Absolute photofission cross section of 209Bi in the energy range from 40 to 65 MeV

Nuclear Physics A342 (1980) 37-52

(1

@ North-Holland Publishing Co., Amsterdam

Not to be reproduced by photoprint or microfilm without written permission from the publisher

ABSOLUTE

PHOTOFISSION

IN THE ENERGY

OF ‘“Bi FROM 40 TO 65 MeV

CROSS SECTION

RANGE

H.-D. LEMKE and B. ZIEGLER Max-Planck-Institut fiir Chemie, D-6500 Mainz, W Germany M. MUTI’ERER and J. P. THEOBALD Institut

fiir Kemphysik der Technischen Hochschule Darmstadt, D-6100 Darmstadt, W Germany and N. C&JAN Max-Planck-Institut fiir Chemie D-6500 Mainz, W Germany and Centre d’Etudes Nucliaires de Bordeaux-Gradignan, F-331 70 Gradignan, France Received 26 November 1979

photofission cross section of ‘OgBi has been measured with monoenergetic y-radiation between 40 and 65 MeV photon energy. Cross-section data have been obtained with an accuracy between 9 and 20%. The experimental result is compared with the excitation function calculated on the basis of the statistical model. In order to reproduce the measured data on ati, the (-y,n) cross section must decrease with increasing photon energy faster than the experimental total (y, n) cross section. This behaviour can possibly be explained by the assumption that after photon absorption a compound nucleus is formed only for a small, and with photon energy decreasing, fraction of all decays.

Abstract: The absolute

E

PHOTOFISSION

“‘Bi(y, f), E = 40-65 MeV; measured cz; deduced total photoabsorption u for compound nucleus formation.

1. Introduction The photofission

cross section of bismuth has already been measured with bremsstrahlung in the photon energy range from 30 to 1000 MeV [refs. ‘-‘)I. There exists also a measurement of the electrofission cross section for electron energies between 25 and 70 Me’V [ref. “)I. For the analysis of these experiments, i.e. the determination of the cross section from measured fission yields as a function of electron or photon-spectrum end-point energy, the shape of the real or virtual y-spectrum is of capital importance. There is not yet, however, an exact bremsstrahlung theory, which simultaneously takes shielding effects by atomic electrons, Coulomb corrections to electron wave functions, multiple scattering and energy loss in the bremsstrahlung target into account 5*6).Since the fission cross section grows steeply with increasing photon energy, the fission yield is mainly determined by the high-energy part of the bremsstrahlung spectra. This unfortunately is where the 17

38

H.-D. Lemke et al. 1 Photofission

shape of the spectrum is particularly uncertain. Cross sections deduced from bremsstrahlung ‘) and electrofission experiments “) disagree in the common energy range by more than 30%. A model calculation ‘) shows that the use of differently approximated bremsstrahlung spectra introduces uncertainties of up to *20%. Therefore, a measurement with monoenergetic y-radiation has been performed at the positron annihilation facility of the linear electron accelerator laboratory in Mainz 8). The technical parameters of this photon source restrict the y-energy range to between 40 and 65 MeV. The photon flux is more than 100 times smaller for the monochromatic than for a modest bremsstrahlung y-source. The low y-intensity demands therefore a fission-fragment detector with high efficiency and large sensitive area. The evaluation of cross section measurements with monochromatic y-radiation is comparatively simple, since the experimental fission yield, corrected for self-absorption of fragments in the sample layers and for background count rates, is directly proportional to the photofission cross section, the number of nuclei in the target, and the photon flux ‘).

2. Experimental

setup

The experimental setup is shown in fig. 1. In a tantalum conversion target 140 MeV electrons generate bremsstrahlung, which is partly converted into electron positron pairs. The positrons emitted in the forward direction into a solid angle of 1.65 x lo-* sr are analysed in energy and focussed onto a low-2 annihilation target. There, monochromatic photons are generated by two-photon annihilation in flight. The full relative width at half-maximum of the monochromatic photon line amounts to 2.85% at 40 MeV and 2.60% at 65 MeV. The collimated photon beam of about 2 x lo6 y/s hits the fission-fragment detector, which is a multiple ionization chamber with 32 chamber gaps, each of which contains one bismuth target layer. The average Bi thickness is 2.34*0.06 mg/cm*, the diameter of the 32 chambers is 15.2 cm and the purity of the bismuth metal 99.99995%. The total amount of Bi irradiated is about 13.4 grams. The detector with its associated electronic circuit is shown in fig. 2. A detailed description is published elsewhere 9). Behind the fission chamber, the photon flux is measured with a replica of the i’*“), which is an absolutely calibrated ionization chamber. NBS-P2-quantameter

3. Experimental 3.1. ABSOLUTE

PHOTON

FLUX

procedure

DETERMINATION

The experimental procedure is prescribed by the fact that the annihilation photons are, even from low-Z conversion targets, accompanied by bremsstrahlung. However, as the cross section for positron annihilation is proportional to the atomic

H.-D. Lemke et al. / Photofksion

-Experimental

39

Hall

+--=-It tt P2

FD

N

Fig. 1. Positrons are produced in the magnet hail at the conversion target CT; they are energy anafysed by the 90” magnet system St -Ss and the energy defining slit ES. Positrons are fed through the collimator C into the experimental hall, where they are focussed by the quadrupol magnets Q3 onto the ann~h~ation target AT. Nickel collimators NC define the dimension of the mon~hromatic r-beam, which irradiates the fission detector PD. The calibrated quantameter P2 of the NBS-PZ-type measures the y-intensity.

-

Bi- target

Fig. 2. Block diagram of the electronic circuit with chamber-piate connections. The bismuth targets are only evaporated onto negative electrodes. The alternate polarities of the vohages applied to adjacent chambers, the difference amplifiers and the analog multiplexer connected to them provide compensation of background ionization 9).

number 2 while that for bremsstrahlung goes with Z(Z + 1) of the target material, the bremsstrahlung contribution can be subtracted by using two different annihilation targets with atomic numbers Z1 and Z2 and target thicknesses adjusted in a way that the same intensity of bremsstrahhmg is produced in both targets. The difference of fission-fragment spectra measured alternately in the photon fluxes from both targets contains only the fission yield from monochromatic photons as

40

H.-D. Lemke et al. / Photofission

Photon

energy

Fig. 3. Schematic plot of the photon spectrum composed of bremsstrahlung (B,(E)) and annihilation y radiation (M,(E)). The hatched difference spectrum contains only a part of the y-line spectrum; bremsstrahlung from the Be and Cu targets cancel. T+ is the kinetic energy and mc’ the rest energy of the positrons.

illustrated schematically in fig. 3. Doing so, it is assumed that the shapes of the two bremsstrahlung spectra are identical for both atomic numbers Z1 and Z2 of the target materials. In order to avoid differences due to other than Z2 proportional bremsstrahlung contributions (Coulomb corrections are proportional to Z4, screening effects to approximately 22.5), a moderate value for the larger Z is advisable. We have chosen the target pair Be and Cu. As already mentioned, the fission yield has been recorded by the multiplate ionization chamber in the fluxes from the alternating Be and Cu targets. The ionization currents of the quantameter is in both cases proportional to the energy flux of the radiation and can be expressed by Kl,,

1; =

(Y(E)[Bi(E) + Mi(E)]E dE

I0

(1)

with the following notation: I+ is the ionization current (A), i labels Be or Cu, E is the photon energy (MeV), E,,, is the bremsstrahlung end point energy (MeV), B(E) is the bremsstrahlung photon-number spectrum (MeV-’ . s-l), M(E) is the annihilation photon-number spectrum (MeV-’ - s-l), a(E) is the experimental calibration factor of the quantameter which has only a weak energy dependence (Cb . MeV-‘). For electron-induced bremsstrahlung, a similar expression holds 1; = I0

EmaX or(E)Bi(E)E dE .

(2)

If we define the ratio of the two electron induced ionization currents, f- =

G/I&

as a measure for the ratio of the annihilation

9

target thicknesses weighted by the

41

H.-D. Lemke et al. / Photofission Z(Z

+

1) proportional

bremsstrahlung yield factors, we can calculate the difference E I;, -f-l:” = msXa U%%,(E) (4) - f-MG)IE dE I0

in which the bremsstrahlung contribution cancels. The integrand represents the ionization current induced by the narrow y-line with energy Eo. The flux of monochromatic photons no can therefore be written as no=

,(Ei)Eo (IL -f-G).

(5)

During the measurements, the ratio of the two positron induced ionization currents can also be determined in the alternating y-fluxes from the Be and Cu targets, respectively,

f += &L/Id” ,

(6)

and the photon flux can be written as I+Be

no=

dEo)Eo

(1-ff’ >*

f- and f’ as functions of the

Fig. 4 shows the measured electron and positron ratios monochromatic photon energy Eo.

L5

50

55

(7)

60

65

4

P

Energy (MeVl

+

(L 127 LO

I

I

L5

50 Energy

Fig. 4. The ratios f- and f

I 55

I 60

I 65

(MeVl

(subsect 3.1) as functions of electron and positron total energy.

42

H.-D. Lemke et al. / Photofission

Consequently, the difference of the rates of fission events n; induced by the monochromatic parts of the spectra is given by ny=nfBe-f-np=nr

Be

f- IL --7TnfCU, f IC”

(8)

where n; is the rate of fission events with the Be target and rtp with the Cu target. rrf represents the net fission yield. The accuracy of the ratios f- and f’ determines the error of the photon-number measurement. Since the monochromatic energy flux is energy independent and the bremsstrahlung yield increases with energy, the positron ratio falls off with increasing photon energy and approaches the electron ratio (fig. 4). This reduction of monochromatic y-intensity relative to the bremsstrahlung puts an upper limit to the useful photon range. For the pair of target materials Be and Cu this limit is 70 MeV. The lower end of the useful photon energy range follows from the fact that the positrons are analysed by a magnet with constant dp/p. Towards smaller energies, dp and also the photon intensity passing the energy slit is proportional to E. This decrease of photon flux and the smaller fission cross sections limit the measurement to photon energies above 35 MeV. Consequently, the experiment is not suitable for a precise determination of the fission barrier height. The quantameter calibration was checked with a calorimeter placed in bremsstrahlung beams of different end-point energies rr). The ionization current for a given radiant flux was found in agreement with the original NBS calibration within less than 2% [ref. “)I. 3.2. BISMUTH

TARGET

DEFINITION

The bismuth metal is evaporated onto 30 urn thick aluminum backings which are also the negative electrodes of the multiple ionization chamber. The average target layer thickness has been determined by weighing to be 2.34 f 0.06 mg/cm’, a value supported by an X-ray absorption scanning+. For each of the plates, both methods agree within 2.5%. A typical thickness profile is shown in fig. 5, where the radial dependence due to the evaporation geometry is obvious. Within the dimension of the y-beam area, the bismuth layer thickness is (4.3*0.8)% higher than the average thickness.

3.3. FRAGMENT

ABSORPTION

IN THE

BISMUTH

TARGETS

The pulse-height distribution of the fission fragments has been calculated with a Monte Carlo code using known data on mass, energy, nuclear charge and angular distributions for fission fragments of bismuth ‘**r3). Details of this calculation are t We thank Prof. Fricke, Mainz, for supporting

the X-ray sample scanning work.

H.-D. Lemke et al. / Photofission

f

C---d,=

F 2.30 -t-------------dBi

1

8

6

I

1

L Distance

43

9.Lcm ---+ = 15.2 cm-----------_1-

I

I

2

0

2

from

center

0

E

I

I

L

6

0

I

Fig. 5. Bismuth target profile as measured by X-ray absorption. dui is the diameter of the Bi layer area, d, the diameter of the collimated monochromatic photon beam.

published elsewhere 7*9). In this way, not only could the fission-fragment pulseheight distribution be extrapolated to zero amplitude, but also the relative number of fragments absorbed in the target layers could be determined. The reliability of this method has been verified in a series of measurements with good statistical accuracy in a high-intensity bremsstrahlung beam. Several different target thicknesses were employed. Fig. 6 shows a comparison of calculated and measured fission-fragment pulse-height distributions. For the error on the absolute cross section by background subtraction and self-absorption correction, an upper limit of 5% is estimated.

3.4. URANIUM

IMPURITIES

As the photofission cross section of uranium at 40 MeV photon energy is about three orders of magnitude larger than that of bismuth, the uranium content in the Bi 150 -

5 g 100 5 \ In 5 s

so-

O0

100

200 Channel

300

LOO

500

number

Fig. 6. Comparison of calculated and measured fission-fragment pulse-height distribution. The background, approximated by an exponential function, is well separated from the fragment distribution.

44

H.-D. Lemke et al. / Photofission

samples as well as in the Al backings has been analysed with mica track detectors in the thermal column of the Karlsruhe reactor FR2+ in an integrated flux of 4.7 x 1Ol7 neutrons/cm*. The relative uranium impurities (U/Bi or U/Al atomic ratios) turned out to be 9 x lo-‘* (*50%) in the bismuth samples, and 8 X 10e7 (*50%) in the aluminum backings. The contribution of these small impurities to the fission yield is negligible for all photon energies. 3.5. FAST NEUTRON

INDUCED

FISSION

Fast photoneutrons are emitted mainly from the tantalum conversion target in the magnet hall (fig. 1). The fast neutron background penetrating through the 3 m thick heavy concrete wall from the magnet hall into the experimental hall grows more rapidly with increasing electron energy than the positron intensity. Therefore, the electron energy was kept constant at 140 MeV. Fast neutrons are distributed almost uniformly over the experimental hall. Their contribution to the observed fission yield was measured by placing the detector just outside the photon beam, maintaining all other experimental conditions. The upper limit for neutron induced fission events, including fission of uranium impurities, turned out to be 0.2% of the photofission counts. 4. Results Fission-fragment pulse-height distributions have been recorded at photon energies between 40 and 65 MeV (table 1). The pulse-height distributions for the highest photon energy are displayed in fig. 7, together with a difference spectrum as described in subsect. 3.1. Summing up all difference spectra obtained at the different photon energies allows a comparison with calculated spectra (fig. 8) and thus the TABLE Summary

E+ (MeV) 65 60 55 50 47.5 45 42.5 40

1

of data with monochromatic

J% (MeV) 64.45 59.49 54.52 49.55 47.07 44.59 42.10 39.60

No (1cl’O) 1.70 1.41 3.88 9.95 10.40 30.50 16.29 32.92

NY-f 234*47 188*33 314*39 407 f 42 263*37 664*58 243 f 29 208*31

photons

cy,r ( 10m3’cm’) 61.5* 12.2 59.4* 10.3 36.lk4.4 18.2* 1.9 11.4~1~1.6 9.7kO.8 6.6ZtO.8 2.9kO.4

E’ is the kinetic energy of the positron (MeV); E. is the c.m. energy of the annihilation line (MeV); No is the total number of monochromatic photons for that energy; NY,, is the total number of fission events produced by No and mYv.‘ is the fission cross section deduced from No and NY.r.

t We thank the Kernforschungszentrum

Karlsruhe GmbH for supporting the sample analysis work.

45

H.-D. Lemke et al. / Photofission I

120 z g

I

80-

5 \ s2

I

i'

a.1

$ titt LO-

+tt+

++

+

0 0

I 0

100

t-t ( ++++++++t++++++++&+*

200 Channel

120 -

O0

I

100

I

200 Channel

120 -

I

I

300

LOO

500

number I

I

300

LOO

500

number I

I

zi C 5

80C.)

5 In 5 s

co-

0 0

100

200 Channel

300

LOO

500

number

Fig. 7. Fission-fragment pulse-height distribution from measurements with the Be and Cu annihilation targets [(a) and (b)], with contributions from bremsstrahlung and annihilation photons. c shows the difference distribution due to part of the monochromatic y-spectrum only.

extrapolation to zero pulse height and subtraction of the background. The final data are summarized in table 1, The photofission cross section in column 5 of table 1 is plotted in fig. 9, where also the results of Tiirck et al. “) and Moretto et al. ‘) are displayed. The errors are statistical errors only.

H.-D. Lemke et al. J Photofission

46 300.

I

I

I

1

5 = 200 -

0 5 \ In T 3 loos

0. 0 Channel

number

Fig. 8. Sum of all difference distributions together with the fission fragment response curve calculated by a Monte Ca;lo code (full line), and the exponential function for the background. 100

/-

0. /'

Turck >, P

,.n’ ./’ ;’ 10 -

,‘P

6 ! 5

5 f

4

Moretto

_

P,/’

f

/‘P

5_

P:

,/”

*09BIly,fl

.!; 2/

I 50

’ LO Photon

I 60

energy

(MeV)

Fig. 9. The result of the present measurement. The dashed curve represents data of Moretto et al. ‘), the dashed-dotted curve data of Tiirck et al. 4).

5. Discussion

of the results

The measured photofission cross section has been compared excitation function calculated using the statistical model r4),

with the fission

E-B,

VYf --2--

ffYf _

UYT

uyn

fi2 4MR2

10

~209(E-&-WdK

(9)

E-S,

p20,3(E-S,,-~)~

dc

'

I0

with the following notations: E is the excitation energy in the compound nucleus, u,?r is the total photoabsorption cross section which is, in a good approximation, equal to the cross section for photoneutron emission cry,,, ~209 is the nuclear level density of

H.-D. Lemke et al. / Photofission

47

“‘Bi at saddle-point deformation, p208 is the nuclear level density of the residual nucleus 208Biat ground-state deformation, Bt is the fission barrier height of “‘Bi, S. is the neutron separation energy of 2oQBi(7.45 MeV), h4 is the neutron mass, R is the Bi and h2/4MR2 is equal to 0.142 MeV. Therefore for the nuclear radius of 2oQ calculation of the photofission cross section one needs: (i) The total photoabsorption cross section in the energy range between 40 and 65 MeV photon energy. In this energy range the “quasideuteron effect”, i.e. the initial or final-state interaction of the absorbing nucleon with one closeby neighbour, competes with the giant-resonance reaction. Since compound nucleus formation is a condition for the validity of formula (9), it is not at all certain, which part of the measured total photoneutron cross section has to be inserted into formula (9). (ii) The level densities as functions of excitation energy and deformation in the fission degree of freedom. There exist approximate formulas 15)as well as numerical results from microscopic calculations 16). One can correct them also for the contributions of the low-lying collective states “), but this correction vanishes at higher excitation energies (-30 MeV), where the calculated level densities take automatically more complex nuclear states into account I’). (iii) The height Bf of the fission barrier. This value is known either from cross section measurements close to the fission threshold 4, or from calculations 19)with a semi-empirical mass formula. The experimental barrier from (e, e’f) data “) is 24.3 f 1.5 MeV, the theoretical barrier is 23.9 MeV [ref. “)I. A systematic theoretical study of fission barriers for elements in the lead region is given in ref. 20). In a first step we try to reproduce the measured data by a calculation using the following input: (a) For the total photoabsorption cross section, data on 208Pb measured with monochromatic -y-radiation in the same energy range 21).

Fig. 10. Nuclear surfaces for three deformations used in the level density calculations. Circles show results from the liquid drop model parametrisation by Nix *4).

48

H.-D. Lemke et al. / Photofission

(b) For the level densities, numerically calculated values based on a microscopical model ‘*). The saddle-point shape of *09Bi was described by a Cassini oval 23), with a deformation parameter of E = 0.8 or E = 0.9. Fig. 10 shows the corresponding shapes, together with that predicted by Nix 24). The ground state of *“Bi has been assumed to be spherical (E = 0.0). Concerning the nuclear parameters, they were chosen to reproduce the experimental single-particle and single-hole energies in the lead region 25). The resulting level densities are plotted in fig. 11 and the spin cut-off parameters used to determine the relative population of three possible spins in the compound nucleus (5 g and 9) are plotted in fig. 12. (c) For the fission barrier height: 25.6 MeV (for E = 0.8) or 24.9 MeV (for E = 0.9). Under these conditions the experimental data are fairly well reproduced as can be seen in fig. 13. However, the slope of the calculated excitation function differs considerably from that of the experimental cross section curve. Attempts ‘) to see the

5 0 0

I

I

I

1;

30

L5

Excltatlon

05 Nuclear

energy

60

(MeVI

10

15

temperaturelMeV1

Fig. 11. Numerical level densities used in the statistical model calculations r’), plotted as functions of excitation energy (a) and nuclear temperature (b) for the two most probable saddle-point deformations E = 0.8 and 0.9 of the fissioning nucleus so9Bi [(l) and (2)], and for the ground state (E = 0) of the residual nucleus so8Bi (3). Curves are shown with and without (dashed curves) pairing force.

IX-D. Lemke et al. / Photofisjion

49

I& 300 z E i 200

Fig. 12. Spin cut-off parameters as a function of nuclear temperature. The dotted curves correspond to microscopic calculations while the solid ones to smooth (Fermi gas) values.

LO

loo-

60

50 Photon

energy

(MeVI

,

0

LO

l3t = 2.5.9 MeV-

@

E,

=25.8MeV

60 energy

MeV

0

50 Photon

6‘ =23.8

I MeVI

H-D. Lemke et al. j Photofission

50

influence of the choice of the level densities and fission barrier heights on the shape of the calculated excitation function show that reasonable variation of the level-density parameters did not change the slope (energy dependence) of the calculated cross section while its mean value could be restored by more or less drastic modifications of the fission barrier height. It has been suggested recently **) that such discrepancies between experimental and caIculated fission excitation functions could be explained by the inclusion of an arbitrary excitation-ener~ dependence of the collective ~ntributions to the level densities. This dependence should be determined from the fit to the experimental data. Such an analysis ‘*) of the fission cross section of 2’oPo indicates that already at 30 MeV excitation energy the collective corrections are already very small. Since the slope of the curve calculated without collective corrections (fig. 13) differs considerably from experiment even beyond this energy and since 209Bi is expected to behave similar with 210PO one can hardly invoke the abovementioned explanation here. These difficulties in interpreting the ‘09Bi data lead us to the assumption that only part of the total photoabsorption cross section represents compound nuclear processes. If we use eq. (9) to calculate the total cross section OyT= uCfrom the measured fission cross section, we get 8 values between 40 and 65 MeV which can be intepreted as that part of total photoabsorption competing with fission and passing through compound-nucleus formation. This 0;: is compared in fig. 14 with the total (‘y, n) cross section measured by the Saclay group *‘). Since uCfollows the trend of the tail of the lorentzian curve fitted to the giant resonance part of the Saclay total photoabsorption cross section data (dashed line in fig. 14), it is obvious that we can reproduce the slope of our experimental photofission cross section curve, if we use only this part of the total photoabsorption cross section, which describes the excitation of a giant resonance. The difference between the measured total (‘y, n) cross section above

1 Saclay **ePb

”

30

to

50

f

Bt=238MeV

f

a,=231

60

70

-

MeV

80

Photon energy IMeVI

Fig. 14. Total photoneutron cross sections (crosses) given in ref. ‘*I. The dashed fine is the tail of a iorentzian function fitted to the El -giant resonance. For two fission barrier heights, the photo cross section for compound nuclear reactions o, is plotted.

H.-D. Lemke et al. / Photofission

51

40MeV and the u, values deduced from photofission, is evidence for nuclear excitations which decay by particle emission before the compound state is formed 26). With this interpretation, the most probable fission barrier height is 23.4 MeV assuming E = 0.9. 6. Conclusion The present experiment

has given photofission cross section data between 40 and 65 MeV photon energy with an accuracy between 9 and 20%. The values obtained are smaller than those from electrofission 4), but larger than those deduced from a bremsstrahlung measurement ‘). A calculation based on the statistical model of nuclear reactions relates the fission cross section to the total photoabsorption cross section. It reproduces fairly well the mean fission cross section in the energy range considered, but not the slope of the measured excitation function. If, however, we consider as competing with the photonuclear reaction only the giant resonance excitation, which proceeds through compound-nucleus formation, we get agreement between calculated and measured photofission excitation functions, with a fission barrier height close to 24 MeV. The remaining part of the total photoabsorption cross section above the tail of the giant resonance curve (80% at 60 MeV) presumably represents decays through precompound nuclear states, for which particle emission is dominant. We thank Prof. U. Kneissl for critical comments on the interpretation of the data and Dr. Tiirck for discussions and his help with the analysis of uranium impurities at the Kernforschungszentrum Karlsruhe GmbH. Last but not least we thank Prof. H. Waffler for his support of this work. References 1) L. G. Moretto, R. C. Gatti, S. G. Thompson, J. T. Routti, J. H. Heisenberg, L. M. Middleman, M. R. Yearian and R. Hofstadter, Phys. Rev. 179 (1969) 1176 2) J. M. Ranjuk, V. M. Sanin and P. V. Sorokin, Ukr. Fiz. Zh. 14 (1969) 408 3) R. C. Jensen and R. V. Warnock, J. Inorg. Nucl. Chem. 30 (1968) 2011 4) D. Tiirck, H. G. Clerc and H. Trlger, Phys. Lett. 63B (1976) 283; D. Tiirck, Thesis, Darmstadt (1975) 5) H. W. Koch and J. W. Motz, Rev. Mod. Phys. 31(1959) 920 6) U. Fano, H. W. Koch and J. W. Motz, Phys. Rev. 112 (1958) 1679 7) H. D. Lemke, Thesis, Mains (1979) 8) A. Hauptmann, Thesis, Mainz (1972) 9) H. D. Lemke, B. Ziegler, J. Foh, M. Mutterer and J. P. Theobald, Nucl. Instr. 169 (1980) 89 10) J. S. Pruitt and S. R. Domen, J.R. NBS &%A(1962) 11) H. Burckhart, R. Diehl and B. Ziegler, Nucl. Instr. 159 (1979) 1 12) M. Areskoug, H.-A. Gustafsson, G. Hyltdn and B. Schriider, Z. Phys. A282 (1977) 333 13) T. E. Drake, H. L. Pai and I. Nascimento, Nucl. Phys. A259 (1976) 317 14) R. Vandenbosch and J. R. Huizenga, Nuclear fission, (Academic Press NY, 1973) Chap. VII and references therein

52

H.-D. Lemke et al. / Photofission

15) R. Vandenbosch and .I. R. Huizenga, Nuclear fission, (Academic Press, NY, 1973), p. 233 16) L. G. Moretto, Proc. Int. Symp. on physics and chemistry of fission, Rochester (1973), paper IAEA-SM-174/204, Wien (1974) 329 17) S. Bjornholm, A. Bohr and B. R. Mottelson, Proc. Int. Symp. on physics and chemistry of fission, Rochester (1973), paper IAEA-SM-174/205, Wien (1974) 367 18) A. W. Ignatyuk, K. K. Istekov, W. N. Okolovitch and G. N. Smirenskij, Int. Symp. on physics and chemistry of fission, Jiilich (1979), paper IAEA-SM/241-C9 and German translation GSI-tr-79/11 19) W. D. Myers and W. J. Swiatecki, Nucl. Phys. 81 (1966) 1 20) U. Mosel, Phys. Rev. C6 (1972) 971 21) A. Laprstre, H. Beil, R. Berg&e, R. Carlos, J. Fagot, A. Veysierre, J. Ahrens, P. Axei and U. Kneissl, Phys. Lett. 79B (1978) 43 22) N. Carjan, H. Delagrange and A. Fleury, Phys. Rev. Cl9 (1979) 2267 23) V. V. Pashkevich, Nucl. Phys. Al69 (1971) 275 24) J. R. Nix, Nucl Phys. A130 (1969) 241 25) E. Rost, Phys. Lett. 26B (1968) 184 26) V. K. Lukyanov, V. A. Seliverstov and V. D. Toneev, Sov. J. Nucl. Phvs. 2111975) 508