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