Transcript slides

Pion-Induced Fission- A Review
Zafar Yasin
Pakistan Institute of Engineering and Applied
Sciences (PIEAS)
Islamabad, Pakistan
Outline
 Importance of Nuclear Fission
 Experimental Study of Pion Induced Fission
 Theoretical Study
 Systematical Analysis
 Results and Discussion
 Comparison of Pion Fission with Different Probes
Importance of Pion Induced Fission
 Nuclear fission covers the areas ranging from nuclear
structure models to accelerator- driven systems.
 Pion induced fission is as important as fission induced
by nucleons.
 Cascades in heavy nuclear spallation targets are partly
propagated by pions.
 In an Accelerator-Driven Systems, a large number of
pions are produced as energy of protons is in GeV
range.
Inter-Nuclear Cascade, a reaction in an ADS
Pions are produced when energy of protons is
500 MeV or more.
Brief History of Pion fission
 In 1958, pion-induced fission was observed with the
first available pion beam.
 In 1971, first time pion induced fission cross
sections of energetic pions were measured.
 1976, fission by stopped negative pions was studied.
 In 1985, Hicks et. al., had tried to compare pion
fission with the conventional nucleon induced
fission.
 In 1987, major work on pion fission was started by
Dr. H. A. Khan and Prof. R.J. Peterson.
 In 2006, Zafar Yasin, used cascade-exciton model
CEM95 to compute fission cross sections.
Calibration of SSNTDs
Detectors configuration
Schematic diagram of a sandwich representing 2-exposure
geometric configuration.
Schematic diagram of a sandwich representing 4-exposure
geometric configuration.
Experimental Setup for Pion Induced fission
 Four stacks containing
mica and CR-39 detectors
were
prepared
at
PINSTECH, Pakistan, and
were exposed by  - pion
beams at BNL, USA.
 Different sandwiches of
CR-39 and mica containing
Sn, Au and Bi as the target
materials were selected.
The detectors were etched
in 6N NaOH at about 700 to
reveal the fission tracks,
and then scanned using an
optical microscope.
 Fission cross sections
were
calculated
using
track statistics.
(500, 672, 1068 and 1665 MeV) - from AGS
at BNL, USA
TARGET:
Sn, Au, Bi
Theoretical Study

Cross-sections, up to 2500 MeV, of different nuclei
are calculated using the code CEM95 and results are
compared with the experimental data and with the
cross-sections obtained using systematic analysis.

Three stages are incorporated in the code: the
cascade, pre-equilibrium, and compound nucleus
stage.

The model uses the Monte Carlo Method to simulate
all three stages of the reactions.

Two methodologies have been incorporated in
CEM95, one is the direct Monte Carlo simulations
and other is the Monte Carlo sampling by means of
statistical functions.
Theoretical Study
 According to the statistical weight method the fission
cross sections are estimated as,

f

 in
N in
Nin
 W 
i 1
f
i
Where,
σf = Microscopic fission cross- section
σin= Total reaction cross-section
Nin= Total number of simulated inelastic interactions
Wf = The probability of the nucleus to fission at any
of the chain stages and is determined from the
following expressions:
Systematics of Fission Cross Sections
 There is incongruity among the fission cross sections of
the experimental data itself as well as among the
theoretical and experimental data-points.
 The systematics and theoretical study is also necessary
in the sense that the cost of experiments at accelerators
is high, and beam time is short.
 The systematics used to estimate the positive pioninduced fission is based on the systematics performed
for proton induced fission.
 The systematics used for proton induced fission is
possible for pion-induced fission because, it is well
known that the fission induced by protons is similar to
pion-induced fission.
 The Fukahori and Pearlstein proposed the following (p, f)
cross section parameterization for the nuclei from 181Ta to
209Bi,


 f  E p   P1 1  exp P3  E p  P2   1  P4 ln E p 

Where σf is the fission cross section (mb), Ep is the
incident proton-energy (MeV) and P1, P2 , P3, are fitting
parameters known as the saturation cross-section, the
apparent threshold-energy and the increasing rate,
respectively. The parameter P4 was introduced by A.V.
Prokofiev, in order to reproduce the decrease of the fission
cross sections at high energies.
 The parameters Pi,are obtained by the least square method
in a form proposed by Fukahori and co-workers,
2


Pi  Z 2 / A  exp Qi ,1  Qi ,2  Z 2 / A   Qi ,3  Z 2 / A  


Where Q i, j are fitting parameters that are used from a
published data from Prokofiev. Z is the charge number and
A is the mass number of the corresponding compound
nucleus. For positive pions Z = Zt +1 and A = At , where Zt
and At are the charge and mass of the target, respectively.

The parameters P2, P3 and P4 found for the actinide targets
having large cross-section data ( 232Th, 238U, 235U) are
nearly equal within the uncertainty limits.
 So, it was convenient to use weighted average values for
all studied actinides.
 The only remaining free parameter P1, was fitted to the
experimental data for the actinides with less extensive data
base (233U, 237Np, and 239Pu). The parameterization obtained
for P1 (Z2/A) was as follows:


P1  Z 2 / A  R11 1  exp R13  Z 2 / A  R12 
R11, R12, and R13 are fitting parameters having values
2572, 34.99, and 2.069, respectively. The values for the
parameters P2, P3 and P4 are 12.1, 0.111 and 0.067,
respectively.
Results and Discussion
Fig. 1 Computed and predicted
fission cross sections induced
by positive pions in 209Bi are
shown as solid and dotted
curves, respectively. Fission
cross sections are compared
with the experimental data,
shown as solid squares.
Fig. 2 Computed and predicted fission
cross sections induced by positive
pions in 231Pa are shown as solid
and dotted curves, respectively.
Fission cross sections are compared
with the experimental data, solid
squares.
Fig. 3 Computed and predicted
fission cross sections induced by
positive pions in 232Th are shown
as solid and dotted curves,
respectively. Fission cross
sections are compared with the
experimental data, solid squares.
Fig. 4 Computed and predicted
fission cross sections induced by
positive pions in 238U are shown
as solid and dotted curves,
respectively. Fission cross
sections are compared with the
experimental data, solid squares.
Results and Discussion
Fig.5 Fission probability as a
function of pion K.E. for Sn, Bi and
U.
Fig.6 Fission probability as a
function
of
fissility
for
different pion energies.
Comparison of Fissilities by Photons, Protons and
Pions
The curves are from the
cascade-evaporation
Monte-Carlo code for
200 MeV photons (solid
curve),
190
MeV
protons (dashed curve),
80 MeV positive pions
(dashed-dotted curve).
Black
points
are
experimental data for
photons, asteric for
protons
and
white
points for pions.
Comparison with other Probes
 Across the (3, 3) resonance, no new mechanisms
were observed for pion induced fission.
 At the same excitation energy, angular momentum
and nucleonic composition, the fissility values for
photon, proton and pion induced fission are in
substantial agreement.
 A semi-empirical correlation for proton induced
fission is also valid for positive pion induced fission,
at least for actinides.
Conclusions
 Firstly, the pion induced fission cross sections are useful to
understand the basics of Nuclear Physics and for current Nuclear
applications.
 Secondly, the new approach used in CEM95 to compute the fission
cross sections shows a reasonable agreement between the
computed and measured fission cross sections.
 Thirdly, the systematic used to predict proton induced fission
cross sections is also valid for positive pion induced fission cross
sections, at least for actinides.
 Thirdly, the comparison of computed, predicted and experimental
values of fission cross- sections brings new information. For
example, the experimental value for 231Pa at 150 MeV seems to be
in error. A similar situation was found for many of the data points
for 209Bi.
Thank You