neutron induced resonance reactions

Frank Gunsing, CEA/Saclay Joint ICTP-IAEA Workshop on Nuclear Reaction Data for Advanced Reactor Technologies, Trieste, 26-5-2008 1

I R F U

Neutron induced resonance reactions

Frank Gunsing

CEA/Saclay

DSM/IRFU/SPhN

F-91911 Gif-sur-Yvette, France

[email protected]


I R F U

Neutron-nucleus reactions

Reaction: • X + a Y + b• X(a,b)Y• X(a,b)

Examples of equivalent notations:

Reaction cross section , expressed in barns, 1 b = 10–28 m2

Neutron induced nuclear reactions:• elastic scattering (n,n)• inelastic scattering (n,n’)• capture (n,)• fission (n,f)• particle emission (n,), (n,p), (n,xn)

Total cross section tot: sum of all reactions

238U + n 239U*238U + n 239U + 238U(n,)

10B + 1n 7Li + 4He10B + n 7Li + 10B(n,)


I R F U

Neutron-nucleus reactions

Reaction: • X + a Y + b• X(a,b)Y

Cross section: function of the kinetic energy of the particle a

Differential cross section:function of the kinetic energy of the particle aand function of the kinetic energy or the angleof the particle b

Double differential cross section: function of the kinetic energy of the particle aand function of the kinetic energy and the angleof the particle b

aa

XX YY bb


I R F U Cross sections n et f

neutron energy (eV)

cro

ss s

ecti

on

(b

arn

)


I R F U

10-3

10-2

10-1

100

101

102

0 10000 20000 30000 40000 50000

En (eV)

tota

l cro

ss s

ecti

on

(b

arn

)

56Fe + n

Interference of potential and n

transmissionT = exp(–n.T)

0<T<1


I R F U The nucleus as a quantum system

neutrons protons –V0

0

level scheme representation:excited states of a nucleus(shell model and other states)

ground state

1st excited state

2nd excited state

3rd excited state

AXe

xcita

tion

en

erg

y

nuclear state

shell model representation: configuration of nucleons in their potential

po

ten

tial d

ep

th



neutrons protons

po

ten

tial d

ep

th

–V0

0

AX

nuclear state



ground state

1st excited state

2nd excited state

3rd excited state

exc

itatio

n e

ne

rgy



neutrons protons –V0

0

AX

nuclear state



ground state

1st excited state

2nd excited state

3rd excited state

po

ten

tial d

ep

th

exc

itatio

n e

ne

rgy

Frank Gunsing, CEA/Saclay Joint ICTP-IAEA Workshop on Nuclear Reaction Data for Advanced Reactor Technologies, Trieste, 26-5-2008

10

I R F U

Decay of a nuclear state

state with a life time :

definition (Heisenberg):

Fourier transform gives energy profile:

eigen state,transitition E0Ef life time

E0 E

I(E) / 2

(E E0 )2 2 / 4

(t) 0e iE0t / e t / 2

E0

Ef


11

I R F U Neutron-nucleus reactions

Solve Schrödinger equation of system to get cross sections.Shape of wave functions of in- and outgoing particles are known, potential is unknown. Two approaches:

• calculate potential (optical model calculations, smooth cross section)• use eigenstates (R-matrix, resonances)

Conservation of probability density:


12

I R F U R-matrix formalism

+

entrance channel

+

exit channelcompound nucleus

partial incoming wave functions:

partial outgoing wave functions:

related by collision matrix:

cross section:

Internal region (r<ac compound nucleus):• wave function is expansion of eigenstates .

External region (r>ac, well separated particles):• no interaction, Schrödinger equation solvable.


13

I R F U Find the wave functions

separation distance

external region

internal region

match value and derivate of

Internal region: very difficult, Schrödinger equation cannot be solved directly solution: expand the wave function as a linear combination of its eigenstates.using the R-matrix:

External region: easy, solve Schrödinger equationcentral force, separate radial and angular parts.solution: solve Schrödinger equation of relative motion:

• Coulomb functions • special case of neutron particles (neutrons): fonctions de Bessel


14

I R F U The R-matrix formalism


15

I R F U

D =100 keVSn =10 MeV

A+1X

AX

D =10 eVn +

En

En

Compound neutron-nucleus reactions

compound nucleus reaction

+


16

I R F U

The R-matrix formalism

• The R-matrix formalism is adapted to describe compound nucleus reactions.

• Typically used for neutron-induced reactions at low energy (En<10 MeV, resonance region).

• The resonance parameters are properties of the excited nuclear levels:

- in the resolved resonance region (RRR), to each level (resonance) corresponds a set of parameters:

- in the unresolved resonance region (URR)average parameters are used:

10-3 10-1 101 103 105 107

En (eV)

tota

l cro

ss s

ecti

on thermal,

25 meV

resolvedresonances

unresolvedresonances


17

I R F U

• A same set of resonance parameters is used to produce all resonant reactions,• at low energies mainly elastic scattering and capture (and fission).

• In a measurement, one does not measure a cross section, but a reaction yield or• transmission factor.

• The measured reaction yield is not equally sensitive to all parameters, additional• constraints can be necessary to extract RP from measurement.

Resonance parameters


18

I R F U Neutron-nucleus reactions

Optical model calculations• gross structure• average cross sections• optical model potential • high energy, many channels

R-matrix resonance description• fine structure (resonances)• highly fluctuating cross sections• resonance parametrization• low energy, few channels

10-5 10-3 10-1 101 103 105 107 109

neutron energy (eV)

cap

ture

cro

ss

sect

ion

ne

utr

on

flu

x

thermalspectrum

stellarspectrum

whitesource

fissionspectrum

measurements calculations


19

I R F U

197Au

neutron energy (eV)tota

l cro

ss s

ecti

on

(b

) thermal RRR URR

resonances, R-matrix

OMP

Compound nucleus reactions


20

I R F U

6Li

27Al

55Mn

197Au

208Pb

241Am

neutron energy (eV)

tota

l cro

ss s

ecti

on

(b

)


21

I R F U Statistical model

The nucleus in the vicinity of Sn is described by the Gaussian Orthogonal Ensemble (GOE)

The matrix elements are random variables with a Gaussian distribution.

• Consequences: • The partial width have a Porter-Thomas distribution. • The spacing of levels with the same Jπ have approximately a Wigner distribution.

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3x = D / <D>

Wigner distribution

P(x

)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 1 2x =

i / <

i>

2=1

P(x

)

Porter-Thomas distribution


22

I R F U Distribution of the spacing of two consecutive levels


23

I R F U Distribution of neutron widths

N(t ) N(0) P(x)dxt


24

I R F U Level density

Sn

Separated states are available- at low excitation energy

- in the region just above Sn

énergie d'excitation U

den

sité

de

niv

eau

x

Sn


25

I R F U Known nuclei


26


stable


27


stable–

EC, +


28

I R F U Level spacing D0


29



30



31

I R F U Neutron separation energy

N

Z

4 - 10 MeVpour noyaux stables


32

I R F U Neutron separation energy


33

I R F U Fission of 235U+n and 238U+n

239U

238U

fissionactivation

Sn = 4.8 MeV

6.6 MeVn + 6.2 MeV

236U

235U

fissionactivation

Sn = 6.5 MeV

n +


34

I R F U Measurement of (n.xn) by gamma-ray spectroscopy

182W

181W

180W 6.7 MeV

8.1 MeV

gammasignature

excitationbyneutron

example: 182W(n,3n)180W

9/2+

0+

0+

183W

6.2 MeV

1/2–


35

I R F U

0 1 2 3 4 5 6 7

E (MeV)

197Au(n,)In

ten

sité

rel

ativ

e

Simulated gamma-ray spectrum


36

I R F U Moderation of neutrons

0.00 0.02 0.04 0.06 0.08 0.100

0.01

0.02

0.03

0.04

0.05

0.06

0.07

rela

tive

pro

bab

ility

dn

/dE

neutron energy (eV)

T = 300 K

thermal neutron spectrum

0 1 2 3 4 5 60.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

rela

tive

pro

bab

ility

neutron energy (MeV)

235U(nth

,f) emitted neutrons

H2O

moderator

Maxwell-Boltzmann velocity distribution: thermal neutrons:


37

I R F U Evaluated nuclear data libraries

Libraries• JEFF - Europe• JENDL - Japon• ENDF/B - US• BROND - Russia• CENDL - China

Common format: ENDF-6

Contents:Data for particle-induced reactions (neutrons, protons, gamma, other)but also radioactive decay data

Data are indentified by “materials” (isotopes, isomeric states, (compounds) )ex. 16O: mat = 825 natV: mat = 2300 242mAm: mat = 9547


38

I R F U The library JEFF-3.1


39

I R F U Files for a materialfrom report ENDF-102

1 General information 2 Resonance parameter data 3 Reaction cross sections 4 Angular distributions for emitted particles 5 Energy distributions for emitted particles 6 Energy-angle distributions for emitted particles 7 Thermal neutron scattering law data 8 Radioactivity and fission-product yield data 9 Multiplicities for radioactive nuclide production 10 Cross sections for photon production 12 Multiplicities for photon production 13 Cross sections for photon production 14 Angular distributions for photon production 15 Energy distributions for photon production 23 Photo-atomic interaction cross sections 27 Atomic form factors or scattering functions for photo-atomic interactions 30 Data Covariances obtained from parameter covariances and sensitivities 31 Data covariances for nubar 32 Data covariances for resonance parameters 33 Data covariances for reaction cross sections 34 Data covariances for angular distributions 35 Data covariances for energy distributions 39 Data covariances for radionuclide production yields 40 Data covariances for radionuclide production cross sections


40

I R F U Example: part of an evaluated data file


41

I R F U

A+1X

Ex

Neutron Capture Gamma-Ray Detection

A+1Xradioactive

• Activation- cross sections integrated over known neutron spectrum - applicable to some nuclei only- no time of flight

• Total energy detection- cEx, requires weighting function- neutron insensitive detector

example: C6D6 liquid scintillator

• Total absorption detection- requires = 4π, efficiency 100%- capture/fission discrimination in possible, example BaF2 total absorption

calorimeter

• Level population spectroscopy- applicable to some nuclei only- feasible with HPGe detectors,


42

I R F U Measuring a reaction yield using the time-of-flight technique

time zero

sample

production target,neutron source

reaction productdetector

flight length L

Pulse of charged particles


43


sample


flight length L




44


sample


flight length L




45


sample


flight length L

time of flight t




46


sample


flight length L

time of flight t

Kinetic energy of the neutron by time-of-flight




47

I R F U

Resolution

The resolution can be expressed equivalenty in time, distance and energy:

• neutron time-of-flight:• flight length:• neutron kinetic energy:

Lt

neutronstart

neutronstop

Neutron time-of-flight experiment

distribution

time-energy relation


48

I R F U Measured reaction yield

isolated Breit-Wigner resonance, decaying quantum state with half-life =h/


49



Doppler broadened


50


resolution broadened andshifted


Doppler broadened


51


real measurement with background

Doppler broadened


resolution broadened andshifted


52

I R F U Further Reading

Books/Papers• K. S. Krane, Introductory Nuclear Physics, Wiley & Sons, (1988).• G. F. Knoll, Radiation Detection and Measurement, Wiley & Sons, (2000).• P. Reus, Précis de neutronique, EDP Sciences, (2003).• J. E. Lynn, The Theory of Neutron Resonance Reactions, Clarendon Press, Oxford, (1968).• F. Fröhner, Evaluation and analysis of nuclear resonance data, JEFF Report 18, OECD/NEA (2000).• C. Wagemans, The Nuclear Fission Process, CRC, (1991).• A. M. Lane, R. G. Thomas, “R-matrix theory of nuclear reactions”, Rev. Mod. Phys. 30 (1958) 257.• G. Wallerstein, et al., “Synthesis of the elements in stars: forty years of progress”, Rev. Mod. Phys. 69 (1997) 995.

Web siteswww.nea.fr www.nndc.bnl.govwwwiaea.orgwww.cern.ch/ntof www.irmm.jrc.be


53

I R F U Conclusion

• Neutron induced reactions are important nuclear data necessary for a wide range of fields ranging from nuclear structure and astrophysics to advanced nuclear technology applications.

• The R-matrix formalism is adapted to describe compound nucleus reactions at low energy (En<10 MeV, resonance region).

• Resolved resonances need to be measured accurately, they cannot be predicted by nuclear models.


54

I R F U

Rapport de branchement 209Bi + n

209BiJπ=9/2+

210BiJπ=1–

Jπ=9–

– (5 d)

(3x106 y)

210PoJπ=0+ (138 d)

271 keV

210Bi*neutron


55

I R F U L’origine des déchets nucléaires

U (94.5%)

Pu (1%)autres actinides (0.5%)produits de fission (4%)

combustibleusé

238U (97%)

235U (3%)

combustiblefraisQuantité des déchets en France:

2500 kg/an par habitant dont 1 kg radioactif dont 20 g hautement radioactif

Loi Bataille:

recherche 1991 - 2006

• séparation et transmutation • stockage profonde • conditionnement et entreposage


56

I R F U Réduire la radiotoxicité:la transmutation en complément de stockage

• produits de fission • actinides mineurs transmutation par capture de neutrons transmutation par fission induite par dans flux de neutrons thermique neutrons dans flux de neutrons rapide

Composition des déchetsClefs CEA 46 (2002)


57

I R F U Réduire la radiotoxicité des déchets: le cylce du thorium

N

Z


58

I R F U

99Tc

– (2x105 y)99Ru

100Tc

– (15.8 s) 100Ru

(n,)

100Tc*

– (12 h) 130Xe

129I

130I

– (1.6x107 y)129Xe

(n,)

130I*

Réduire la radiotoxicité des déchets: la transmutation


59

I R F U Produits de fission:temps de vie versus rendement


60

I R F U

Resolution

GELINA (0o)n_TOF


61

I R F U

Resolution

neutron induced resonance reactions

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