucleus. At energies below intrinsic excitation, it is expected that only K = 0 channels are available in photo fission of dipole character. Fission through these channels will have an angular distribution given by W(O) = sin20. At energies corresponding to intrinsic excitation, K = 1 channels and new K = 0 channels become available. The K - - 1 channels are characterized by the distribution W(O) = 1 __k sin20. The total angular distribution will therefore be smoothed out. These two properties have been studied with bremsstrahlung of different maximum energies 2-7), but a few measurements with mono-energetic photons s - x~) have been 209

210

E. ALBERTSSON AND B. FORKMAN

reported. In this work are reported new data o n T h 232 with mono-energetic photons and some bremsstrahlung data on Th 232 and U 23s, with a well-defined m a x i m u m energy just greater than the barrier height. A c~treful comparison is made with the other available data.

2. Experimental Arrangements and Measurements Both mono-energetic g a m m a radiation and bremsstrahlung were used in the present study ofphotofission. The fission fragments were recorded in soaked nuclear emulsions. The reaction F19(p, ~?)O 16 was used as a source of mono-energeticgamma-rays. Protons f r o m a 3.5 MeV van de Graaffgenerator bombarded a calcium fluoride target. The g a m m a radiation from this reaction consists of three components with energies 6.14, 6.92 and 7.12 MeV. The relative number of the three various gamma-rays is a function of both proton energy and the target thickness and is given in detail by Ask 12). TABLE 1 Relative composition o f the radiation f r o m the reaction Fla(p, u~,)O 16 at different p r o t o n energies and a target thickness o f 200 keV

v)

1.4

2.5

2.1

6.14

0.76

0.19

0.12

6.92

0.11

0.60

0.15

7.12

0.13

0.21

0.73

The values used in the present work is given in table 1. As a point-source of gammarays with high intensity was required to give good geometry, a rotating, watercooled target was used. With such a target, it was possible to have a proton current of 12/zA and still have a focussing spot with a diameter of less than 0.15 cm on the target without destroying it. The exposure times were about 20 h, corresponding to 1012 photons per sr. In all cases a target thickness of 200 keV was used. While a thicker target would have been preferable in the E v = 1.4 MeV exposure, it was found to crack when heated by the well-focussed proton beam. The bremsstrahlung was obtained from a 6.5 MeV microtron in which the electrons hit a platinum target, at a frequency of 25 pulses per second. The duration of each pulse was 2 /~s and the current 10-15 mA. In the uranium exposure, the emulsions were irradiated for 4 h and in the thorium exposure for 7.5 h. The distance between the target and the emulsions was in both cases 50 cm. To remove photons of lowenergy in the bremsstrahlung, lead with a thickness of 3.5 cm was placed as a filter between the target and the emulsions. This produced an unimportant change in the

ANGULAR DISTRIBUTIONS

211

spectrum above 5 MeV, while permitting a considerable reduction in the background in the emulsions. At first Ilford K minus 1 and K minus 2 emulsions were tried as detectors. It was impossible, however, to obtain a satisfactory separation between alpha and fission tracks, since an unexpectedly high grain density in the alpha tracks was observed. Ilford Inc. recommended a change to the K.O type, suggesting that thorium might extract the copper due to which the emulsions of type K minus 1 and K minus 2 have low sensitivity. When this was done, there were no futher difficulties on this point. The emulsions were soaked for 12 h in either a 5 ~o thorium nitrate solution or a 15 ~ uranyl nitrate solution. The plates were washed with water and were allowed to dry in an atmosphere with 60-70 ~ relative humidity to avoid cracking. After drying, the emulsions hardened again and were wrapped in thin aluminium foils. In the bremsstrahlung exposure of thorium, it was necessary to use a 10 ~ thorium solution in order to obtain enough tracks. Higher concentrations made the separation between alpha and fission tracks difficult. Here were also some difficulties with cracking at the higher thorium concentration. This problem was solved by placing the wrapped emulsions in an excicator with a relative humidity of 76 ~o during the exposure. Such high humidity, also produces a fading, which reduced the background in the emulsions and made a longer exposure possible. After the exposure, the emulsions were washed with running water for two hours to extract the thorium or uranium salt and were then developed in the usual manner. The shrinkage factor was determined using standard methods. The plates were in all cases mounted parallel to the incoming gamma-beam. Only tracks with a dip angle less than 25 ° were accepted. The distribution of the angle between the gamma-beam and the horisontal projection of the tracks was determined and corrections made to obtain the true angular distribution.

3. Experimental Results All the angular distributions obtained show a strong anisotropy, as is expected from earlier experiments 2-1 o). The distributions are shown in fig. 1 where the distributions from ref. s) are also given for comparison. The mono-energetic distributions have been calculated using the composition of the radiation given in table 1. No significant difference has been observed between the results at 6.9 MeV and 7.1 MeV. The distribution obtained is marked 7.0 MeV in the figure. An expression of the form W(O) = a + b s i n 2 0 + c sin 2 20 has been used to fit the experimental points. F r o m the Z2 test and the random errors obtained, it was evident that only the 6.1 MeV exposure on thorium shows a significant c term, which, however, must be further verified before anything is concluded. In the other cases, a new fitting was made with IV(O) = a + b sin 2 0. The method of maximum likelihood has been used, since it also gives a reasonable estimate of the random errors in the parameters. Fig. 1 shows the fitting to the experimental results. The values of the parameters obtained from the fitting are then corrected for the smothing effects cor-

212

E. ALBERTSSON AND B. FORKMAN

responding to the size of the accepted dip angle, different geometrical factors in the experimental arrangement and the scattering of the fission tracks. All these factors are easy to calculate, and the errors in the corrections have been estimated to be of no importance. Table 2 gives the corrected values of the parameters. I

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60 ' ° '

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30 °

l

60 °

l

90 °

0

Fig. 1. Angular distributions from pure 6.1 MeV and 7.0 MeV photon excitation and from 6.5 MeV bremsstrahlung excitation in the present work and in ref. a), TABLE 2 Coefficients in the angular distribution /,V(0)= a+b sin20-Fc sin2 20 in photofission of thorium and uranium Element

Photon energy (MeV)

Th 2a2

U23S

a) Ref. s).

a

b

c

6.1 7.0 6.5 (brernsstr.)

0.124-0.03 0.25 -4-0.04 04-0.05

0.894-0.05 0.78 + 0.06 1.274-0.07

0.144-0.06

6.1 a) 7.0 a) 6.5 (bremsstr.)

0.074-0.08 1.00=[=0.22 0.174-0.03

1.00-4-0.10 0.704-0.22 0.934-0.05

0.50=[=0.12 0.05=[=0.20

213

ANGULAR DISTRIBUTIONS

4. Analysis Most experimental work studying the angular distribution of the fragments in photo fission has been performed with bremsstrahlung 2-7). It is more interesting, however, to study how the angular distribution varies with'the excitation energy. An attempt has been made to transfer the results obtained with bremsstrahlung to mono-energetic photon excitation. The growing of the isotropic term has been chosen as a measure of the behaviour of the angular distribution W(O) with energy. Then it is not needed, at this stage, to discuss the multipolarity of the photon absorption. Two functions are defined which represent this, behaviour; f ( E ) when the nucleus is excited with mono-energetic photons of energy E and g(Eo) when it is excited with bremsstrahlung of maximum energy E o. We then have

g(Eo) =

f:°

a(E)N(E, Eo)f(E)dE,

(1)

where a(E) is the cross section for the photofission process and N(E, Eo) is the bremsstrahlung spectrum. The following normalization of W(O) has been performed: .f~o" W(O) dO = 1. From this normalization it follows that the isotropic term cannot exceed 2/7~. a{ E o

0.~

a~

6

7

8

9 10 11 12 13 Max Brernsstrahlung energy (MeV)

1/*

15

16

Fig. 2. Increase of the isotropic term a in IV(0) with maximum bremsstrahlung energy. The curve is the fitted function g(Eo). The experimental points are from the following papers. 0 • (Th, U) present work; • (U) Baz et al. ~); × I frh, U) Baerg et al. 4); © (Th) Faissner et al. s); • (U) Carvalho et al. e); & (Th) Ballariny 7). F r o m the experimentally known g(Eo) we tried to obtain the function f ( E ) from eq. (1), but found the numerical difficulties too great. Instead we assumed that f ( E ) is a function of type {1 + e x p ([B-E]IEp)} -1, which has the same form as the HillWheeler penetration function 13), with free parameters B and Ep. We then chose

214

e.

ALBERTSSON

AND

B.

FORKMAN

the parameters which gave the best fit to the known O(Eo) values. The fitting is shown in fig. 2. The experimental points in fig. 2 have been obtained from refs. 3-7) and the present paper. The results from Winhold and Halpern 2) are omitted because their values differ in some respects from. more recent ones. The energy errors indicated in some points are due to experimental difficulties in calibrating a betatron. F r o m the figure it is seen that our assumption about the f function gives a satisfactory fitting to the experimental g(Eo) points. The ~r functions used in the calculations were taken from Katz et al. 1+) with a correction at energies close to threshold taken from ref. is). The Schiff spectrum was used as N(E, Eo). From the fitting, we obtained o

i

i

i

i

i

i

r

E .~ 0.6

1 i 0.4

+i

/4

0.:

Photon energy (MeV)

Fig. 3. Increase o f the isotropic term a in W(O) with p h o t o n energy. The curve is the function f ( E ) = 2 / ~ ( l q - e x p ([B--E)/Ep)} -z with B = 7.4 for thorium and B = 6.5 MeV for uranium and. Ep = 0.5 M e V for both. The experimental points are from the following papers: o(Th) present work; • (U) F o r k m a n et aL a); • (U) Takekoshi 9); ~ A (Th, U) Carvalho et aL zo).

a value of Ep = 0.5 MeV for both thorium and uranium. The B value is 7.4 MeV for thorium and 6.5 MeV for uranium and thus markedly different for the two elements. Fig. 3 shows the fitted f functions which have the same shape but are displaced from each other by an amount of 0.9 MeV. The figure also contains the experimental resuits obtained with mono-energetic photons in the present paper and in refs. s-1 o). In refs. s, 9), photons from the F(p, ~?) reaction were used and in ref. lO) from the reaction Ti(n, ?). We have recalculated the isotropic term given by ref. s). Takekoshi 9) has not allowed for the mixture of the three different gamma energies in the reaction F(p, a?); however, the value in fig. 3 is corrected for this. Preliminary results given by Rabotnov et al. x1) with a comparable technique seem to be in agreement with the present work. Regarding the experimental errors, we see in fig. 3 that the fitting of the

ANGULAR DISTRIBUTIONS

215

assumed f functions to the experimental points is quite satisfactory. Both the bremsstrahlung and the mono-energetic photon results thus show that the growth of the isotropic term has a behaviour in accordance with the assumedffunction. 5. Discussion

From the analysis, it is seen that the angular distribution of the photofission fragments from even nuclei has almost no isotropic term at energies close to the fission barrier height. For fission channels close to threshold the K value thus is a good quantum number. The observation that the anisotropy quickly vanishes as the excitation energy is increased is a more complicated problem. A. Bohr suggests that the anisotropy will not be weakened before intrinsic excitation first occurs 1). The energy needed to break up a nucleon pair is of the order of one MeV for a nucleus at its stable shape. For a nucleus deformed to the fission-barrier shape, some indication exists that the same quantity is about twice as large 16,17). Two facts therefore seem to contradict the assumption that the smoothing process is due to intrinsic excitation. The first is that the process starts well below the expected energy for intrinsic excitation and the second that there exist great differences in the energy for the process to start for different nuclei. Different. other possibilities, however, exist that can account for the smoothing process. One is that other types of I = I - , K = 1 states are available below intrinsic excitation. Let us discuss this possibility and try to find the expected states in the energy gap between the saddle point and the energy of intrinsic excitation. The situation is strongly dependent on the form of the potential at the saddle point. Wheeler 18) has thoroughly discussed the expected level scheme for a quadrupole deformed nucleus. Strong proofs, however, exist for the nucleus to be in stable octupole deformation at the saddle point 19). In fig. 4, some of the expected states are shown for the two types of potential. In both cases we see that I = 1-, K = 1 states are available below the intrinsic excitation. The smoothing process of the angular distribution can then be explained. The potential for ~a 0 deformation has two minima separated by a hill if the nucleus has a stable octupole deformation. The K = 0 rotational band, close to the saddle point, is fully developed in such a potential, with both plus and minus states 2°'21). The energy gap between a plus state and the next minus state is increased due to inversion, but this effect will be negligible if the potential hill is of the order of several MeV as is proposed by Johansson 19). At the saddle point the pear-shaped nucleus will probably be less soft for ~a 0 vibration than the cigar-shaped nucleus in its ground state, and we need more energy to excite such a vibration. Thus at the saddle point the ~30 vibrational band will lay higher in a pear-shaped nucleus than in a cigarshaped one. We should also expect a coupling between the states in the low-lying rotational band, and the corresponding states in the c~30 vibrational band with the same spin values. This will further increase the energy gap between them.

216

E.

ALBERTSSONAND B. FORKMAN

The inversion also causes a splitting o f all states with K # 0 in a plus and a minus state. For K # 0 we thus have four sublevels for each J value arising f r o m the K

[ntr;nslc excitation energy

_ _

5-

5* 2- -

- -

1-53-

- -

3÷

cff22

°(22

- - - -

~.

6-

_ _

r-

.

.~.:

.....

5* 4-

/ 3*

;:

c(30

5-

m

I: d30

/3~ddle point energy

K=0

K=I

K=2

K=O

K=I

K=2

Fig. 4. Expected energy levels with low spin values in the energy gap between the saddle point energy and the intrinsic excitation energy for a stable quadrupole and a stable octupole deformation. The splitting from Coriolis coupling is schematic and overstated.

ANGULAR DISTRIBUTIONS

217

degeneracy and the inversion doubling. The splitting on account of the tunnelling motion is still small, but we get a splitting f r o m Coriolis coupling which is schematically shown in fig. 4. The position of the 1- K = 1 states and the admixture of 1 K = 0 states in them are strongly dependent of the position of the 1 - K = 0 states. The admixture of K = 1 states in the lowest 1 - K = 0 state must be small, however, on account of the anisotropy in the angular distribution. Let us assume that only two I = 1 - states are available for fission, one with K = 0 and the other doubly-degenerate, with [KI = 1. If the states are well separated, the first channel is completely opened before the second is accessible. It is then possible directly to compare the fission width of the second state with our f function which gives the increase of the isotropic term F2 = ( 1 + exp ([B + fl - EI/Ep)} - x,

(2)

where B and Ep are the free parameters in t h e f f u n c t i o n and fl is 1.4 Ep. Thus ( B + r ) is the energy position of the second state and Ep is the barrier f o r m factor, which for a fission channel 15) has the value 0.085 MeV. The Ep value obtained from the f function is 0.5 MeV showing that the two-channel picture is too simple. In fig. 4 we see that this is indeed the case. We expect to have two 1 - K = 0 states. The upper of these and the 1 - K = 1 states are perturbed states. We also may have a splitting of the K degeneracy if the nucleus is not axial symmetric. The 2 + states and 1 +states available may very well affect the angular distribution and contribute to the smoothing process. Thus we have enough parameters to explain the high Ep value in the f function. We can expect differences from element to element in the smoothing process depending on the position of the mentioned states. It is a little unexpected, however, to find such a great difference in the B value for Th 232 and U 23s. The Th 232 nucleus is more elongated at the saddle point than U 23s, and we should expect to find the a3, vibrational states at a lower energy in Th 232 than in U 23s. To get a fair estimate of the position of the different states a detailed calculation must be made as m a n y different factors are involved. A strong quadrupole part in the angular distribution from U 23s was reported in ref. s) at 6.14 MeV excitation with mono-energetic photons. This was also seen by Takekoshi 9). There has, however, been some discussion about this quadrupole term by R a b o t n o v et aL '1) since they did not observe it. When we exposed U 23s with 6.5 MeV bremsstrahlung we expected to see the quadrupole term, but this was not the case. A difference in the mode of fission between a 6.14 MeV excitation and a 6.5 MeV bremsstrahlung excitation can be explained in the following way. In a small energy region of excitation above the 6.0 MeV threshold of the (y, n) process, we should expect E2 photofission to be favoured, as the (y, n ) p r o c e s s will strongly compete with E1 photofission. This is due to the spin value of the U 237 ground state which is predicted to be ½+. When new states with higher spins are available, the E2 photofission will be suppressed. The E2 resonance around 6 MeV predicted by Shevchenko

218

E. ALBERTSSON A N D B. FORKMAN

e t a/. 22) should be remembered in this discussion. Finally the 6.14 MeV photons have a very narrow energy width (F ~ 0.05 meV) which is much smaller than the expected level spacing in U 23s. This could very well lead to an accidental favouring of 2 + excitation. A new experiment, however, with higher precision is needed to solve the question about the quadrupole term in the angular distribution from U 2as at 6.14 MeV excitation. Very recently Soldatov e t a/. 23) report in a letter new results on the anisotropy in the angular distribution of fission fragments from U 23s, which was excited with bremsstrahlung from a microtron. The growing of the isotropic term with the maximum bremsstrahlung energy agrees quite well with earlier resuls shown in fig. 3. At excitation energies below the fission barrier height they report a strong quadrupole term in the angular distribution which is of interest in the discussion of available fission channels and of the quadrupole term at 6.14 MeV excitation.

The authors wish to express their gratitude to Professor S. A. E. Johansson and Professor S. G. Nilsson for many fruitful discussions and to Mrs. K. Malmqvist for her help with numerical calculations on the computer SMIL. References 1) A. Bohr, First U.N. Int. Conf. on the Peaceful Uses of Atomic Energy, Vol. 2 (United Nations, Geneva, 1955) p. 151 2) E. J. Winhold and I. Halpern, Phys. Rev. 103 (1956) 990 3) A. I. Baz et al., Second U.N. Int. Conf. on the Peaceful Uses of Atomic Energy, Vol. 15 (United Nations, Geneva, 1958) p. 184 4) A. P. Baerg et al., Can. J. Phys. 37 (1959) 1418 5) H. Faissner and F. GOnnenwein, Z. Phys. 153 (1958) 257 6) H. G. de Carvalho, A. G. da Silva and J. Goldemberg, Nuovo Cim. 19 (1961) 1131 7) M. V. Ballariny, Notas Fis. 10 (1963) 205 8) B. Forkman and S. A. E. Johansson, Nuclear Physics 20 (1960) 136 9) E. Takekoshi, J. Phys. Soc. Japan 15 (1960) 2129 10) H. G. de Carvalho et aL, Nuovo Cim. 29 (1963) 463 11) N. S. Rabotnov et aL, Congr6s International de Physique Nucl6aire, 4e/C337 Vol. II, Paris (1964) p. 1135 12) L. Ask, Ark. Fys. 19 (1961) 219 13) D. L. Hill and J. A. Wheeler, Phys. Rev. 89 (1953) 1102 14) L. Katz, A. P. Baerg and F. Brown, Second U.N. Int. Conf. on the Peaceful Uses of Atomic Energy, Vol. 15 (United Nations, Geneva, 1958) p. 188 15) T. Kivikas and B. Forkman, Nuclear Physics 64 (1965) 420 16) J. J. Griffin, Phys. Rev. 132 (1963) 2204 17) H. C. Britt et aL, Phys. Rev. Lett. 11 (1963) 343 18) J. A. Wheeler, Fast neutron physics, Part II, ed. by J. B. Marion and J. L. Fowler (Wiley and Sons, New York, 1963) chapt. V, S 19) S. A. E. Johansson, Nuclear Physics 22 (1961) 529 20) G. Herzberg, Infrared and Raman spectra of polyatomic molecules (D. van Nostrand, New York, 1945) 21) A. Bohr and B. R. Mottelson, Lectures on nuclear structure and energy spectra, Institute for Theoretical Physics and Nordita, Copenhagen (1962) to be published 22) V. G. Shevchenko, N, P. Yudin and B. A. Yur'ev, JETP (Soviet Physics) 18 (1964) 128 23) A. S. Soldatov et aL, Phys. Lett. 14 (1965) 217