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.

1. EXPERIMENTAL METHOD1.1. 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 0,0940265693 MeV 6,32182 0,103318862 MeV 5,74052 0,093818562 MeV repeated 5,63605 0,092111180 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.

1

2. ANALYSIS METHOD2.1. 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.

Isotope1 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

)()(

)(

111

)()( 0

irrreal tirr

t

t

foillive

real

areaP

aabspyield e

tee

mtt

CCoiEIBECS

N

Peak area Self-absorption correction

Beam correction

Decay during cooling and measurement

γline intensity

Detector efficiency

Correction for coincidences

Square-emitter correction

Weight normalization

Decay during irradiation

Dead time correction

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:

N yield=Sp

I γ . ε p (E )t realt live

1m foil

e (λ .t0 )

1−e ( λ.t real )

λ . tirr1−e( λ.t irr )

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 ε p (E ) Detector efficiency, function of the

energy peak described as :

With the coefficients:

2.4. Corrections2.4.1. 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 COI207Bi 569,702 0,9832155

7207Bi 1063,662 0,9790039

4206Bi 516,18 0,9159576206Bi 803,1 0,8946496

6206Bi 1718,7 0,9059344

9205Bi 703,44 0,9613656

5205Bi 1764,36 0,9997822205Bi 987,62 0,9689493

4204Bi 374,72 0,9079406

3204Bi 899,15 0,8829897

8204Bi 984,02 0,9394917

7203Bi 825,2 0,9583559

7203Bi 896,9 0,8746888

8203Bi 847,3 0,9416033

7202Bi 960,67 0,9213730

5202Bi 422,18 0,9460913

4202Bi 657,4 0,9464673

2

2.4.2. Beam correction

3

εP(E )=exp( a+b . ln (E )+c .( ln (E))²+d .( ln(E))3+e .( ln(E ))4 )

{a=−144 ,19554 ¿ {b=89 ,083642 ¿ {c=−20 ,834704 ¿ {d=2 ,127329 ¿ ¿¿¿

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 0,99999999206Bi 0,99997447205Bi 0,99998959204Bi 0,99966009203Bi 0,99967560202Bi 0,99810667201Bi 0,99816411

2.4.3. Background correctionThe 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 0,86813992359 MeV first 0,868139923

66.4 MeV 0,58870651172.8 MeV 0,44319145489.3 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 Technology data, we obtained μ/ρ [cm2/g] dependent on E[MeV]

For Bi, ρ=9,79 cm3/g D, the thickness, comes from the mass

known and the dimensions also knownThanks to the CurveExpert software I could summarize results of the evolution of the self absorption correction with the energy:

2.5. Cross section calculationsOnce 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 :

σ=N yield . S . AN n . N A

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+0980 6,3691E+0993 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 determinationCross-section measurements must take account of the numerous sources of uncertainties. The first to be calculated was the statistical uncertainty ΔNyield_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

4

Cabs=μ .D

1−e− μ. D

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

If

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 intensity uncertainty 10% : neutron spectra uncertainty 3 % : detector efficiency uncertainty

Which give the final uncertainty on cross-sections:

3. RESULTS3.1. 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

5

N yieldaverage=

∑i=1

n N i

ΔNi2

∑i=1

n 1ΔN

i2

ΔN i=aerrdeimos .N i

ΔN yield average= 1

√∑i=1n 1ΔN

i2

X2=

∑i=1

n (N yield average−N i )2

ΔNi2

n(n−1)

X2<1⇒ incertainty=ΔN yieldaverage

X2>1⇒ incertainty=ΔN yieldaverage.√X2

Δσ=σ .√ΔN ieldaverage2+ΔB

eam2+ΔN

eutron2+ΔD

etector2

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

4. CONCLUSIONActivation 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.

ACKNOWLEDGMENTSI 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

6