Determination of experimental cross-sections by activation method
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Determination of experimental cross-sections by activation
method
Pierre-Jean Viellenave Tutor: Dr. Vladimir Wagner
Nuclear Physics Institute, Academy of Sciences of Czech Republic
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Contents
Introduction
Spectrum analysis with DEIMOS32
Cross-sections calculation
Statistical analysis (incertainty calculation)
Results
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Introduction
My work consists:
In analysing gamma spectrums from experiment with DEIMOS32…
Experiment = measurement of radioactive sample (activated by activation method in a cyclotron) with different configurations
…To get experimental cross-sections
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Spectrum analysis with
DEIMOS32Gamma lines peak analysis with the software DEIMOS 32
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Spectrum analysis with
DEIMOS32We’re able to plan possible reactions and isotopes produced
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Spectrum analysis with
DEIMOS32Comparison between the result tables from DEIMOS 32 analysis and the internet data base (decay data search) on gamma lines to identify the isotopes
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Spectrum analysis with
DEIMOS324 isotopes found from (n,2n) to (n,4n) reactions and 1 isotope (198Au) found from (n,gamma) reaction.
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Cross-sections calculation
Nyield calculation:
)()(
)(
11
1
)(
)( 0
irrreal tirr
t
t
foillive
real
areaP
aabspyield e
t
e
e
mt
t
CCoiEI
BECSN
Peak area Self-absorption correction
Beam correction
Dead time correction Decay during cooling and measurement
γline intensity
Detector efficiency
Correction for coincidences
Square-emitter correction
Weight normalization
Decay during irradiation
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Cross-sections calculation
Detector efficiency (given):
Nyield approximation:
173815,0
18474,3
3295,18
6493,36
d
c
b
a
)()(
)(
11)(
0
irrreal tirr
t
t
live
real
P
pyield e
t
e
e
t
t
EI
SN
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Cross-sections calculation
Nyield calculation:
)()(
)(
11)(
0
irrreal tirr
t
t
live
real
P
pyield e
t
e
e
t
t
EI
SN
Sp: peak areaIγ: gamma line intensity (in %)Treal & Tlive: datas from exp.λ: decay constant
Tirr: irradiation timeT0: beam end – start of measurement
2/1
)2ln(
T
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Cross-sections calculation
Cross-section calculation:
Nn: neutrons number (depends on experiment) mfoil: foil massS: foil size (in cm2)
A: mass number (197 for Au)NA: Avogadro’s number (6,022.1023 {mol-1})
Afoiln
yield
NmN
ASN
..
..
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Statistical analysis
N yield_average calculation for each isotope => to increase the precision:
n
i i
n
i i
i
averageyield
N
N
N
N
12
12
_ 1 ideimosi NaerrN .
Aerr: incertainty of peak area (data from DEIMOS)
So =>
n
i i
averageyield
N
N
12
_1
1
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Statistical analysis
N yield_average calculation for each isotope => to increase the precision:
n
i i
n
i i
i
averageyield
N
N
N
N
12
12
_ 1 ideimosi NaerrN .
Aerr: incertainty of peak area (data from DEIMOS)
So =>
n
i i
averageyield
N
N
12
_1
1
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Statistical analysis
Finally:
)1(1
2
2_
2
n
N
NN
X
n
i i
averageyieldi
averageyieldNX _2 yincertaint1
2_
2 .yincertaint1 XNX averageyield
With:
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Results
0 2 4 6 8 10 12 1417800
18000
18200
18400
18600
18800
332,983 keV
Series1Series5Series7Series9
Measurement
Num
ber
of
nucle
i
197Au (n, 2n) 196Au
0 2 4 6 8 10 12 1418200
18400
18600
18800
19000
19200
19400
355,684 keV
Series1Series5Series7Series9
Measurement
Num
ber
of
nucle
i (1
0^
6)
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Results197Au (n, 4n) 194Au
0 2 4 6 8 10 12 1412450
12500
12550
12600
12650
12700
12750
12800
194Au (328 keV)Series5Series7Series9
Measurement
Nu
mb
er o
f ra
dio
acti
ve
nu
clei
0 2 4 6 8 10 12 1411300
11400
11500
11600
11700
11800
11900
12000
12100
194 Au (293 keV
Series5
Series7
Series9
Measurement
nu
mb
er o
f ra
dio
nu
clid
e [1
0^6]
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Results197Au (n, 2n) 196m2Au
0 2 4 6 8 10 12 141000
1100
1200
1300
1400
1500
1600
147,81 keV
Series1Series5Series7Series9
Measurement
Num
ber o
f nuc
lei (
10^6
)
0 2 4 6 8 10 12 14800900
100011001200130014001500
188,27 keV
Series1Series5Series7Series9
Measurement
Num
ber
of
nucle
i
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Results
Comments:
Fluctuations are purely systematical
Nyield-average isn’t depending on the configuration
But the difference of Nyield-average (calculated for each gamma line and isotope) is bigger than the uncertainty of weighted average. It comes from the systematic uncertainty of efficiency determination.
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Thank you for your attention !!!