Detection of Neutrons: Part II Ralf Nolte Table of Contents - - PowerPoint PPT Presentation

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Detection of Neutrons: Part II Ralf Nolte Table of Contents - - PowerPoint PPT Presentation

Detection of Neutrons: Part II Ralf Nolte Table of Contents Introduction Neutrons in Science and Technology Interaction of Neutrons with Matter Neutron Detection General Properties of Detectors Detectors for Thermal and


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Detection of Neutrons: Part II

Ralf Nolte

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  • Introduction

– Neutrons in Science and Technology – Interaction of Neutrons with Matter

  • Neutron Detection

– General Properties of Detectors – Detectors for Thermal and Slow Neutrons – Detectors for Fast Neutrons

  • Recoil Detectors: Prop. Counters, Scintillation Detectors, Recoil Telescopes
  • (Fission) Ionization Chambers
  • Techniques for Neutron Measurements

– Time-of-flight – Spectrometry – Spatial Neutron Distribution

  • Absolute Methods, Quality Assurance

– Associated particle methods – Key comparison

Table of Contents

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Recoil Detectors: Proton Telescopes

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Recoil Telescopes as Reference Instruments

  • Scintillation detector used as primary reference instrument?

– Properties of the scintillators show variations: Light output, H/C ratio – Full angular distribution for n-p scattering required – Interference from 12C(n,x) interactions – Detection efficiency difficult to calculate ‘accurately’ (1-2% uncertainty)  Calibration required!

  • Way-out: Recoil Proton Telescopes (RPTs)

– Only n-p scattering contributes – Restricted range of scattering angels – ‘Localized’ response function – Efficiency determined by geometry, radiator mass and diff. cross section – Detection efficiency small: e = 10-4 - 10-5 – Energy range depends of radiator thickness

p 2 n p

cos   E E

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The Classical Low-Energy Telescope: T1 of PTB

Los Alamos in-beam design:

  • Two CO2 prop. counters: DE
  • Surface barrier detector: E
  • Radiator – source distance:

20-35 cm

  • 1 mm Ta aperture:

(20.980.01) mm

  • Energy range :

 1.2 MeV – 15 MeV using three radiators  up to 20 MeV with degrader foils

  • Single rates: < 104 s-1
  • Coincidence rate: 0.5 – 2 s-1

P1  P2  SB

  • Coincidence resolution: 2 µs
  • Multi-parameter DAQ
  • Prop. Counters P1 and P2

Radiator Si SB Diode Aperture

n

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T1: Recoil Proton Spectra

  • D(d,n)3He, D2 gas target, Ed,0 = 7.11 MeV, <En> = 10.02 MeV

P2 - P1 P1 + P2 - SB recoil protons SB

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T1: Analysis

  • Calculation of the efficiency:

– (Semi)analytical integration – Monte Carlo simulation – Relativistic kinematics for CM → LAB! – Anisotropic source: D(d,n)

 

 

Y n N A A d d A E E A

A A np H geo p 2 1 2 2 2 2 1 1 geo n np n p p np

d d cos cos , d d

1 2

 e  e                                    

 

En = 8.4 MeV

  • Main contributions to uncertainty

– Counting statistics: uN/N = 1% - 2% – Efficiency: ue/e = 1% –

  • Diff. n-p cross section: uA/A = 0.2% - 1%
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Cu coll. + DE-E

RPT Design Exercise: 75 MeV

Test of a proton recoil telescopes for TLABS neutron beam facility:

  • Neutron Source: natLi (8 mm) + p (75 MeV):

quasi-monoenergetic spectrum, <En,0+1 > = 71.6 MeV (FWHM  3.2 MeV)

  • Collimated beam (50  50 mm)2

DE1-DE2-E

… which one made the race?

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RPT Design Exercise: Results

  • Good particle discrimination with 500 µm Si-PIPS as DE detectors
  • Less neutron induced coupling with DE1-DE2-E scheme

E DE TOF E

Double stage RPT: Cu-coll. + DE-E

DE2 E TOF E

Triple stage RPT: DE1-DE2-E

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Fast Neutrons: Ionization Chambers

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  • Electrical field:
  • Charge per unit track segment:
  • Voltage change induced by drift along dx:
  • Integration along frag. track:

Fission Ionization Chambers

Drift velocities: v = µ·E/p, vel >> vion  Ion-induced signal suppressed by time constant of the pre-amp. Electron-induced signal depends on the location of the ionizing event

fissile layer

+HV electrons fission frag. d ions  x r U0

d U E         r E W e q d d

ff

x E q U CU d d  r d r r E W C e U

R

d ) cos 1 ( d d 1          

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FF energy loss in the fissile deposit

Simulated Pulse-Height Spectra

Monte Carlo calculations:

  • (A, Z) of the fissioning system: multiple-chance fission!
  • Range data for U3O8 and Ar/CH4
  • Model for the surface roughness: <ra>
  • FF distributions: Y(En, Aff, Zff)
  • FF anisotropy: W(CM) = (1+B·cos cm)/2
  • Incomplete momentum transfer
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Analytical Calculation of the Detection Efficiency

Absorption of fragments in the fissile layer: Higher order contributions:

  • Anisotropic fragment emission
  • Momentum transfer

99 . 94 . ... 2 1

ff f

     R t e

 t R

  • Uncertainty: ue /ef ≈ 1% - 2%

depends very much on sample quality

Ref.: G.W. Carlson, NIM 119 (1974) 97-100 W() = (1+B cos())/2

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Electro-sprayed 238U3O8 layers

238U-PPFC

Fission Fragment Detection Efficiency

  • Background at small pulse heights

– a decay of fissile nuclei – recoil nuclei from backing materials

  • Extrapolation of fission events

into this region

– thickness and ‘roughness’ of deposits – biasing scheme

20 40 60 80 100 120 140 160 180 200

10 20 30 40 50 60 70 80 90 100

natPb-PPFC

En = 145 MeV

light charged particles (normalized) fission fragments

counts pulse height / arb. units 100 200 300 400 500 50 100 150 200 250 300

counts per bin pulse height / arb. units

fission fragments

a particles

238U-PPFC

Painted 238U3O8 layers

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242Pu Fission Chambers for Cross Section Measurements

  • 242Pu layers produced by

molecular plating (U. Mainz)

– mPu = 42 mg, 242Pu: 99.9668 % – eight layers: 116 mg/cm2 – Aa= 6.17 MBq – Rsf = 34 s-1

  • Number of fissile atoms NPu:

– Spontaneous fission rate t1/2 = (6.77 ± 0.07)1010 a – Narrow-geometry alpha counting

  • Fast pre-amp.’s: a pile-up!
  • Continuous P10 flow (nanofilters)
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The Measurement of Neutron Energy Distributions: TOF Methods

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TOF Spectrometry: Principles

  • Neutron energy determined from a velocity measurement:
  • Energy resolution:

Time and distance resolution contribute in same way:  express flight time dt by an equivalent distance ddeq

n g Dt d

 2

2

1 1 , ) 1 ( c v mc E t d v        g g

2 2

, ) 1 (                 d d t t v v v v E E d d d d g g d

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Measurement of TOF Distributions

  • Start signal: neutron detector
  • Stop signal: beam pick-up
  • Inverted time scale: TOF = tstop – tstart
  • Measured neutron flight time: tm = TOFg + d/c – TOFn

NB: Measured flight time tm includes time spent in target and detector!

Quasi-monoenergetic source ‘White’ source

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Width of TOF Peaks

  • Contributions to the width of TOF peaks :

– Beam: time spread of the beam pulse dtbeam – Source: beam transit time dtsrc = dsrc/v energy-loss broadening dEsrc = fkin(Ebeam,En)·(dE/dx)·dsrc kinematical broadening fkin(En,)·d slowing-down time dtslow ≈ A/Ssv – Sample: kinematical spread dEspl = fkin(En,)·d – Detector: transit time dtdet = ddet/v multiple scattering spread dtms

  • Total TOF spread:
  • Relative importance of time and energy broadening

depends on the details of the setup:

– Masses of projectiles and target nuclei: source and sample – Flight paths: source and sample

 

         

j j j j j j i i

E E l E t t t

2 n, 2 n, n, 2 2

2 ) , ( d d d

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Time Response of Organic Scintillation Detectors

  • Multiple scattering affects time response:

– Width of the main peak: flight time through det. – Exponential tails for pancake-like detectors (d >> l) – Non-Gaussian time response: R(E,t) – Modeled with Monte Carlo codes

12C(n,n)12C 1H(n,n)1H time / 0.1 ns

  • Calc. (NRESP7)

Exp.

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Example: PTB TOF Spectrometer

En,0 = 10 MeV

– d tbeam = 1.6 ns – dEn,src = 106 keV – dsrc = 17 cm, ddet = 12 m  dEn/En = 1.4 % for En,det = 2 MeV 1.8 % for En,det = 10 MeV

D(d,n)

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Example: PTB TOF Spectrometer

Kinematical broadening

– Polyethylene (PE) sample – Incident energy: En,0 = 10.21 MeV – Scattering angle:  = 29.3°

Separation of TOF peaks

 Vanadium sample  En,0 = 10.21 MeV   = 36.8°

12C(n,n')12C* 12C(n,n)12C 1H(n,n)1H

CH2

51V

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Self-TOF Spectrometers

  • Source of the TOF Start/Stop signal:

– Pulsed beam (pick-up, RF) – Time-correlated associated particle (TCAP) – Recoil particle double-scattering experiment  self-TOF spectrometry

  • Example: TOFOR spectrometer at JET

– Designed for DD plasmas: <En> = 2.5 MeV – Energy resolution: DE/E ≈ 7% – Dynamic range: 105

5 start det.‘s BC-418 32 stop det.‘s BC-420 neutron beam

2 n 2 n n'

2 ) ( cos          t R m E E E a

  • Ref. : M. Gatu-Johanson et al., NIMA 591 (2008) 417-430

g n

  • mult. scat.
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TOF Spectrometry of Incompletely Pulsed Beams

Pulsed beams with rep. frequency f and flight path d  Frame-overlap threshold: ‘only one pulse at a time’

2 c 2 c c

2 1 ) 1 ( mv mc E f d vc        g

Possible workarounds:

  • Spectrometry using recoil detectors
  • Bonner Sphere spectrometry

 Spectral fluence FE for E > Ec from TOF measurement

  • Combination of measurements at different flight paths d

and Monte Carlo calculations for very low energies

n g d c/f

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Lead Slowing-Down Spectrometer (LSDS)

  • Semi-empirical relation between

energy and slowing-down time t:

  • K and t0 :

– MC simulations – resonance analysis

  • Very high neutron flux
  • Energy range 0.1 – 100 eV
  • Application:

– Reactions with rare isotopes – Fission of very radioactive isotopes – Fission of isomers

E

2 0)

( ) ( t t K t E  

Detectors inserted in the moderator: – Compensated fission chambers – Solar cells with fissile layers – …

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Neutron Detectors for TOF Measurements

  • 6LiGlas Detectors:

– Suitable for neutron range En < 1 MeV – Strong photon sensitivity, stong energy dependence around 250 keV res. – Complicated time response due to 250 keV resonance: dt ≈ 3 - 4 ns – Sensitive to (epi)thermal background neutrons:   1/v

  • Fission Chambers

– Secondary standard cross sections: 235,238U(n,f) – Low but calculable detection efficiency: reference instrument – Slow time response requires long flight paths: dt ≈ 3 - 6 ns

  • Organic scintillation detectors: working horses for TOF meas.

– Fast response: dt ≈ 1 - 2 ns, often limited by PMT‘s – High detection efficiency: e ≈ 10 – 20% – Many sizes and shapes possible: 1 cm - 1 m –

  • Diff. n-p cross section is primary standard

– Discrimination of photon background by PSD – Quenching requires low pulse-height thresholds for En < 1-2 MeV

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The Measurement of Neutron Energy Distributions: Unfolding Methods

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Need for ‘Non-TOF’ Spectrometry

  • There are situations where TOF cannot be used:

– Accelerators based sources with high rep. rates: f > 0.1 - 1 MHz – Neutron diagnostics at nuclear fusion experiments – Sources without well-defined flight paths: Transmission through shields, fusion benchmarks – Neutrons in the environment – …

  • But there is a way-out:

The spectral neutron distribution (dF/dE) is related to the distribution of ‘events’ (dN/dL) in the detector:

(Fredholm integral equation of the first kind)

The attempt to solve this equation is called ‘spectrometry’

 

F   F  

j j j i i E L

R N E E L R N

,

d ) , (

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Spectrometric Methods

  • High-resolution spectrometry

– Spectrometry of recoil nuclei:

  • rganic scintillation detectors

recoil telescopes – Spectrometry using reaction products:

3He counters and ionization chambers

sandwich spectrometers diamond detectors – Capture-Gated spectrometry  Make response matrix R as diagonal as possible!

  • Low-resolution spectrometry

– Multi-sphere spectrometry – Spectrometry using threshold activation foils

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Unfolding Problem

  • Unfolding problem:

How to get from Nj (data space) to Fj (space of possible solutions)

  • Problem of unfolding:

– There is a multitude of solutions Fj which produce the same Nj – The response Rj,i is not exactly known – The Nj have uncertainties ui 

Nota bene:

  • There is no exact solution!
  • What is needed is a consistent approximate solution
  • Usually prior information is available and must be included

F  

j j j i i i

R u N

,

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Technical Approaches to Unfolding

  • Direct matrix inversion:

but: (RT·R)-1 is usually ill-conditioned if it exists at all:  ‘noise’ is amplified, Fj < 0 possible!  More suitable methods are required:

 Iterative procedures: usually black-magic recipes!  Stochastic methods: Monte Carlo, genetic algorithms, …  Regularisation: add constraints to enforce smoothness  Least-squares adjustment: usually linearization required  Bayesian parameter estimation: requires an analytical model  Maximum entropy principle: justifiable from information theory consistent treatment of prior information and uncertainties

Ref: M. Reginatto: Radiat. Meas. 45 (2010) 1323-1329

N R R R R N     F  F  

 T 1 T

) ( ... ), ( diag ,

  • rth.

, with ) (

2 1 1 1 T

    S  S   

 

g g g i

T

V U U V R R

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The PTB scintillation spectrometer : Response Matrix

Ref.: A. Zimbal et al., PoS(FNDA2006) 035 www.pos.sissa.it

2” x 2” BC501A cell

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Measurements at JET

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Ohmic and NBI Heated JET Discharges (DD)

Ohmic + NBI heating Ohmic heating

FWHM = 126 keV  Ti = 2.3 keV

  • Passsive (offline) gain stabilization: fLED ≈ 1 kHz
  • Unfolding with MAXED using a flat (uninformative) prior

Ref.: A. Zimbal et al., PoS(FNDA2006) 035 www.pos.sissa.it

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The Dark Side of Unfolding: Artefacts

Artefacts result from imperfect response function:

  • Calc. response matrix: cross sections, e.g. 12C(n,n'3a ),

light yield L(En), resolution DL/L

  • Exp. response matrix: imperfect CFD timing (walk effect),

imperfect satellite subtraction

T(d,n), Ed = 643 keV,  = 0°: 2"2" BC501A detector with A = 7.2%, B = 10.5%

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Few-Channel Unfolding: Multi-Sphere Spectrometry

BS spectrometer NEMUS

  • 3He detector inside moderators
  • bare counter: (epi)thermal
  • 12 PE spheres (3"-18"): En < 20 MeV
  • 4 PE/(Pb,Cu) spheres: En < 1 GeV
  • Response matrix: MCNPX
  • Precise dimensions
  • Measured PE densities
  • Calibrated 3He pressures
  • Regular stability checks
  • Background studied in UDO

underground laboratory

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Analysis: Bayesian Parameter Estimation

  • Response functions are very similar
  • Components of neutron spectra known

– Thermal peak : ≈ 25 meV – Slowing-down cont.: ≈ flat – Evaporation peak: ≈ 2-3 MeV – ‘Spallation’ peak: ≈ 100 MeV

 Analytical model and Bayesian parameter estimation

priors Model, Data, Bayes theorem posteriors  The ‘spallation’ peak (100 MeV) cannot determined only from the data!

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20 µs 2"2"

Capture-Gated Spectrometry

  • Full-energy events in doped organic scintillators

‘tagged’ by capture signal  response ‘more diagonal’

  • Triggers: 10B(n,a)7Li

Q = 2.79 MeV

6Li(n,t)4He

Q = 4.78 MeV (preferred!)

  • PH signal only from fast recoils: tint << tlife

Total pulse height L(En) not prop. to En!

Ref.: B.M. Fisher, NIMA 646 (2011) 126 – 134

  • T. Aoyama, NIMA 333 (1993) 492- 501
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Example: 5""3 boron-loaded detector (BC454 )

12C(n,n) + 1H(n,n)

Ref.: T. Aoyama, NIMA 333 (1993) 492- 501

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LED (2x) Photodiodes (2x) EJ254XL Scintillator “Orb” PMT

NASA Mars Mission

Gd shield

Radiation detectors on NASA Mars Rover:

  • Charged Particle Detector (CPD)
  • Capture-Gated Fast Neutron Detector (FND):

 EJ254XL 10B-loaded scintillator  Calibration: LED + Diode  PMT readout  En = 0.5 – 8 MeV

Courtesy: C. Zeitlin, Southwest Research Institute, Boulder (Colorado)

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Modern Spectrometry with RTPs: Proton Tracking

Recoil telescope with track reconstruction:

  • E detectors: Ep
  • DE detector: track reconstruction, p

 En = Ep / cos2p

  • Example: TPR-CMOS (IRSN Cadarache)

Neutrons Convertisseur CMOS Diode Si(Li)

1 2 3

Z X Y

Ref.: J. Taforeau: Un spectromètre à pixels actifs pour la métrologie des champs neutroniques, Thèse, Université de Strasbourg 2013 Deteriorated Ti(T) target AmBe source

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Spectrometry using Exothermic Reactions

  • 6Li(n,t)4He, Q = 4.78 MeV,

3He(n,p)T, Q = 0.76 MeV

  • High thermal cross section:  = 0(v0/v) for En < 100 keV

Q c c c c E

th th f n

  

 Spectrometry by detection of both reaction products:

  • (epi)thermal peak: cth
  • fast peak: cf
  • zero bias: c0

NB: constant W-value assumed !

  • Proportional counters
  • Ionization chambers with Frisch grid
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3He and 6Li Sandwich Spectrometers

6Li spectrometer:

  • High recoil energies
  • Good g suppression
  • Resolution depends on

radiator thickness

  • En,min = 100 - 500 keV

SB-det.

3He Spectrometer

Ref.: H. Bluhm et al., NIM115 (1974) 325-337

3He Prop. Counter

3He spectrometer

  • Small recoil energies
  • n/g interference
  • High efficiency
  • Small energy loss
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Spectrometry using scCVD Diamond Detectors

Single-crystal chemical vapor deposition diamond detectors (scCVD):

  • Neutron detection via 12C(n,a)9Be: full-energy peak
  • Large displacement energy (42 eV/atom)  high radiation hardness
  • High thermal conductivity  operation at elevated temperature
  • But: large band gap (5.5 eV)  resolution not as good as silicon (1.11 eV)

 Very attractive material for neutron spectrometers

Ref.: H. Kagan, NIMA 546 (2005) 222-227

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The Measurement of Spatial Neutron Distributions

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The Micromegas Beam Imager for n_TOF

  • Neutron detection:

6Li, 10B converter

– Counting gas: p, He recoil

  • Energy-resolved images: 10 eV – 20 MeV
  • Several 1-dim. and 2-dim. (strips or pixels) read-out schemes
  • Spatial resolution: ≈ 0.5 mm

6Li(n,t) 1H(n,n) 4He(n,n)

Ref: J. Pancin et al. NIMA 524 (2004) 102-114

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Micromegas Results

  • Ref. : F. Belloni et al., Mod. Phys. Letters A 28 (2013) 1340023
  • Profile of the n_TOF neutron beam:

– Converter: LiF, 10B4C – Readout anode: 6 cm  6 cm with 106 x and y strips, Gassiplex readout chip

  • Determination of beam coverage factors for large sample
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Absolute Methods, Key Comparisons

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Stability and Consistency of Neutron Measurements

  • Ref. detectors depend on ref. materials

– Purity of gases (H2, CH4, C3H8): RPPC – Tristearin (C57H110O6) radiators: RPT –

235,238U deposits: FC

 Test of stability and consistency  Comparison with ‘absolute methods’

2 4 6 8 10 12 14 16 0.90 0.95 1.00 1.05 1.10

  • Feb. 83
  • Aug. 83
  • Oct. 85
  • Nov. 07

(FD1/FRPT) En / MeV

(FD1/FRPT) = 0.995 s.dev. = 0.019

RPT1 DD H19 H21 FP3/200m FC16 UF4 FC16 U3O8 RPT1 DD H19 H21 FP3/200m

0.90 0.95 1.00 1.05 1.10

En = 8.4 MeV Y = (5.45 +/- 0.04) 10

4 sr
  • 1

Y / Y

En = 15 MeV Y = (2.217 +/- 0.020) 10

4 sr
  • 1

Stability Consistency

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Standards: Absolute Methods Traceability of detector calibrations to the SI requires ‘Absolute’ methods for neutron production:

  • Manganese bath: 56Mn(n,g) in a saturated MnSO4 solution

  • nly for radionuclide sources

 50% correction for capture and leakage  0.5 % uncertainty of the emission rate

  • Time-correlated associated particles (‘tagged neutrons’):
  • 252Cf(s.f.):

standard technique, relies on <n> 

  • D(d,n)3He:

standard technique, difficult 

  • T(d,n)4He:

standard technique 

  • H(n,n)p:

low count rates 

  • D(g,n)p:

requires a tagged bremsstrahlung beam

  • D(p,n)2p:

very difficult

  • Uncertainty of (TC)AP method: 1% - 1.6%

for T(d,n)4He, En ≈ 14.2 MeV

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252Cf(s.f.) Ionization Chamber

  • Low-mass parallel-plate IC with 252Cf source:

Aa = 4.5 MBq  Rsf = 1.4105 s-1 time resolution:  1 ns

  • Neutron ‘tagged’ by fission fragments
  • Prerequisites:
  • Evaluated 252Cf neutron spectrum and
  • Corrections:
  • deadtime and uncorrelated stops
  • fragment detection efficiency
  • neutron emission anisotropy
  • neutron transport, air scattering

n

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TCAP: T(d,n)4He, D(d,n)3He

‘Tagging’ of neutrons by the associated charged particle

  • T(d,n)4He, Ed = 150 keV
  • n = 26.5°, a = -150°
  • En = 14.48 MeV, Ea = 2.46 MeV
  • no (d,d) background
  • 3He(d,p)4He can be a problem
  • ‘routine’ 14 MeV standard
  • D(d,n)3He, Ed = 4 MeV
  • n = 40°, 3He = -59.8°,
  • En = 6.13 MeV, E3He = 1.14 MeV
  • strong (d,d) and (d,p) background

requires DE-E separation of 3He

  • Problem of all TCAP experiments:

Loss of correlation due to angular straggling!

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TCAP with T(d,n) at Ed,0 = 150 keV

n a d

  • Shape of the associated neutron cone:

– Tritium depth profile in Ti(T) target – Position of the beam spot

  • Modeling of the transport of

150 keV d in Ti(T) is a challenge!

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Metrological Cooperation: Key Comparisons

  • Organized within the CCRI(III) of the BIPM
  • Regular Key Comparisons (every 10 years)
  • Results go into the KCDB: www.bipm.org
  • the ‘usual suspects’:
  • CIAE (PR China)
  • LNE / IRSN (France)
  • IRMM (EU)
  • NPL (UK)
  • NMIJ (Japan)
  • NIST (USA)
  • PTB (Germany)
  • VNIIM (Russia)
  • Typical uncertainties:

 KCRV: 1 – 1.5 %  Standard deviation: 2 – 4 % CCRI(III)-K11 (2010-2011)

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Summary:

Neutron detection means conversion to charged particles:

  • Products of two-particle reactions with high Q value
  • Recoil particles
  • Fission fragments

Measurements techniques:

  • Time-of-flight spectrometry
  • Unfolding of signal distributions

Normalization:

  • relative to cross sections standards
  • ‘absolute’ neutron counting
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Tributes

Horst Klein

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Physikalisch-Technische Bundesanstalt Braunschweig und Berlin Bundesallee 100 38116 Braunschweig

  • Dr. Ralf Nolte

AG 6.42 Neutron Metrology Telefon: 0531 592-6420 E-Mail: ralf.nolte@ptb.de www.ptb.de

Thank you for your attention!

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Additional Material

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High-Energy Telescopes

Neutron energies above 20 MeV pose special challenges:

  • Large proton ranges: degraders, thick stopping detectors
  • Charged particles from n+12C: high-resolution DE-E particle discrimination
  • Neutron induced coincidences: more coincidence conditions
  • ‘Grey’ apertures: active collimation by veto detectors (En > 100 MeV)

Proton recoil telescope T2: En = 20 – 60 MeV

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TOF Variants : Slowing-Down Spectrometry

Heavy (A = 208) non-absorbing moderator with constant isotropic scattering cross section:

  • Small mean log. energy loss per collision:
  • Rel. std. deviation of

slowing-down time: , mean energy: Time dependence of the velocity v:

3

10 5 . 9 3 2 2

    A 

2 2 2

10 7 . 5 3 2

   A tE

tE

 11 . 3 8

2 2

  A E

E

) ( 2 ) (

s

v v t t v  S  

Pb cross section

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Lead Slowing-Down Spectrometer (LSDS)

  • Semi-empirical relation between

energy and slowing-down time t:

  • K and t0 :

– MC simulations – resonance analysis

  • Very high neutron flux
  • Energy range 0.1 – 100 eV
  • Application:

– Reactions with rare isotopes – Fission of very radioactive isotopes – Fission of isomers

E

2 0)

( ) ( t t K t E  

Detectors inserted in the moderator: – Compensated fission chambers – Solar cells with fissile layers – …

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The LANSCE Slowing-Down Spectrometer

  • High-purity lead cube: V = (1.2 m)3
  • WNR beam (800 MeV p), tungsten target
  • Resolution: DE/E ≈ 0.29

Ref.: D. Rochman et al., NIMA 550 (2005) 397-413

Resolution broadening