- Email: [email protected]
Energy dependence of negative pion-induced fission in tin
Radiation Measurements 43 (2008) S188 – S190 www.elsevier.com/locate/radmeas
Energy dependence of negative pion-induced fission in tin H.A. Khan a , M.I. Shahzad a , Z. Yasin b,∗ , I.E. Qureshi a , G. Sher a , S. Manzoor a , R.J. Peterson c a Physics Research Division, PINSTECH, P.O. Nilore, Islamabad, Pakistan b Department of Nuclear Engineering, PIEAS, P.O. Nilore, Islamabad, Pakistan c Nuclear Physics Laboratory, University of Colorado, Boulder, CO 80309-0446, USA
Abstract Microscopic fission cross-sections are calculated for negative pion-induced fission of tin. The target–detector assemblies were prepared by sandwichin thin layers of tin (∼ 1 mg/cm2 ) between sheets of CR-39 plastic which are used as dielectric track detectors. Stacks of such sandwiches, having 4-geometric configuration, were irradiated at normal incidence with negative pion beams at the AGS of Brookhaven National Laboratory, USA at energies 500, 672, 1068 and 1665 MeV. After exposure, the detector sandwiches were etched for the tracks of the particles produced as a result of interactions of negative pions with the target atoms. The tracks produced by the pion-induced fission fragments of tin were separated from the total tracks observed using etching time and track length criteria. Using the track statistic of fission fragments, the experimental fission cross-sections induced by negative pions in tin have been calculated and compared with theoretical fission cross-sections computed for pions at 400–1800 MeV energies using the cascade-exciton model code CEM95. Experimental and theoretical values of fission cross-sections have been compared with the data available in literature. An increasing trend of cross-sections with the energy of the incident pion is observed in both data and calculations. © 2008 Elsevier Ltd. All rights reserved. PACS: 25.80.Hp; 24.60.Dr Keywords: Fission cross-sections; Pions; Tin; Cascade-exciton model; CEM95
1. Introduction Nuclear cross-sections at intermediate and higher energies are important because of the large number of applications, particularly to spallation neutron sources and accelerator driven nuclear waste transmutation systems (Iwamoto et al., 2001). For these applications, protons are used as projectiles to generate the neutron flux. But it is well known that when the energy of the incident proton increases above 500 MeV, pions are produced from the primary proton reactions. The produced pions induce secondary reactions in the thick target system. The absorption of a pion may results in transfer of its full rest mass as well as kinetic energy to the target, leading to high nuclear excitations. Under these circumstances nuclei with high fission barriers are also subjected to disintegration under bombardment with pions. Hence, the pion-induced reactions are very important. ∗ Corresponding author. Tel.: +92 51 220 7381; fax: +92 51 922 3727.
E-mail addresses: [email protected], [email protected] (Z. Yasin). 1350-4487/$ - see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.radmeas.2008.04.011
Pion-induced fission cross-sections and fission probabilities at energies below 500 MeV have been measured for a wide range of nuclei using dielectric track detectors (Khan et al., 1987, 1991; Peterson et al., 1995, 2001). But at higher energies and for light nuclei, the pion-induced fission cross-section data are severely lacking. We had earlier performed experiments with negative pions of energies 500, 672, 1068 and 1665 MeV incident on light as well as heavy targets. The preliminary results based on the statistics of observed fission events for the reactions, (1068 MeV) Cu, Sn, Au, Bi, were reported previously (Khan et al., 1999). The fission cross-sections induced by negative pions in gold and bismuth at energies 500, 672, 1068 and 1665 MeV have been reported recently (Yasin et al., 2006). In the present work, negative pion-induced fission crosssections of natural tin are measured at energies of 500, 672, 1068 and 1665 MeV using CR-39 track detectors. Fission cross-sections are computed up to 1800 MeV using the cascadeexciton model CEM95. The approach used in CEM95 to compute the cross-sections for fission is the same as is used in our recentpaper (Yasin et al., 2006) i.e. the change of the ratio
H.A. Khan et al. / Radiation Measurements 43 (2008) S188 – S190
of the level density parameter is taken into account with the change in the incident energy of the projectile. A reasonable agreement was obtained between the computed and measured cross sections. 2. Experimental set up Four stacks of mica and CR-39 detectors were prepared at PINSTECH, Pakistan. The target materials were sandwiched within the stack in the form of coatings on selected detectors. The target coating was done in such a way that multiple sandwiches of detector–target–detector combinations were created as shown in Fig. 1. Stacks were exposed at normal incidence to different negative pion beams of energies 500, 672, 1068 and 1665 MeV. The beams were obtained using the D6 beam line of the alternating gradient synchrotron (AGS) at Brookhaven National Laboratory (BNL), USA. The beam profile was monitored with the help of an array of wire chambers placed just down stream of the samples. The pions falling on the targets were monitored with a fast plastic scintillator placed in front of the stack, keeping a low pion flux for reliable counting. The integrated pion counts of 1.888 × 1010 , 2.020 × 1010 , 1.796 × 1010 and 1.104 × 1010 were achieved for energies 500, 672, 1068 and 1665 MeV, respectively. Out of the four stacks, four sandwiches, one sandwich from each stack which contained tin as target material, involving eight pieces of CR-39 detectors, were used for measurements reported in the present work. After exposures, the detectors were unmounted and those containing target layers were weighed before dissolving target material in aqua regia. Another weighing after removal of target yielded the specific thickness of the coated target. To reveal the fission tracks, the detectors were etched in 6 N NaOH at (70 ± 1) ◦ C for 25 min to reveal the tracks. The fission tracks were manually counted using an optical microscope at a magnification of 400×.
Beam of Incident Particles
DETECTOR
T A R G E T
DETECTOR
Fig. 1. A schematic diagram of experimental set-up using 4-detection geometry.
Calibration for our track lengths was obtained from the spontaneous fission of 242 Pu, from exposure without beam. For pion-induced fission of tin similar track length distribution was obtained as for 242 Pu. The shape of this distribution of track lengths is similar to that found in emulsion for uranium fission induced by a variety of probes. 3. Theoretical modeling Fission cross-sections for − -induced fission of tin are computed using the cascade-exciton model (CEM) code CEM95 (Mashnik, 1995). A detailed description of the initial version of the CEM was given in Gudima et al. (1983), and the code CEM95 used for calculating fission cross-sections can be seen from Prokofiev et al. (1999). The parameters used for calculating the fission cross-sections, including fission barriers, choice for shell and pairing corrections and many others were the same as used earlier for other pion-induced fission (Yasin and Shahzad, 2006). Only the ratio of the level density parameters, af /an to the fission and neutron emission channels, was changed to well illustrate the experimental data. The ratio of the level density parameters used was in the range 1.16–1.1 to match the data. 4. Results and discussion The parameters used for calculating fission cross-sections induced by − mesons on tin at different energies are shown in Table 1. Fission cross-sections are calculated by f =
Total number of pions
500 672 1068 1665
1.888 × 10 2.020 × 1010 1.796 × 1010 1.104 × 1010 10
Target thickness (mg/cm2 ) 0.649 0.900 0.605 0.771
R N
where R is the number of binary events per unit area of one detector, N are the number of target nuclei in a unit area falling in the path of the beam and is the pion fluence. More tracks observed in the forward hemisphere are due to the pion momentum transfer; these were averaged for the fission cross-section. If there is zero momentum transfer, there would be one track per fission event in each of the detectors as required for a symmetric binary decay. Experimentally measured and theoretically calculated fission cross-sections of tin induced by negative pions are plotted in Figs. 2 and 3. Solid curves show the calculated fission crosssections using the code CEM95, whereas squares represent the experimental cross-sections. In Fig. 2 computed cross-sections
Table 1 The parameters used for calculating fission cross-sections induced by − mesons on
− Energy (MeV)
S189
119 Sn
at different energies
Number of events Forward detector
Backward detector
808 4957 1942 –
558 1940 1449 –
Average no. of tracks per detector
Fission cross-sections (mb)
683 3448 1695 2666
11 37 30 62
S190
Fission cross section (mb)
103
H.A. Khan et al. / Radiation Measurements 43 (2008) S188 – S190
0
500
1000
1500
2000
2500 103
102
102
101
101
100
100
CEM95 Experimental
10-1 500
1000
1500
2000
10-1 2500
Pion K.E (MeV) Fig. 2. Energy dependence of negative pion-induced fission crosses sections of 119 Sn. Fission cross-sections are compared with the experimental data, shown as solid squares, from Peterson et al. (1995) and Khan et al. (1997).
103
0
500
1000
1500
2000
2500 103
are deviations in the experimental data points. This is due to the fact that there are many other parameters that account for the differences in the experimental values. The errors in the experimental values are due to the errors in the measurements of pion beam, in the target thickness measurement, and in the counting statistics. Target thickness accounts for the more differences in the cross-sections because if the target thickness is greater than the range of the fission fragments in the target then some fission fragments are absorbed in the target before reaching the detector. The main conclusion in the present work is that for lighter nuclei such as tin, etc. there is an increasing trend of fission cross-sections with the energy of the pion, up to the highest pion energy selected i.e. 1665 MeV. This indicates an increase of excitation energy of the compound nucleus with the incident pion energy. Acknowledgements We thank Dr. Steapen G. Mashink for useful discussions on the parameters used in the code. We are also thankful to Higher Education Commission of Pakistan for funding this research work.
Fission cross section (mb)
References 102
102
101
101
100
100
CEM95 Experimental
10-1 500
1000
1500
2000
10-1 2500
Pion K.E (MeV) Fig. 3. Energy dependence of negative pion-induced fission crosses sections of 119 Sn. Cross-sections for fission are compared with the present measured experimental data.
for fission are compared with our previous measured fission cross-sections (Peterson et al., 1995; Khan et al., 1997) and in Fig. 3 with the present measured experimental values. A good agreement is observed among the theoretical calculations and the experimental ones, although there is more deviation among the experimental data. An increase in cross-sections with the energy of the incident pions is observed in both the techniques i.e. experimental and theoretical. The scatter among the experimental data points is due to use of different detectors (CR-39, Makrofol) having different detection thresholds. Although in the present experiment we have used only the CR-39 detectors to avoid errors due to different detection thresholds, yet there
Gudima, K.K., Mashnik, S.G., Toneev, V.D., 1983. Cascade-exciton model of nuclear reactions. Nucl. Phys. A 401, 329–361. Iwamoto, Y., et al., 2001. Measurements of neutron production double differentials cross-sections for intermediate energies pion incident reactions. J. Nucl. Sci. Technol. 38 (6), 363–369. Khan, H.A., Khan, N.A., Peterson, R.J., 1987. Fission induced in nat. U, nat. Pb, 197 Au, and 165 Ho by 80 and 100 MeV + and − . Phys. Rev. C 35, 645–650. Khan, H.A., Khan, N.A., Peterson, R.J., 1991. Mass dependence of positive pion-induced fission. Phys. Rev. C 43, 250–253. Khan, H.A., Qureshi, I.E., Shahzad, M.I., Manzoor, S., deBarros, S., Peterson, R.J., 1997. Pion-induced fission in tin and bismuth observed with Makrofol detectors. Radiat. Meas. 28, 287–290. Khan, H.A., Qureshi, I.E., Shahzad, M.I., Manzoor, S., Farooq, M.A., Sher, G., Khan, E.U., Peterson, R.J., 1999. Preliminary results of fission induced by (1068 MeV) − in Cu, Sn, Au and Bi using CR-39 detectors. Radiat. Meas. 31, 559–562. Mashnik, S.G., 1995. Computer code CEM95, OECD Nuclear Energy Agency Data Bank, Paris, France. Peterson, R.J., de Barros, S., de Souza, I.O., Gasper, M.B., Khan, H.A., Manzoor, S., 1995. Mass and energy dependence of pion-induced fission. Z. Phys. A 352, 181–189. Peterson, R.J., deBarros, S., Schechter, H., Mashnik, S.G., daSilva, A.G., Suita, J.C., 2001. Fission probabilities across the -nucleon delta resonance. Eur. Phys. J. A 10, 69–71. Prokofiev, A.V., et al., 1999. Cascade-exciton model analysis of nucleoninduced fission cross-sections of lead and bismuth at 45–500 MeV energies. Nucl. Sci. Eng. 131, 78–95. Yasin, Z., Shahzad, M.I., 2006. Pion-induced fission evaluations for 208 Pb, 209 Bi, 232 Th and 238 U across the (3, 3) resonance in the frame work of cascade-exciton model. Nucl. Phys. A 773, 221–229. Yasin, Z., Shahzad, M.I., Qureshi, I.E., Sher, G., Peterson, R.J., 2006. Experimental studies and cascade-exciton model analysis of negative pion induced fission in gold and bismuth. Nucl. Phys. A 765, 390–400.
Energy dependence of negative pion-induced fission in tin H.A. Khan a , M.I. Shahzad a , Z. Yasin b,∗ , I.E. Qureshi a , G. Sher a , S. Manzoor a , R.J. Peterson c a Physics Research Division, PINSTECH, P.O. Nilore, Islamabad, Pakistan b Department of Nuclear Engineering, PIEAS, P.O. Nilore, Islamabad, Pakistan c Nuclear Physics Laboratory, University of Colorado, Boulder, CO 80309-0446, USA
Abstract Microscopic fission cross-sections are calculated for negative pion-induced fission of tin. The target–detector assemblies were prepared by sandwichin thin layers of tin (∼ 1 mg/cm2 ) between sheets of CR-39 plastic which are used as dielectric track detectors. Stacks of such sandwiches, having 4-geometric configuration, were irradiated at normal incidence with negative pion beams at the AGS of Brookhaven National Laboratory, USA at energies 500, 672, 1068 and 1665 MeV. After exposure, the detector sandwiches were etched for the tracks of the particles produced as a result of interactions of negative pions with the target atoms. The tracks produced by the pion-induced fission fragments of tin were separated from the total tracks observed using etching time and track length criteria. Using the track statistic of fission fragments, the experimental fission cross-sections induced by negative pions in tin have been calculated and compared with theoretical fission cross-sections computed for pions at 400–1800 MeV energies using the cascade-exciton model code CEM95. Experimental and theoretical values of fission cross-sections have been compared with the data available in literature. An increasing trend of cross-sections with the energy of the incident pion is observed in both data and calculations. © 2008 Elsevier Ltd. All rights reserved. PACS: 25.80.Hp; 24.60.Dr Keywords: Fission cross-sections; Pions; Tin; Cascade-exciton model; CEM95
1. Introduction Nuclear cross-sections at intermediate and higher energies are important because of the large number of applications, particularly to spallation neutron sources and accelerator driven nuclear waste transmutation systems (Iwamoto et al., 2001). For these applications, protons are used as projectiles to generate the neutron flux. But it is well known that when the energy of the incident proton increases above 500 MeV, pions are produced from the primary proton reactions. The produced pions induce secondary reactions in the thick target system. The absorption of a pion may results in transfer of its full rest mass as well as kinetic energy to the target, leading to high nuclear excitations. Under these circumstances nuclei with high fission barriers are also subjected to disintegration under bombardment with pions. Hence, the pion-induced reactions are very important. ∗ Corresponding author. Tel.: +92 51 220 7381; fax: +92 51 922 3727.
E-mail addresses: [email protected], [email protected] (Z. Yasin). 1350-4487/$ - see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.radmeas.2008.04.011
Pion-induced fission cross-sections and fission probabilities at energies below 500 MeV have been measured for a wide range of nuclei using dielectric track detectors (Khan et al., 1987, 1991; Peterson et al., 1995, 2001). But at higher energies and for light nuclei, the pion-induced fission cross-section data are severely lacking. We had earlier performed experiments with negative pions of energies 500, 672, 1068 and 1665 MeV incident on light as well as heavy targets. The preliminary results based on the statistics of observed fission events for the reactions, (1068 MeV) Cu, Sn, Au, Bi, were reported previously (Khan et al., 1999). The fission cross-sections induced by negative pions in gold and bismuth at energies 500, 672, 1068 and 1665 MeV have been reported recently (Yasin et al., 2006). In the present work, negative pion-induced fission crosssections of natural tin are measured at energies of 500, 672, 1068 and 1665 MeV using CR-39 track detectors. Fission cross-sections are computed up to 1800 MeV using the cascadeexciton model CEM95. The approach used in CEM95 to compute the cross-sections for fission is the same as is used in our recentpaper (Yasin et al., 2006) i.e. the change of the ratio
H.A. Khan et al. / Radiation Measurements 43 (2008) S188 – S190
of the level density parameter is taken into account with the change in the incident energy of the projectile. A reasonable agreement was obtained between the computed and measured cross sections. 2. Experimental set up Four stacks of mica and CR-39 detectors were prepared at PINSTECH, Pakistan. The target materials were sandwiched within the stack in the form of coatings on selected detectors. The target coating was done in such a way that multiple sandwiches of detector–target–detector combinations were created as shown in Fig. 1. Stacks were exposed at normal incidence to different negative pion beams of energies 500, 672, 1068 and 1665 MeV. The beams were obtained using the D6 beam line of the alternating gradient synchrotron (AGS) at Brookhaven National Laboratory (BNL), USA. The beam profile was monitored with the help of an array of wire chambers placed just down stream of the samples. The pions falling on the targets were monitored with a fast plastic scintillator placed in front of the stack, keeping a low pion flux for reliable counting. The integrated pion counts of 1.888 × 1010 , 2.020 × 1010 , 1.796 × 1010 and 1.104 × 1010 were achieved for energies 500, 672, 1068 and 1665 MeV, respectively. Out of the four stacks, four sandwiches, one sandwich from each stack which contained tin as target material, involving eight pieces of CR-39 detectors, were used for measurements reported in the present work. After exposures, the detectors were unmounted and those containing target layers were weighed before dissolving target material in aqua regia. Another weighing after removal of target yielded the specific thickness of the coated target. To reveal the fission tracks, the detectors were etched in 6 N NaOH at (70 ± 1) ◦ C for 25 min to reveal the tracks. The fission tracks were manually counted using an optical microscope at a magnification of 400×.
Beam of Incident Particles
DETECTOR
T A R G E T
DETECTOR
Fig. 1. A schematic diagram of experimental set-up using 4-detection geometry.
Calibration for our track lengths was obtained from the spontaneous fission of 242 Pu, from exposure without beam. For pion-induced fission of tin similar track length distribution was obtained as for 242 Pu. The shape of this distribution of track lengths is similar to that found in emulsion for uranium fission induced by a variety of probes. 3. Theoretical modeling Fission cross-sections for − -induced fission of tin are computed using the cascade-exciton model (CEM) code CEM95 (Mashnik, 1995). A detailed description of the initial version of the CEM was given in Gudima et al. (1983), and the code CEM95 used for calculating fission cross-sections can be seen from Prokofiev et al. (1999). The parameters used for calculating the fission cross-sections, including fission barriers, choice for shell and pairing corrections and many others were the same as used earlier for other pion-induced fission (Yasin and Shahzad, 2006). Only the ratio of the level density parameters, af /an to the fission and neutron emission channels, was changed to well illustrate the experimental data. The ratio of the level density parameters used was in the range 1.16–1.1 to match the data. 4. Results and discussion The parameters used for calculating fission cross-sections induced by − mesons on tin at different energies are shown in Table 1. Fission cross-sections are calculated by f =
Total number of pions
500 672 1068 1665
1.888 × 10 2.020 × 1010 1.796 × 1010 1.104 × 1010 10
Target thickness (mg/cm2 ) 0.649 0.900 0.605 0.771
R N
where R is the number of binary events per unit area of one detector, N are the number of target nuclei in a unit area falling in the path of the beam and is the pion fluence. More tracks observed in the forward hemisphere are due to the pion momentum transfer; these were averaged for the fission cross-section. If there is zero momentum transfer, there would be one track per fission event in each of the detectors as required for a symmetric binary decay. Experimentally measured and theoretically calculated fission cross-sections of tin induced by negative pions are plotted in Figs. 2 and 3. Solid curves show the calculated fission crosssections using the code CEM95, whereas squares represent the experimental cross-sections. In Fig. 2 computed cross-sections
Table 1 The parameters used for calculating fission cross-sections induced by − mesons on
− Energy (MeV)
S189
119 Sn
at different energies
Number of events Forward detector
Backward detector
808 4957 1942 –
558 1940 1449 –
Average no. of tracks per detector
Fission cross-sections (mb)
683 3448 1695 2666
11 37 30 62
S190
Fission cross section (mb)
103
H.A. Khan et al. / Radiation Measurements 43 (2008) S188 – S190
0
500
1000
1500
2000
2500 103
102
102
101
101
100
100
CEM95 Experimental
10-1 500
1000
1500
2000
10-1 2500
Pion K.E (MeV) Fig. 2. Energy dependence of negative pion-induced fission crosses sections of 119 Sn. Fission cross-sections are compared with the experimental data, shown as solid squares, from Peterson et al. (1995) and Khan et al. (1997).
103
0
500
1000
1500
2000
2500 103
are deviations in the experimental data points. This is due to the fact that there are many other parameters that account for the differences in the experimental values. The errors in the experimental values are due to the errors in the measurements of pion beam, in the target thickness measurement, and in the counting statistics. Target thickness accounts for the more differences in the cross-sections because if the target thickness is greater than the range of the fission fragments in the target then some fission fragments are absorbed in the target before reaching the detector. The main conclusion in the present work is that for lighter nuclei such as tin, etc. there is an increasing trend of fission cross-sections with the energy of the pion, up to the highest pion energy selected i.e. 1665 MeV. This indicates an increase of excitation energy of the compound nucleus with the incident pion energy. Acknowledgements We thank Dr. Steapen G. Mashink for useful discussions on the parameters used in the code. We are also thankful to Higher Education Commission of Pakistan for funding this research work.
Fission cross section (mb)
References 102
102
101
101
100
100
CEM95 Experimental
10-1 500
1000
1500
2000
10-1 2500
Pion K.E (MeV) Fig. 3. Energy dependence of negative pion-induced fission crosses sections of 119 Sn. Cross-sections for fission are compared with the present measured experimental data.
for fission are compared with our previous measured fission cross-sections (Peterson et al., 1995; Khan et al., 1997) and in Fig. 3 with the present measured experimental values. A good agreement is observed among the theoretical calculations and the experimental ones, although there is more deviation among the experimental data. An increase in cross-sections with the energy of the incident pions is observed in both the techniques i.e. experimental and theoretical. The scatter among the experimental data points is due to use of different detectors (CR-39, Makrofol) having different detection thresholds. Although in the present experiment we have used only the CR-39 detectors to avoid errors due to different detection thresholds, yet there
Gudima, K.K., Mashnik, S.G., Toneev, V.D., 1983. Cascade-exciton model of nuclear reactions. Nucl. Phys. A 401, 329–361. Iwamoto, Y., et al., 2001. Measurements of neutron production double differentials cross-sections for intermediate energies pion incident reactions. J. Nucl. Sci. Technol. 38 (6), 363–369. Khan, H.A., Khan, N.A., Peterson, R.J., 1987. Fission induced in nat. U, nat. Pb, 197 Au, and 165 Ho by 80 and 100 MeV + and − . Phys. Rev. C 35, 645–650. Khan, H.A., Khan, N.A., Peterson, R.J., 1991. Mass dependence of positive pion-induced fission. Phys. Rev. C 43, 250–253. Khan, H.A., Qureshi, I.E., Shahzad, M.I., Manzoor, S., deBarros, S., Peterson, R.J., 1997. Pion-induced fission in tin and bismuth observed with Makrofol detectors. Radiat. Meas. 28, 287–290. Khan, H.A., Qureshi, I.E., Shahzad, M.I., Manzoor, S., Farooq, M.A., Sher, G., Khan, E.U., Peterson, R.J., 1999. Preliminary results of fission induced by (1068 MeV) − in Cu, Sn, Au and Bi using CR-39 detectors. Radiat. Meas. 31, 559–562. Mashnik, S.G., 1995. Computer code CEM95, OECD Nuclear Energy Agency Data Bank, Paris, France. Peterson, R.J., de Barros, S., de Souza, I.O., Gasper, M.B., Khan, H.A., Manzoor, S., 1995. Mass and energy dependence of pion-induced fission. Z. Phys. A 352, 181–189. Peterson, R.J., deBarros, S., Schechter, H., Mashnik, S.G., daSilva, A.G., Suita, J.C., 2001. Fission probabilities across the -nucleon delta resonance. Eur. Phys. J. A 10, 69–71. Prokofiev, A.V., et al., 1999. Cascade-exciton model analysis of nucleoninduced fission cross-sections of lead and bismuth at 45–500 MeV energies. Nucl. Sci. Eng. 131, 78–95. Yasin, Z., Shahzad, M.I., 2006. Pion-induced fission evaluations for 208 Pb, 209 Bi, 232 Th and 238 U across the (3, 3) resonance in the frame work of cascade-exciton model. Nucl. Phys. A 773, 221–229. Yasin, Z., Shahzad, M.I., Qureshi, I.E., Sher, G., Peterson, R.J., 2006. Experimental studies and cascade-exciton model analysis of negative pion induced fission in gold and bismuth. Nucl. Phys. A 765, 390–400.