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Low Energy Neutron Data for Nuclear Technology
J.L. Tain
Instituto de Física Corpuscular
C.S.I.C - Univ. Valencia
IP EUROTRANS-ITC2 Santiago de Compostela, June 6-10, 2006
Layout of the lectures
• Low energy neutron reactions: a catalogue• R-Matrix formalism: short introduction. Data bases.• Cross section measurements: general ideas• Neutron beam production• Experimental techniques:
– Total cross section– (n,) cross section– Fission cross section– Elastic cross section– Inelastic cross section– (n,xn) cross section– (n,p), (n,), …
For energies going from meV to (say) 20 MeV
Neutron reactions at low energies
A neutron is absorbed to form a “compound nucleus”:
n + AZ A+1Z*
which lives for a short time and decays:
A+1Z* n + AZ (elasticelastic)
A+1Z* n + AZ* (inelasticinelastic)
A+1Z* A+1Z*’ + (radiative captureradiative capture)
A+1Z* A1Z1* + A2Z2* + xn (fissionfission)
A+1Z* A+1-xZ* + xn (n multiplicationn multiplication)
…
Other contributions:
The CN formation probability is higher for certain neutron energies En corresponding to quasi-bound or virtual states: resonances
ER = Sn + EnSn : neutron separation energy of CN ( <10MeV ) level separation D0 ~ 1 eV – 100 keV
A
A+1
= n + + f + …
( = n + + f + ...)
Life-time Energy-width:
~ 1 meV – 100 keV
log En
1/v resolved unresolved overlapping
log
resolution
> D0 : overlapping resonances
< D0, > E: resolved resonance region (RRR)
< D0, < E: unresolved resonance region (URR)
1/v: thermal
Shape of neutron cross-section
• In the RRR region, is described using the R-Matrix formalism, in one of its usual approximations.
• In the URR region, average are described by Hauser-Feshbach statistical theory
• At higher energies cross section are described using Optical Model and other reaction models
• It is a parametric approach since nuclear theory cannot predict the values.
• Experimental information is strictly necessary.
Single Level Breit-Wigner Formalism: (n,)
(E) = 2 gJ
n
(E-ER’)2 + ¼2
For -capture into an isolated spin J resonance at ER:
= / 2E (neutron wavelength)
gJ = 2J + 1
2(2I + 1)
(spin stat. factor;
|I - ± ½| J |I - + ½| )
(E) = n(E) + + …; (FWHM)
n(E) = E/ER n(ER) , =0
… and the channel radius Rc
n+197Au, =0, J=2
ER = 4.9 eV
n = 15.2 meV
= 122.5 meV
En (eV)
(
ba
rn)
R-Matrix
SLBW formalism: elastic and capture cross sections
P0 = 0 = k RC = , S0 = 0
P = 2 P-1 / ((- S-1 )2 + P-12)
S = 2(-S-1) / ((- S-1 )2 + P-12) -
= -1 – tan(P-1 / ( -S-1))
ER’ = ER + n(ER)S(ER) - S(E)
2P(ER)
= (E-ER’)2
n = n(ER)
P(E)
P(ER)
n
1 + 2
1 = gJ
4
k2
k = 2E /
= gJ [ sin2 + cos 2 + sin 2 ]n
1 + 2
1 n
1 + 2
4
k2
gJ = 2J + 1
2(2I + 1)
ELASTICCAPTURE
potential resonant interference
(n,)
(n,n)
238U
, I, J, ER , n(ER), , Rc
Statistical Nuclear Model
Cross sections are described by average strength functions (S) and level densities ()
Hauser-Feshbach
lJcnnn
lJcn
lJc SEJESET ,,22
nn
nnl
nlJn E
eVEEP
EP
10
widthchannelreduced:
strengthchannel:
ontransmissichannel:
lJc
lJc
lJc
S
T
25.125.022
2exp
212
1
2
)1(exp
4
12,,
tEa
EaJJJEJ
x
xx
fJ XL
XLL
x
EfEEJ
12
,,
1 20
2220
2
2008
1 1068.8
EEE
EEfE
'''''''
''''''
'''
2'Jll
Jlc
Jlc
Jlc
lJc
Jcc T
TTg
k
yy
yyPPT ,
2
1exp
2
1
d
dxxxPW
,
4
1exp
2
1 2
Porter-Thomas fluctuations:
Wigner fluctuations:
• From the analysis of experimental data on capture, total, fission, … cross-sections, resonance parameters are obtained for every nucleus.
• All the information is combined, cross-checked for consistency, etc, in a process called “evaluation” until a recommended set of parameters is obtained.
• This information is published in a Evaluated Nuclear Data File using an accepted standard format (ENDF-6)
• There exist several files:
• BROND-2.2 (1993, Russia)
• CENDL-3 (2002, China)
• ENDF/B-VI.8 (2002, US)
• JEFF-3.0 (2002, NEA+EU)
• JENDL-3.3 (2002, Japan)
Neutron Reaction Data
Measurement of cross-sections (energy differential)
r(E) =Number of reactions
Number of target nucleus per unit area Number of neutrons of energy E
Nn nT Nr
Needs:
• sample of known mass and dimensions
• count the number of incident neutrons of energy E
• count the number of reactions
… but there are a number of experimental complications
ENbarnn
NE
nT
rr
1
Cross sections can also be:• Reaction product angle differential • Reaction product energy differential • Reaction product multiplicity dependent• Energy weighted• …
Neutron Beams
• Need to span a huge energy range: 1meV – 20MeV
• Since neutrons cannot be accelerated, they have to be produced by nuclear reactions at certain energy and eventually decelerated by nuclear collisions (moderated)
• Energy determination:
• kinematics of two-body reaction
• mechanical selection of velocities (“chopper”)
• Time Of Flight measurement
•Sources:
• Radioactive
• Nuclear detonations
• Reactor
• Light-ion accelerator
• Electron LINACS
• Spallation
2
2
2
1
t
lmE nn
High Flux Reactor at the Institut Laue-Langevin (Grenoble)
• thermal 1015 n/cm2/s
ForschungsZentrum Karlsruhe Van de Graaf
• 7Li(p,n)7Be, Q= -1.644MeV
• Ep ~ 2MeV En ~ 5-200keV
• Rate: 250kHz, t = 0.7ns
30keV > Thresh.
Geel Electron LINear Accelerator
• (,n), (,f) on U (bremsstrahlung)
• Ee ~ 100MeV, Ie ~ 10-100A
• Rate: 100-800Hz, t ~ 0.6-15ns
… GELINA
U-TARGET & H2O MODER.
NEUTRON SPECTRA
H2O MODERATOR
n yield vs. Ee
CERN neutron Time Of Flight
n_TOF
• p-spallation on Pb target
• Ep = 20GeV, Ip = 7x1012 ppp
• Rate: 2.4s-1 , t = 14ns
PROTON BEAM LINE
p current monitor
p-intensity pickup
Entrance to the target
Water cooled Pb target
n beam tube
shielding
NEUTRON BEAM LINE
shielding
n_TOF
Bending magnet
2nd collimator
shielding
EXPERIMENTAL AREA
n monitor
Sample changer
BEAM DUMP
n monitor
… n_TOF
• The characteristics of the spallation-moderation process and the collimators in use determine the neutron beam parameters: intensity- energy distribution, energy resolution and spatial distribution.
TARGET:
80x80x60 cm3 Pb + 5cm H2O
SPALLATION PROCESS: ~600 n/p
MODERATION:
= ln(Ei/Ef) 1+ ln
( (H)=1, (Pb)=0.01 )
A-1
A+1
(A-1)2
2A
Intensity distribution
… n_TOF
The statistical nature of the moderation process produces variations on the time that a neutron of a given energy exits the target assembly
Resolution Function
… also important: time spread of beam
RF
t beam
Beam energy-resolution
time vs. energyRF @ 5eV
RF @ 180keV
… n_TOF
22
2
t
t
l
l
E
E
n
n
The collimation system determines the final number of neutrons arriving to the sample an its spatial distribution
Neutrons on sample
10-5
Beam profile
4cm
… n_TOF
Counting neutrons
Common reactions used for neutron detection:
Elastic scattering:
• n + 1H n + 1H
• n + 2H n + 2H (abund.=0.015%)
Charged particle:
• n + 3He 3H + 1H + 0.764 MeV (abund.=0.00014%)
• n + 6Li 4He + 3H + 4.79 MeV (abund.=7.5%)
• n + 10B 7Li* + 4He 7Li + 4He + 0.48 MeV +2.3 MeV (abund.=19.9%, b.r.=93%)
Radiative capture:
• n + 155Gd 156Gd* -ray + CE spectrum (abund.=14.8%)
• n + 157Gd 158Gd* -ray + CE spectrum (abund.=15.7%)
Fission:
• n + 235U fission fragments + ~160 MeV
• n + 239Pu fission fragments + ~160 MeV
• n + 238U fission fragments + ~160 MeV
Neutron Intensity Monitoring:
• Reaction: n + 6Li t +
• Si detectors
Si
Si
Si
Si 200g/cm2 on 3m Mylar
… n_TOF
Counting neutrons
Neutron Monitors
6Li(n,t)
Scintillator + Photomultiplier 10B(n,)7Li
Ionisation Chamber
…GELINA
Counting reactions
Total reaction cross sections
• Transmission measurements: counting the neutrons disappearing from the beam
En
outsamplen
insamplen
Te
EN
ENET
SAMPLE+FILTERS
GELINA
NEUTRON MONITOR
Background correction using black resonance filters
101 102 103 104 105 10610-4
10-2
100
Total Background filters Average Values Fit
Res
pons
e (c
ount
s / n
s)
Neutron Energy / eV
Black Resonance Filters
Nucleus Energy eV
109Ag 5.20 186W 18.83 182W 21.06 209Bi 800.00 23Na 2850.00
32S 102710.00
Techniques for radiative capture (n,) detection:
• Detection of the capture nucleus
• Activation measurements
• Detection of -ray cascade
• Total Absorption Spectrometers
• Total Energy Detectors
• Moxon-Rae Detectors
• Pulse Height Weighting Technique
• High Resolution Ge detectors
n
Activation measurement
• Irradiation: A(n,)A+1
• A+1 radioactive with suitable T1/2
• Measurement of characteristic -ray of known I with Ge detector
FZK Karlsruhe
C = 1 - (1 - i)i=1
m
i : total efficiency for -ray of energy Eip
i : peak efficiency for -ray of energy Ei
Define:
Then:
total efficiency for cascade:
pC = p
ii=1
m
peak efficiency for cascade:
E1
E2
E3
EC
If pi = 1, i p
C = C = 1 Total Absorption Spectrometer
Total Energy Detector
If i « 1 & i = kEi , i C i = k Ei = k EC
i=1
m
i=1
m
Detection of -ray cascade
n_TOF Total Absorption Calorimeter
• 40 BaF2 crystals
• /4 = 95%
• E 6%
… n_TOF
(from Karlsruhe 4 BaF2 detector)
BaF2(n,) contamination
= 95% BACKGROUND REDUCTION
Total Energy Detectors
• Moxon-Rae type detectors:
The proportionality between efficiency and -ray energy is obtained by construction:
(,e-) converter + thin scintillator + photomultiplier
e-
Maximum depth of escaping electrons increases with E …
But … proportionality only approximate (need corrections)
Not much in use nowadays
Bi-converter
C-converter
Mo-converter
Bi/C-converter
/
E
E
• Pulse Height Weighting Technique:
Total Energy Detectors
The proportionality between efficiency and -ray energy is obtained by software manipulation of the detector response (Maier-Leibniz):
If Rij represents the response distribution for a -ray of energy Ej:
Rij = ji=1
imax
Wi Rij = Eji=1
imax
it is possible to find a set of weighting factors Wi (dependent on energy deposited i) which fulfil the proportionality condition (setting k=1):
for every Ej
Rij
E = 9MeV
E = 2MeV
Wi
Detectors: C6D6 liquid scintillators
Advantage: low neutron sensitivity
Also detector dead material is important …
Optimized BICRON
HOME MADE:
• C-fibre cell
• No cell window
• No PMT housing
… and surrounding materials
= 3-5%
Fission cross section
• Detection of fission products
1 10 100 1000 10000 100000 1000000 1E7 1E80.00.10.20.3
1
10
n_TOF James Lestone ENDF-B/VI
f, b
arns
En, eV
Problems:• strong energy loss• angular distribution• often -decay contamination
… n_TOF
PPAC assembly
Ionization chamber
Gas used: Ar (90 %) CF4 (10 %).
Gas pressure: 720 mbarElectric field: 600 V/cmGap pitch: 5 mmDeposit diameter: 5 cmDeposit thickness: 125 µg/cm Support thickness: 100 µm (Al)Deposits on both sides.Electrode diameter: 12 cmElectrode thick.: 15 µm (Al) Windows diameter: 12 cm (KAPTON 125 µm)
… n_TOF
Fission Ionization Chamber Assembly
PPAC FIC
… n_TOF
Inelastic scattering measurements
• Detection of neutrons
• Detection of -ray from de-excitation cascade
Measurement of scattered neutron energies by TOF requires monochromatic beams
Elastic scattering measurements
• Detection of neutrons
238U
En=465 keV
n-source: 7Li(p,n)
Tohoku University
Kinematics determines neutron energy and resolution
Neutron multiplication (n,xn) cross sections
• Detection of the residual nucleus: activation measurements (see before)
• Detection of neutrons (ambiguity due to limited neutron efficiency)
• Detection of -ray from de-excitation cascade
In order to transform -ray production cross section into reaction cross section it is required a complete knowledge of the level scheme
Angular distribution effects have to be corrected
FZK
ORELA
(n,p), (n,), … cross sections
• Activation measurements• Direct detection of p, , …
• At low energies thin samples windowless detectors (similar to fission)• At high energies Si detectors
Acquiring the data: full train of detector pulses
• Digitizer: 8bit-500MS/s FADC + 8MB memory
• On-line “zero” suppression
TOF & EC6D6
from pulse-shape fit
of PMT anode signal
• t = 2ns
• En down to 0.6eV
• 0.5 MB/pulse/detector
Dead-time and pile-up corrections
Yield:
• Self-shielding:
• Multiple scattering correction: elastic collision(-s) + reaction
Sample effects:
Analysing the data:
shielded
Single-scattering
ENn
NE
nT
rr
EN
NEY
n
rr
EE
eEY rEnr
T
1
nEnEY rTr ,
...
)1()1(
)1(
...
111
0
210
rnr
rr
rrrr
TTY
TY
YYYY
• Thermal (-Doppler) broadening
T = 300K
58Ni(n,)
ER =136.6keV
Beam effects:
• Resolution Function
-5 0 5 10 1510-4
10-3
10-2
10-1
100 En = 1 - 10 eV
Res
pons
e /
(1/
cm)
Distance / cm
For a fix neutron energy center-of-mass energy varies because of thermal vibrations
A given TOF corresponds to a distribution of neutron energies orEnergy distribution of “monochromatic” neutron beam
Use a R-Matrix code as SAMMY to fit the data and extract the parameters: ER, , n, …
197Au(n,)
ER= 4.9eV
56Fe(n,)
ER= 1.15keV
RF
T broad. single-scattering
double scattering
Y =
Slowing Down Spectrometer: LSDS (LANL-Los Alamos)
Time-energy relation
MC simulation
Lead block + sample+counters
%E
ΔE30
20tt
KE
Pile oscillator method
OAK RIDGE
The oscillating motion of a sample in the neutron field of a reactor induces oscillations in the field (global and local) whose amplitude is proportional to the absorption cross section
Needs correction for scattering
Bibliography:
1. The Elements of Nuclear Interaction Theory, A. Foderaro, MIT Press, 1971
2. Neutron Sources for Basic Physics and Applications, Ed. S. Cierjacks, NEA/OECD, Pergamon Press, 1983
3. Neutron Radiative Capture, Ed. R.E. Chrien et al., NEA/OECD, Pergamon Press, 1984
4. Evaluation and Analysis of Nuclear Resonance Data, F.H. Froehner, NEA-OECD, JEFF Report 18, 2000
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