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Fission barrier of 209Bi measured by electron induced fission
Volume 49B, number 4
PHYSICS LETTERS
29 April 1974
F I S S I O N B A R R I E R . O F 209Bi M E A S U R E D BY E L E C T R O N I N D U C E D F I S S I O N D. TURCK, W. ZIGA and H.-G. CLERC lnstitut fiir Kernphysik, Technische Hochschule, Darmstadt, Germany Receded 8Mareh1974 For 2°9Bi an eleetrofission cross section below 10 -36 era2 was measured by the observation of correlated binary fission tracks in mica detectors. From the cross-sectiondata between 28 and 41 MeV electron energy, a fission barrier of 25.5 ± 1.5 MeV was deduced. The method offers the possibility to measure fission barriers ar low angular momentum and for nuclei not accessibleotherwise. During the past ten years, measurements of the fission barrier of several compound nuclei below radium were reported [1--4]. These experiments, in which proton and a-particle beams were used to produce excited compound nuclei, are of course restricted to nuclei which can be formed by absorption of the projectile in a suitable target nucleus. The fission barrier, however, is a quantity of interest for many nuclei. For example, the barrier of stable lead isotopes is predicted to vary between 24 and 28 MeV as a function of neutron number due to pronounced shell effects near N = 126 [5]. Furthermore, in the interesting region of the medium heavy nuclei with 100 ~
Darmstadt 70 MeV electron scattering facility [8]. Mica detector target sandwiches were used to register the fission fragments in 4~r-geometry. The electron beam passed through the target detector sandwich. The sandwich consisted of two mica sheets, each about 10 mg/cm 2 thick, and of high purity 209Bi, 0.5 - 4 mg/cm 2 thick, evaporated on one of the mica sheets. For the very low cross section measurements, a special target detector sandwich was developed which allowed recording a binary fission event as a correlated pair of tracks. The sandwich can be operated under vacuum conditions which is necessary for its application to electrofission. A fission rate of 0.5 h -1 could easily be detected at an electron beam current of 3/~A. The experimental data were corrected for the contribution of photofission due to bremsstrahlung generated by the electron beam passing through the sandwich, and for absorption of fission fragments in the target material. The measured electron-induced fission cross section oe(Eo) is given in fig. 1. The virtual photon formalism [9] developed in plane wave Born approximationwas used to analyze the data. Close to the fission barrier, the fission probability is known to change be several orders of magnitude for changes in the excitation energy of only a few MeV. Therefore it is felt that Coulomb corrections [10] will not alter the result for the fission barrier significantly. The electrofission cross section oe(E0) is related to the photofission cross section o,rf b y
e.o j
o f( t (Eo, e, Ode.
(1)
o 335
Volume 49B, number 4
1 0 -~2
PHYSICS LETTERS
29 April 1974
R / r;o,
0 'e I c m 2
1 0 -4 .
10"33_
10-~-
•
•a !
,f
I0"34_ 10-8-
/
10 -3~.
10 -36-
1 0 .7.
/ 1O'S_ 10 ~L
25
3o
:~s E.,Me~,
Fig. 1. Cross section o e for electron induced fission in 2°9Bi as a function of electron energy E o.
Here K(E o, E,/) is the virtual photon spectrum associated with the electron of energy E o producing nuclear excitations of energy E and multipolarity l [9]. The photofission cross section was obtained by unfolding eq. (1) using a modified computer program of Routti [11]. The procedure employed provides the photofission cross section without any assumption for its shape. In order to obtain the fission probability Ff/Fto t from the photofission cross section o~f, the photoabsorption cross section O.tabs has to be known a.),f = aTabs" F f / F t o t .
The photoabsorption cross section for 209Bi in the energy region which is of interest here (E = 2 6 41 MeV) has not been measured. Therefore experimental (7, xn) cross sections for 203T1were used [12] which coincide with existing data for 209Bi [13] at lower 7-ray energies (E ~< 26 MeV). The resulting fission probability is shown in fig. 2. It can be seen that there is a good overall agreement with the nuclear reaction data [3]. However, the fission probability determined by electron-induced fission shows a tendency to rise slightly faster with excitation energy. This indicates a somewhat higher fission barrier. Assuming only "first chance fission" and neglecting charged particle emission, the fission probability is given by Pf/Pn" By using for Ff/F n an 336
10-9 25
30
35
EIMeV
Fig. 2. Solid line: fission probability r f / r t o t as a function of excitation energy E for 2°9Bi as obtained from unfolding the electrofission cross section; the hatching indicates the statistical uncertainties. The data points are results of KhodaiJoopary [3] for the compound nucleus 2°9Bi produced in the reaction 2°aPb + p.
analytical expression [1] obtained from Fermi gas level densities, a best fit value of Bf= 25.5 -+ 1.5 MeV was obtained for the fission barrier height, This value is slightly larger than the value "of 22.6 + 1.5 MeV which was determined for the compound nucleus 2°9Bi formed in the reaction 2081~o + 1H [3]. In the electrofission experiment, angular momentum and parity are restricted to 7/2 +, 9/2 ÷ and 11/2 ÷ , if E1 absorption is assumed; a corresponding restriction holds for E2 absorption. In the proton induced reaction [3], the average angular momentum is of the same order. From liquid drop model calcula~ tions [14] it can be estimated that the influence of angular momentum of this magnitude on the fission probability is negligible. In contrast to the electrofission case, however, the distribution of angular momentum in the proton induced reaction is broad. It can not be excluded that the special states which are excited in the electrofission experiment are not available at the saddle point slightly above the lowest fission barrier. This would explain the low F f t r n values close to the barrier and the somewhat
Volume49B, number4
PHYSICSLETTERS
higher fission barrier observed in the present electrofission experiment. In conclusion it can be said that electroiission is a reliable tool for determining fission barrier heights. It may be hoped that the measurements can also be extended to nuclei lighter than 2ogBi by the method of detecting correlated fission fragment tracks from electrofission. The authors wish to thank professor P. Brix for his interest in this work and valuable discussions. Thanks are also due to the Linac-staff for their support and to Dr. J.T. Routti for making the computer program LQUHI available to us. The AEG Telefunken computer TR 440 of the Gesellschaft fur Mathematik und Datenverarbeitung in Darmstadt was used for the calculations. This work was supported by the German Bundesministerium fur Forschung und Technologie.
References [l] J.R. Huizenga, R. Chaudhry and R. Vandenbosch, Rev. 126 (1962) 210.
29 April 1974
[2] D.S.Burnett et al., Phys. Rev. 134B (1964) 952. [ 31 A. Rhodai-Joopary,
Ph. D. thesis, University of California, Lawrence Radiation Laboratory Report No. UCRL-16489 (1966). 141GM. Raisbeck and J.W. Cobble, Phys. Rev. 153 (1967) 1270. 151U. Mosel, Phys. Rev. C6 (1972) 971. 161H.J. Krappe and J.R. Nix, Proc. Rochester Conf. on the Physics and chemistry of fission (1973), IAEASM174112. 171J.M. Ran&k, V.M. Sanin and P.V. Sorokin, Ukrainskij Flzit$yj Zurnall4 (1969) 408. 181F. Gudden, G. Fricke, H.-G. Clerc and P. Brix, Z. Phys. 181(1964) 453. 191W.V. Barber, Phys. Rev. lll(1958) 1958) (1642). IlO1 W.W. Gargaro and D.S. Onley, Phys. Rev. C4 (1971) 1032. 1111J.T. Routti, Ph. D. thesis, University of California, Lawrence Radiation Laboratory Report No. UCRL18514 (1969). 1121J. Moffat and D. Reitmann, Nucl. Phys. 65 (1965) 130. 1131R.R. Harvey, J.T. Caldwell, R.L. Bramblett and S.C. Fultz, Phys. Rev. 136B (1964) 126. 1141F. Plasil and W.J. Swiatecki, cited in Nuclear fission by R. Vanden bosch and J.R. Huizinga (Academic Press, N.Y. 1973) p. 246.
Phys.
337
PHYSICS LETTERS
29 April 1974
F I S S I O N B A R R I E R . O F 209Bi M E A S U R E D BY E L E C T R O N I N D U C E D F I S S I O N D. TURCK, W. ZIGA and H.-G. CLERC lnstitut fiir Kernphysik, Technische Hochschule, Darmstadt, Germany Receded 8Mareh1974 For 2°9Bi an eleetrofission cross section below 10 -36 era2 was measured by the observation of correlated binary fission tracks in mica detectors. From the cross-sectiondata between 28 and 41 MeV electron energy, a fission barrier of 25.5 ± 1.5 MeV was deduced. The method offers the possibility to measure fission barriers ar low angular momentum and for nuclei not accessibleotherwise. During the past ten years, measurements of the fission barrier of several compound nuclei below radium were reported [1--4]. These experiments, in which proton and a-particle beams were used to produce excited compound nuclei, are of course restricted to nuclei which can be formed by absorption of the projectile in a suitable target nucleus. The fission barrier, however, is a quantity of interest for many nuclei. For example, the barrier of stable lead isotopes is predicted to vary between 24 and 28 MeV as a function of neutron number due to pronounced shell effects near N = 126 [5]. Furthermore, in the interesting region of the medium heavy nuclei with 100 ~
Darmstadt 70 MeV electron scattering facility [8]. Mica detector target sandwiches were used to register the fission fragments in 4~r-geometry. The electron beam passed through the target detector sandwich. The sandwich consisted of two mica sheets, each about 10 mg/cm 2 thick, and of high purity 209Bi, 0.5 - 4 mg/cm 2 thick, evaporated on one of the mica sheets. For the very low cross section measurements, a special target detector sandwich was developed which allowed recording a binary fission event as a correlated pair of tracks. The sandwich can be operated under vacuum conditions which is necessary for its application to electrofission. A fission rate of 0.5 h -1 could easily be detected at an electron beam current of 3/~A. The experimental data were corrected for the contribution of photofission due to bremsstrahlung generated by the electron beam passing through the sandwich, and for absorption of fission fragments in the target material. The measured electron-induced fission cross section oe(Eo) is given in fig. 1. The virtual photon formalism [9] developed in plane wave Born approximationwas used to analyze the data. Close to the fission barrier, the fission probability is known to change be several orders of magnitude for changes in the excitation energy of only a few MeV. Therefore it is felt that Coulomb corrections [10] will not alter the result for the fission barrier significantly. The electrofission cross section oe(E0) is related to the photofission cross section o,rf b y
e.o j
o f( t (Eo, e, Ode.
(1)
o 335
Volume 49B, number 4
1 0 -~2
PHYSICS LETTERS
29 April 1974
R / r;o,
0 'e I c m 2
1 0 -4 .
10"33_
10-~-
•
•a !
,f
I0"34_ 10-8-
/
10 -3~.
10 -36-
1 0 .7.
/ 1O'S_ 10 ~L
25
3o
:~s E.,Me~,
Fig. 1. Cross section o e for electron induced fission in 2°9Bi as a function of electron energy E o.
Here K(E o, E,/) is the virtual photon spectrum associated with the electron of energy E o producing nuclear excitations of energy E and multipolarity l [9]. The photofission cross section was obtained by unfolding eq. (1) using a modified computer program of Routti [11]. The procedure employed provides the photofission cross section without any assumption for its shape. In order to obtain the fission probability Ff/Fto t from the photofission cross section o~f, the photoabsorption cross section O.tabs has to be known a.),f = aTabs" F f / F t o t .
The photoabsorption cross section for 209Bi in the energy region which is of interest here (E = 2 6 41 MeV) has not been measured. Therefore experimental (7, xn) cross sections for 203T1were used [12] which coincide with existing data for 209Bi [13] at lower 7-ray energies (E ~< 26 MeV). The resulting fission probability is shown in fig. 2. It can be seen that there is a good overall agreement with the nuclear reaction data [3]. However, the fission probability determined by electron-induced fission shows a tendency to rise slightly faster with excitation energy. This indicates a somewhat higher fission barrier. Assuming only "first chance fission" and neglecting charged particle emission, the fission probability is given by Pf/Pn" By using for Ff/F n an 336
10-9 25
30
35
EIMeV
Fig. 2. Solid line: fission probability r f / r t o t as a function of excitation energy E for 2°9Bi as obtained from unfolding the electrofission cross section; the hatching indicates the statistical uncertainties. The data points are results of KhodaiJoopary [3] for the compound nucleus 2°9Bi produced in the reaction 2°aPb + p.
analytical expression [1] obtained from Fermi gas level densities, a best fit value of Bf= 25.5 -+ 1.5 MeV was obtained for the fission barrier height, This value is slightly larger than the value "of 22.6 + 1.5 MeV which was determined for the compound nucleus 2°9Bi formed in the reaction 2081~o + 1H [3]. In the electrofission experiment, angular momentum and parity are restricted to 7/2 +, 9/2 ÷ and 11/2 ÷ , if E1 absorption is assumed; a corresponding restriction holds for E2 absorption. In the proton induced reaction [3], the average angular momentum is of the same order. From liquid drop model calcula~ tions [14] it can be estimated that the influence of angular momentum of this magnitude on the fission probability is negligible. In contrast to the electrofission case, however, the distribution of angular momentum in the proton induced reaction is broad. It can not be excluded that the special states which are excited in the electrofission experiment are not available at the saddle point slightly above the lowest fission barrier. This would explain the low F f t r n values close to the barrier and the somewhat
Volume49B, number4
PHYSICSLETTERS
higher fission barrier observed in the present electrofission experiment. In conclusion it can be said that electroiission is a reliable tool for determining fission barrier heights. It may be hoped that the measurements can also be extended to nuclei lighter than 2ogBi by the method of detecting correlated fission fragment tracks from electrofission. The authors wish to thank professor P. Brix for his interest in this work and valuable discussions. Thanks are also due to the Linac-staff for their support and to Dr. J.T. Routti for making the computer program LQUHI available to us. The AEG Telefunken computer TR 440 of the Gesellschaft fur Mathematik und Datenverarbeitung in Darmstadt was used for the calculations. This work was supported by the German Bundesministerium fur Forschung und Technologie.
References [l] J.R. Huizenga, R. Chaudhry and R. Vandenbosch, Rev. 126 (1962) 210.
29 April 1974
[2] D.S.Burnett et al., Phys. Rev. 134B (1964) 952. [ 31 A. Rhodai-Joopary,
Ph. D. thesis, University of California, Lawrence Radiation Laboratory Report No. UCRL-16489 (1966). 141GM. Raisbeck and J.W. Cobble, Phys. Rev. 153 (1967) 1270. 151U. Mosel, Phys. Rev. C6 (1972) 971. 161H.J. Krappe and J.R. Nix, Proc. Rochester Conf. on the Physics and chemistry of fission (1973), IAEASM174112. 171J.M. Ran&k, V.M. Sanin and P.V. Sorokin, Ukrainskij Flzit$yj Zurnall4 (1969) 408. 181F. Gudden, G. Fricke, H.-G. Clerc and P. Brix, Z. Phys. 181(1964) 453. 191W.V. Barber, Phys. Rev. lll(1958) 1958) (1642). IlO1 W.W. Gargaro and D.S. Onley, Phys. Rev. C4 (1971) 1032. 1111J.T. Routti, Ph. D. thesis, University of California, Lawrence Radiation Laboratory Report No. UCRL18514 (1969). 1121J. Moffat and D. Reitmann, Nucl. Phys. 65 (1965) 130. 1131R.R. Harvey, J.T. Caldwell, R.L. Bramblett and S.C. Fultz, Phys. Rev. 136B (1964) 126. 1141F. Plasil and W.J. Swiatecki, cited in Nuclear fission by R. Vanden bosch and J.R. Huizinga (Academic Press, N.Y. 1973) p. 246.
Phys.
337