Cross-Sections of (N, Xn) Threshold Reactions Studied by Activation Method

Cross-sections of (n, xn) Threshold Reactions studied by activation method

A. Larédo, Nuclear Institute of the Academy of Sciences of the Czech Republic PRI, 250 68 Řež near Prague, Czech Republic, Engineering School ‘Ecole des mines de Nantes’ 44300 Nantes France

Context.Nuclear waste management is one of the most important questions in production of nuclear energy. Lot of long lived radioactive elements are produced in nuclear reactors. The motivation of the studies of (n, xn) threshold reaction cross-sections comes from the ‘Energy plus Transmutation’ project in which Al, Au, Bi, In, Ta, Co and Y foils are used to measure the flux of high energy neutrons produced in spallation reactions. Indeed, radioactive isotopes are produced with nuclear reactions and can be transmuted from long lived radioisotope to short lived radioisotopes by nuclear reactions for which a very intensive neutron source is needed. Spallation reactions of protons (with a hundreds of MeV energy) with heavy nuclei can be used as such source. Threshold reactions are used in various materials to measure high neutron energy flux from spallation reactions. Up to now, no experimental cross-section data existed for energy neutron higher than 20 MeV. That is why, eleven measurements of (n, xn) cross-sections were performed, in two different places (NPI ASCR cyclotron in Rez and TSL cyclotron in Uppsala) supported by EFNUDAT (European Facilities for Nuclear Data measurements). The Uppsala experiment took place in The Svederg Laboratory in Uppsala, Sweden, in February 2010. The neutron source used was a quasi-monoenergetic neutron source based on 7Li(p, n)7Be reaction with a 11-175 MeV energy range. Gamma ray spectra were measured on HPGe detectors and corrections were applied to obtain the final values of cross-sections. This document will focus on the Bismuth cross section measurements.

EXPERIMENTAL METHOD
Neutron production

For the experiment quasi-monoenergetic neutron sources were needed. The production of the neutron flux was based on 7Li(p, n)7Be reaction, high energy protons from the cyclotron were directed to the lithium target.In Uppsala the flux density resulting from this reaction was 105 cm-2s-1. The energies of used proton beams were 62, 70, 80 and 93 MeV. The neutron beam was then formed by a 100 cm long iron collimator with a 12,2 cm hole.

1.2.Sample arrangement

Different Bi foils were used for each energy experiment, Bi materials were all 2,5x2,5 cm2 :

mass [g] / D [cm]
70 MeV / 5,75325 / 0,09402656
93 MeV / 6,32182 / 0,1033188
62 MeV / 5,74052 / 0,0938185
62 MeV repeated / 5,63605 / 0,0921111
80 MeV / 5,9984 / 0,0980331

Samples were placed 373 cm from the Li target, radiation exposure was about 8 hours. Bi foils were placed in the center as shown below:

1.3.Detection

After radiation exposure, gamma spectrums of activated foils were measured on the HPGe detectors, delays from the end of radiation exposure to start of detection could be up to 2 and a half hours for Bismuth foils. Around three measurements were done for each foil, between some hours to few days. In Uppsala the distance between front of HPGe detector and foil was 40 mm.

ANALYSIS METHOD
Spectrum analysis with Deimos32

The first step in the cross section measurement was to analyze every spectrum which was previously acquired using the software DEIMOS32. This analysis consisted of finding the characteristic peaks of the spectrum. The software DEIMOS32 was developed at the Nuclear Spectroscopy Department of the Nuclear Physics Institute in Řež for evaluation of gamma spectrum. Peaks are selected manually or automatically, the software computes, among other data, the peak energy, the peak area and the peak area uncertainty. Once all the spectrum peaks have been selected, the results are saved as a table in a text file (mean of 70 peaks per spectrum).

2.2.Comparison of experimental spectrum and isotope data

Spectrums were acquired for several neutron energies and for different times after radiation exposure. For each spectrum, we determined the present isotopes, following several successive steps. From the Bi209 studied, the (n, xn) reaction diagram was known, so that we could know which isotopes could be found.

For each isotope, a list of the different peaks of gamma emission existed in data base like Decay Data search, thus we compared the peaks recorded from Uppsala spectrum to the isotope peaks in the data base to determine the presence or absence of the isotope in the sample.

With this method 10 isotopes were found, from (n, 2n) to (n, 9n) reactions.

Isotope
1 / Bi201
2 / Bi202
3 / Bi203
4 / Bi204
5 / Bi205
6 / Bi206
7 / Bi207
8 / Bi208
9 / Pb201
10 / Pb203

The energy peaks of these isotopes were noted as well as peak areas.

2.3.Nucleus yield calculation

To compute cross sections, we first need to calculate number of radioactive nuclei(Nyield),produced by neutron activation, from peak areas of gamma emission thanks to the following formula:

These corrections are near to 1 (usually only a few percent), first approximation of this formula is to consider some of correction coefficients equal to 1 what permit to simplify the equation as:

Peak area Sp : given by DEIMOS for each peak
γline intensity Iγ : from decay data search
treal : data from experiment
tlive : data from experiment
Decay constant λ :
T1/2 : data from libraries as decay data search
t0 = Beam end – start of measurement
tirr : time of irradiation
Detector efficiency, function of the energy peak described as:

With the coefficients:

2.4.Corrections

2.4.1.Coincidences correction

When a radionuclide is decaying, it is emitting gamma-ray in cascades with negligible time delay. The problem encountered is that into the detector crystal, the energy register cannot be attributed to the proper emission energy. The signal detected is a sum effect. This is the true coincidence effect. This effect can cause bigger or smaller observable peak area than the real area of the peak. The coincidence correction is added to the calculation to correct this effect; it is dependent on the energy of the peak and also the position of the foil.

Isotope / Energy / COI
207Bi / 569,702 / 0,98321557
207Bi / 1063,662 / 0,97900394
206Bi / 516,18 / 0,9159576
206Bi / 803,1 / 0,89464966
206Bi / 1718,7 / 0,90593449
205Bi / 703,44 / 0,96136565
205Bi / 1764,36 / 0,9997822
205Bi / 987,62 / 0,96894934
204Bi / 374,72 / 0,90794063
204Bi / 899,15 / 0,88298978
204Bi / 984,02 / 0,93949177
203Bi / 825,2 / 0,95835597
203Bi / 896,9 / 0,87468888
203Bi / 847,3 / 0,94160337
202Bi / 960,67 / 0,92137305
202Bi / 422,18 / 0,94609134
202Bi / 657,4 / 0,94646732

2.4.2.Beam correction

The beam correction is dependent on the isotope, the energy of the neutron source, it is included more or less between 0,9 and 1,2.

Isotope / Ba(E=59 MeV)
207Bi / 0,99999999
206Bi / 0,99997447
205Bi / 0,99998959
204Bi / 0,99966009
203Bi / 0,99967560
202Bi / 0,99810667
201Bi / 0,99816411

2.4.3.Background correction

The background correction is dependent on the isotope, the energy of the neutron source. The former Nyield is multiply by the correction to obtain the corrected Nyield.

204Bi / Coef Back ground production
59 MeV second / 0,868139923
59 MeV first / 0,868139923
66.4 MeV / 0,588706511
72.8 MeV / 0,443191454
89.3 MeV / 0,318904664

2.4.4.Self absorption correction

Self-absorption correction was calculated by:

Where:

μ is the volume mass obtain from National Institute of Standards and Technologydata, we obtained μ/ρ [cm2/g]dependenton E[MeV]
For Bi, ρ=9,79 cm3/g
D, the thickness, comes from the mass known and the dimensions also known

Thanks to the CurveExpert software I could summarize results of the evolution of the self absorption correction with the energy:

2.5.Cross section calculations

Once the Nyield were calculated for each peak and each neutron energy, cross-sections could be calculated for each isotope, for a given neutron energy using a average Nyield (mean of Nyield for different times or different peaks but for a same neutron energy). Cross-section is define as:

Nyield : average Nyield of previously calculate, corrections including.
Nn : number of neutrons in peak (per cm²)

For experiment condition and energies

MeV / Nn
65 / 2,9820E+09
70 / 5,3165E+09
80 / 6,3691E+09
93 / 7,6936E+09

Foil mass mfoil (given data from experiment)
Foil size S : (2,5)² cm² = 6,25 cm²
Relative mass A : 208,98 [g.mol-1]
Avogadro’s number NA = 6,022.1023 [mol-1]

2.6.Uncertainty determination

Cross-section measurements must take account of the numerous sources of uncertainties. The first to be calculated was the statistical uncertaintyΔNyield_average coming from the Gauss fit of gamma peaks in the code DEIMOS32.

In the spectrums, more than one line was studied for each isotope, for each neutron energy, the cross-section should be the same for each peak of the isotope as well as for each time for a same peak. That is why, instead of only calculated for one line or one time, we multiplied the calculation so that we could made an average of values and obtained more accurate results.

Let’s take a look on the Nyield_average calculation:

Nyield_average : mean of Nyield for a same neutron energy
Ni : Nyield for a given neutron energy
aerrdeimos : uncertainty on the peak area from the software Deimos32

Then

And

Else

Finally we have to combine the relative uncertainty (from the Deimos data, calculated above) with the uncertainty from:

ΔNyield_average : Statistical uncertainty (Deimos)
10% : Beam intensityuncertainty
10% : neutron spectra uncertainty
3 % : detector efficiency uncertainty

Which give the final uncertainty oncross-sections:

RESULTS
Cross-section of 209Bi(n, 3n)207Bi

The 207Bi is a long lived radioisotope compared to the other radioisotopes studied with T1/2=31,55 years when the others are between minutes and days. As the foils were used before, for other experiments, the areas of peaks registered are a combination of the radiations from the Uppsala experiment and the radiations from previous experiments. In order to get the right cross section we had to subtract the spectra before the Uppsala experiment to the spectra after the Uppsala experiment. Without this subtraction the cross section was well over the model. Because of the statistical uncertainty this calculation is not yet finished and must be improved.

The cross-section results have been compared to THALYS 1.0 calculations and also with the data from the EXFOR Database. You can also observe the results from the experiment from Řež and Uppsala.

3.2.Cross-section of 209Bi(n, 4n)206Bi

3.3.Cross-section of 209Bi(n, 5n)205Bi

3.4.Cross-section of 209Bi(n, 6n)204Bi

3.5.Cross-section of 209Bi(n, 7n)203Bi

3.6.Cross-section of 209Bi(n, 8n)202Bi

3.7.Cross-section of 209Bi(n, 9n)201Bi

CONCLUSION

Activation analysis methods and gamma spectroscopy were used to study cross-sections of threshold reactions in Bi in energy range 62, 70, 80 and 93 MeV. The work presented is the first step in the analysis of the experimental data of the last irradiation in TSL Uppsala performed in February 2010. The good agreement of the experimental cross-sections with the data from EXFOR and with the THALIS model observed is encouraging for the next step of the analysis.

ACKNOWLEDGMENTS

I would like to thank my mentor Dr. Vladimir Wagner for getting me into the Nuclear Physics Institute for a three month internship, for his welcome and for everything I have learned from him. I would also like to thank Mr. Ondřej Svoboda for helping me all along my work. I finally like to thank everyone I worked with during these three months for the very nice welcome I had at the Nuclear Physics Institute of ASCR.

REFERENCES______

[1]O. Svoboda et al., Proceedings of the International Conference on Nuclear Data for Science and Technology – ND2010, Jeju, South Korea (2010)

[2]O. Svoboda et al., EFNUDAT Workshop on “Measurements and models of nuclear reactions” (2010)

[3] O. Kononov et al., Investigations of using near-threshold 7Li(p, n)7Be reaction for NCT based on in-phantom dose distribution