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(500, 672, 1068 and 1665 MeV) - from AGS

at BNL, USA

TARGET: Sn, Au, Bi

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.

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.

According to the statistical weight method the fission cross sections are estimated as,

1

inNin

f f iiin

WN

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:

Theoretical Study

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 pion-

induced 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,

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,

1 3 2 41 exp 1 lnf p p pE P P E P P E

2

2 2 2,1 ,2 ,3/ exp / /i i i iP Z A Q Q Z A Q Z 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:

2 21 11 13 12/ 1 exp /P Z A R R Z A R

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