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 METHOD
1.1. Neutron production
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:
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.
1.3. 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. 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
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2. ANALYSIS METHOD
2.1. Spectrum analysis with Deimos32
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.
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).
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
2.2. Comparison
of
experimental
spectrum and isotope data
The energy peaks of these isotopes were noted as
well as peak areas.
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.
2
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.
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:
Beam
Peak area Self-absorption
correction
correction
N yield 
S p  Cabs ( E )  Ba
I    P ( E )  Coi  Carea
Dead time
correction
Decay during cooling
and measurement
t real 1
  tirr
e (  t0 )
(   t real )
tlive m foil 1  e
1  e (   tirr )
γline intensity
Detector
efficiency
Correction for
coincidences
Weight
Square-emitter
normalization
correction
Decay during
irradiation
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:
𝑁𝑦𝑖𝑒𝑙𝑑 =









𝑆𝑝
𝑡𝑟𝑒𝑎𝑙 1
𝑒 (𝜆.𝑡0)
𝜆. 𝑡𝑖𝑟𝑟
𝐼𝛾 . 𝜀𝑝 (𝐸) 𝑡𝑙𝑖𝑣𝑒 𝑚𝑓𝑜𝑖𝑙 1 − 𝑒 (𝜆.𝑡𝑟𝑒𝑎𝑙) 1 − 𝑒 (𝜆.𝑡𝑖𝑟𝑟 )
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
𝜀𝑝 (𝐸) Detector efficiency, function of the
energy peak described as :
Energy
569,702
1063,662
516,18
803,1
1718,7
703,44
1764,36
987,62
374,72
899,15
984,02
825,2
896,9
847,3
960,67
422,18
657,4
COI
0,98321557
0,97900394
0,9159576
0,89464966
0,90593449
0,96136565
0,9997822
0,96894934
0,90794063
0,88298978
0,93949177
0,95835597
0,87468888
0,94160337
0,92137305
0,94609134
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.
 P ( E )  exp( a  b. ln( E )  c.(ln( E ))²  d .(ln( E )) 3  e.(ln( E )) 4 )
With the coefficients:
Isotope
207Bi
207Bi
206Bi
206Bi
206Bi
205Bi
205Bi
205Bi
204Bi
204Bi
204Bi
203Bi
203Bi
203Bi
202Bi
202Bi
202Bi
a  144,19554
b  89,083642

c  20,834704
d  2,127329

e  0,080924654
2.4. Corrections
2.4.1. Coincidences correction
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Isotope
207Bi
206Bi
205Bi
204Bi
203Bi
202Bi
201Bi
Ba(E=59 MeV)
0,99999999
0,99997447
0,99998959
0,99966009
0,99967560
0,99810667
0,99816411
different times or different peaks but for a same
neutron energy). Cross-section is define as :
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.
204
Bi
𝜎=

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
Coef Back ground production
59 MeV second
59 MeV first
66.4 MeV
72.8 MeV
89.3 MeV
0,868139923
0,868139923
0,588706511
0,443191454
0,318904664
2.4.4. Self absorption correction
Self-absorption correction was calculated by:
Cabs 
Where:
𝑁𝑦𝑖𝑒𝑙𝑑 . 𝑆. 𝐴
𝑁𝑛 . 𝒩𝐴




 .D
1  e   .D

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 known
Thanks to the CurveExpert software I could
summarize results of the evolution of the self
absorption correction with the energy:
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 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
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:
n
N yield _ average 
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
i 1
n

4
2
i
1
 N
i 1

Ni
 N
2
i
Nyield_average : mean of Nyield for a same neutron
energy
Ni : Nyield for a given neutron energy


Ni  aerrdeimos.Ni
aerrdeimos : uncertainty on the peak area from
the software Deimos32
Then
N yield _ average 
1
n
1
 N
i 1
n
And
If
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.
X2 

i 1
N
2
3.2. Cross-section of 209Bi(n, 4n)206Bi
i
 Ni 
2
yield _ average
2
i
N
n(n  1)
X 2  1  incertaint y  N yield _ average
Else X 2  1  incertaint y  N yield _ average. X 2
3.3. Cross-section of 209Bi(n, 5n)205Bi
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:
   . N ield _ average  Beam  N eutron  Detector
2
2
2
2
3.4. Cross-section of 209Bi(n, 6n)204Bi
3. RESULTS
3.1. 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.
3.5. Cross-section of 209Bi(n, 7n)203Bi
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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.
3.6. Cross-section of 209Bi(n, 8n)202Bi
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)
3.7. Cross-section of 209Bi(n, 9n)201Bi
[3] O. Kononov et al., Investigations of using nearthreshold 7Li(p, n)7Be reaction for NCT based on inphantom dose distribution
4. 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.
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