Determination of experimental cross-sections by activation

methodPierre-Jean Viellenave

Tutor: Dr. Vladimir Wagner

Nuclear Physics Institute, Academy of Sciences of Czech Republic

Contents

Introduction

Spectrum analysis with DEIMOS32

Cross-sections calculation

Statistical analysis (incertainty calculation)

Results

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

Spectrum analysis with

DEIMOS32Gamma lines peak analysis with the software DEIMOS 32

Spectrum analysis with

DEIMOS32We’re able to plan possible reactions and isotopes produced

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

Spectrum analysis with

DEIMOS324 isotopes found from (n,2n) to (n,4n) reactions and 1 isotope (198Au) found from (n,gamma) reaction.

Cross-sections calculation

Nyield calculation:

)()(

)(

111

)()( 0

irrreal tirr

t

t

foillive

real

areaP

aabspyield e

tee

mtt

CCoiEIBECS

N

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

Cross-sections calculation

Detector efficiency (given):

Nyield approximation:

173815,018474,33295,186493,36

dcba

)()(

)(

11)(

0

irrreal tirr

t

t

live

real

P

pyield e

tee

tt

EIS

N

Cross-sections calculation

Nyield calculation:

)()(

)(

11)(

0

irrreal tirr

t

t

live

real

P

pyield e

tee

tt

EIS

N

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

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

NmNASN....

Statistical analysis

N yield_average calculation for each isotope => to increase the precision:

n

i i

n

i i

i

averageyield

N

NN

N

12

12

_ 1 ideimosi NaerrN .

Aerr: incertainty of peak area (data from DEIMOS)

So =>

n

i i

averageyield

N

N

12

_1

1

Statistical analysis

N yield_average calculation for each isotope => to increase the precision:

n

i i

n

i i

i

averageyield

N

NN

N

12

12

_ 1 ideimosi NaerrN .

Aerr: incertainty of peak area (data from DEIMOS)

So =>

n

i i

averageyield

N

N

12

_1

1

Statistical analysis

Finally:

)1(1

2

2_

2

nN

NN

X

n

i i

averageyieldi

averageyieldNX _2 yincertaint1

2_

2 .yincertaint1 XNX averageyield

With:

Results

0 2 4 6 8 10 12 14178001800018200184001860018800

332,983 keV

Series1Series5Series7Series9

Measurement

Num

ber

of n

ucle

i

197Au (n, 2n) 196Au

0 2 4 6 8 10 12 1418200184001860018800190001920019400

355,684 keV

Series1Series5Series7Series9

MeasurementNum

ber

of n

ucle

i (10

^6)

Results197Au (n, 4n) 194Au

0 2 4 6 8 10 12 1412450

12500

12550

12600

12650

12700

12750

12800

194Au (328 keV)Series5Series7Series9

Measurement

Num

ber

of r

adio

activ

e nu

clei

0 2 4 6 8 10 12 1411300

11400

11500

11600

11700

11800

11900

12000

12100

194 Au (293 keVSeries5Series7Series9

Measurement

num

ber

of r

adio

nucl

ide

[10^

6]

Results197Au (n, 2n) 196m2Au

0 2 4 6 8 10 12 141000110012001300140015001600

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 n

ucle

i

ResultsComments:

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.

Thank you for your attention !!!