28th Aug. - 1st Sep. 2023

Ministry of Education, Culture, Sports, Science and Technology (MEXT) International
Nuclear Human Resource Development Initiative Project (Subsidy for Promotion of Nuclear
Human Resource Development) "Establishment of New Nuclear Education Center for Future
Society by Strengthening Institutional Collaboration".

Neutron Activation Analysis andElemental Analysis Experiments

Hirotaka Sato

Graduate student
recruitment in progress!

Hokkaido University Graduate School of Engineering Division ofApplied Quantum Science Laboratory of Neutron Beam Scienceand Engineering
Website: https://www.eng.hokudai.ac.jp/labo/QBMA/
1

Contents ①
 Quantum Beam Science and Neutron Beam
Science Particle accelerators (using the electron linear
accelerator at Hokkaido University as an
example) Neutron sources using particle accelerators(focusing on pulsed neutron sources) Neutron energy spectrum
 Neutron transport and detection• Energy decomposition of white neutrons by TOF method• Neutron imaging using two-dimensional position sensitive
detectors

 Reaction cross sections between neutrons andnuclei Radiation Safety of Neutron Beam Facilities
2

Contents ②
 Principles of Elemental Analysis by Neutron
Activation Analysis
 Applications of Neutron Activation Analysis• Investigation of the Cause of Death of Napoleon• The Hayabusa Project Pulse Height Spectra of NaI Scintillation Detectors
 Energy Calibration and Energy Resolution of NaI
Scintillation Detectors
 Backgrounds and their countermeasures Identification and Qualitative Analysis: Elemental(Nuclide) Analysis
 Quantitative analyses: neutron flux estimation,
elemental quantification
3

Time schedule planning (looselyinteracting and having fun!)
Mon.

Tue.

Wed.

Thu.

Fri.

TA 3 people?

TA 3 people?

TA 3 people（morning）

TA 3 people?

8:45-10:15

Education andtraining forradiation facilities

Neutronactivation analysis
experiment (10pps, 15 min)Spectralmeasurements ofactivated samples

additionalpresentation
experiment（Time,distance, shielding,and so on?）10:30-12:00

Explanation offacilities, tour offacilities

NaI scintillation
gamma-rayspectrometer test

Element (nuclide)
identification

Data analysis ofadditional
experiments

presentation

13:00-14:30

Introduction toquantum
beam/Neutronscience

Energy calibration
experiment

Neutron flux
estimation(element
determination)

Research andpresentation
preparation

presentation,summary, anddismissal

14:45-16:15

Introduction to
Accelerators,
Neutron sources, andNeutron engineering

Energy resolution
evaluation,
background

Setting the themeof thepresentation

Research andpresentation
preparation

Black: Lectures, etc.
Blue: Practice
Red: Practicaltraining in acontrolled area

16:30-18:00

Introduction to
Neutron activation
analysis

Discussion(buffer)

Discussion(buffer)

Research andpresentation
preparation

4

Quantum beam science andNeutron beam science5What is a quantum beam?
 Beams of radiation
 Beam：High intensity （large number） and highly directional（same direction） flux
放射線
放射線
放射線
放射線
放射線
放射線
放射線
放射線
放射線
 So, what is radiation?
 Particle beam flowing with high kinetic energy• High energy electromagnetic waves （light and radio-waves =photons）

6

Examples of the use of radiation are manifold.
non-destructive inspection

Investigation of flow velocity and flow rate

Change(absorption)

Welding Inspection

View(transparent)

reinforced plastic
Thickness measurement

From the inside ofroomToyour room
ｔo the edgeof the universe

Investigation of ripening, etc.

Change(absorption)

Selective breeding

New drug development

Germination Prevention

View(transparent)

X-ray examination

X-ray CTCure
(absorption)

Cancer treatment

Use of radiation

Chemical structure
research

Image source: Federation of Electric Power Companies of Japan, Nuclear and Energy Drawings 2015 6-2-5

isotope batterySee(scatter)Make(absorption)

In addition to this Semiconductor processing
 Sterilization of medical instruments
 Pest detoxification
 Synthesis of new elements (Nihonium),etc.

7Interaction of different types of radiation
with different materials

Ionizes and excites matter.
Scattered and absorbed by thesubstance.

Helium-4
nuclei(heavycharged particle)

1 sheet of paper

Electrons(charged
particle)

Aluminum several mm thick

Eectromagnetic
waves(x-rays andgamma rays)

Neutrons
Frequently used as quantum beams formaterials and life sciences.

Fairly strong
electromagnetic interaction
Strong electromagnetic
interaction

10 cm thick lead

10 cm thick water
1 cm thick boron carbide
1 mm thick cadmium
Picture: http://ja.wikipedia.org/wiki/%E6%94%BE%E5%B0%84%E7%B7%9A

8

Time-resolved imaging:
Dynamic radiography/tomography
70 keV X-ray

25 meV neutron

9Neutron properties and applications
⁷Li Atomic

Electron

NeutronMass
質量Radius半径
Spin
スピン
磁気モーメント
Magnetic moment
寿命
Lifetime

 Electrically neutral-27

1.674928(1)×10 kg
0.7 fm- / 2-27-1-9.6491783(18)×10 JT
885.9±0.9 sec

ProtonUnique characteristics
are utilized.

••

High material permeability
Ability to identify light elements and isotopes

 Mass close to the nucleusof an atom•

Capable of nondestructively analyzing
microscopic spatio-temporal information ofmaterials.

 With spin and magnetic
moment•Exploration of magnetic information

http://upload.wikimedia.org/wikipedia/commons/e/e2/Stylised_Lithium_Atom.png

Applications in the fields of materials, life, earth, planet, andphysics•
Atomic and molecular structure•
analysis•
Dynamics analysis of atoms and•molecules•
Fluoroscopy (Imaging)•
Elemental and isotopic analysis•
Particle physics and nuclear physics※画像は全てKEKホームページよりお借りしました。

Applications in the energy sector

Nuclear power generation• Transmutation of long-lived
radioactive waste
Medical applications••(Boron) neutron capture therapy
RI drug production•

Neutron Irradiation Testing(Materials & Electronics)
Moisture meters, ...

Other applications•

10

Mass near nuclear → Matching material analysis
Energy change

gamma rays
X-ray

Time scale

PhotonElectron

Soft X-ray
Ultra-violet rays

NeutronTime to change

Visible light
InfraredElectron motion
Motion of atoms and small molecules

Motion of large or corrective molecule

Size

Reciprocal of momentum
changeCompared to other radiation, it is necessary to lower
the energy to meV.
11

Radiation source ①：
Cosmic rays （Ultra-high energy）

Primary cosmic
rays (protons, etc.)

Secondarycosmic raysPion
→ Muons
Neutrons
Gamma ray
Electrons
There are many othertypes of secondary
cosmic rays.

Primary cosmic rays: Radiation that comes from space. Protons are the main type of cosmic rays.
Secondary cosmic rays: Particles formed when primary cosmic rays react with the atmosphere.
Muons, etc.

12

Radiation source ②:Radioactive isotope (RI)

 Alpha (alpha) radiation sources
Am (Americium)-241 (about 5.5 MeV),
Po (Polonium)-210 (about 5.3 MeV), etc.

 Beta (beta) sources

image source：http://blog-imgs38.fc2.com/w/i/n/wine4wine/R0010667.jpg

Sr-90 (Max. approx. 2.28 MeV),
Na-22 (Beta+ (Positron) source), etc.

 Gamma (gamma) radiation source
Co-60 (Approx. 1.17 MeV & 1.33 MeV),
Cs-137 (Approx. 0.66 MeV), etc.

 Neutron sources: 252Cf, 241Am-Be, etc.
The emission is low and radiation is emitted in all directions.
but easy to use.
13

Radiation source ③：
Accelerator （high intensity・high energy）

Photo: "Electron Accelerator Driven Neutron Experimental Facility" at faculty of engineering, Hokkaido University

High energy neutron source
高エネルギー中性子源

Low energy neutron source
低エネルギー中性子源

Accelerated particles are used as they are,secondary particles are generated and used.

Electron beam
電子ビーム

 Provides high-intensity, highly directional radiation fluxes (Quantum beams).
 A wide variety of radiation that can be generated (from elementary particles to uranium nuclei).
 Small accelerators can be found throughout the city (e.g., radiation therapy units in hospitals).
14

Japan Proton Accelerator Research Complex (J-PARC)
Tokai village, Ibaraki
Pacific Ocean

Materials and Life Science
Experimental Facility(Neutron and Muon)

3 GeV synchrotron(300 m circumference)

HadronExperimental
Facility

Linac(total length 300 m)

Neutrino Experimental
Facility

50 GeV synchrotron(circumference 1.6 km)
15Fire alarm (Smoke detection)

Not widely used in Japanese households...

• Am-241 (Alpha radiation source) is used to ionize smoke.
• Smoke is detected by detecting changes in ionizing
current.
• Capable of detecting smoke with high sensitivity.
• The equipment falls under the category of “Apparatusesloaded with Radioactive Materials," and is therefore subject tosubstantial restrictions.

16Voyager space probe (Launched in1977) in 2005 Currently, Voyager 1 is out of the solar sphere.
Bow shockHeliosheath
Voyager 1

Terminal shock wave surface area

Voyager 2

Heliopause
Heliosphere
Image
画像出典：https://upload.wikimedia.org/wikipedia/commons/e/e5/Voyager_1_entering_heliosheath_region-ja.jpg
source ：https://upload.wikimedia.org/wikipedia/commons/e/e5/Voyager_1_entering_heliosheath_region-ja.jpg

17Radioisotope (RI) batteries

Stable power can be supplied over a long period in places where sunlight is not sufficient to reach.

 An α-ray source (Pu-238, Po-210, etc.) is used.
 The heat generated when alpha rays are absorbed by amaterial is converted into electric power using athermoelectric conversion element.

Image source：
http://commons.wikimedia.org/wiki/File:Pioneer_10_images_the_sun.jpg,
by Donald Davis, PD

18

Neutron scattering analytical imaging of
automotive lithium ion batteries
Hokkaido University - Toyota Motor Corporation
Battery photo

Before charging

After charging

d002 crystal layer
spacing of graphite
anode material [nm].
Layer spacing (nm)Stage 1
Stage 2
Stage 3
Stage 49 cm
Imaging range
9 cm×9 cm

graphite

Neutrons penetrate the cathode andelectrolyte to analysis of the crystal
structure of the anode only

[Layer spacing expanded by charging (penetration of Li ions into the graphite layer)].
Differences exist depending on the location within the product.
19

Prevention of large-scale communication network
failures caused by cosmic rays using accelerator
beams
Joint research between Hokkaido University and NTT

Primary cosmic rays
Secondary cosmicrays(e.g. neutrons)
NeutronElectronic equipment

Electrical noise
↓
Fault

陽子

Silicon nucleus

Secondary ions

High-energy neutrons generated by the accelerator are absorbed byelectronic equipment, and failures are intentionally generated to estimate
the frequency of failures in nature, etc.

20

Experiments on countermeasures against cosmic ray
neutron soft errors in transmission systems for informationand communication networks

21

Detoxification of pests
Melon fly extermination operation in Okinawa• The larvae of the cucurbit fly feed on the contents of vegetables andare highly fecund, which can be devastating to vegetableproduction.
• In the 1970s, an eradication campaign was initiated in Okinawa toprevent the melon fly from invading mainland Japan.
• One of the most effective strategies was the use of a Co-60 gamma
radiation source to irradiate large numbers of melon fly larvae,
rendering them sterile, and then releasing them into the habitat inlarge numbers to suppress their reproduction.
• By 1993, the eradication of the melon fly had been successfully
achieved. The number of flies used exceeded 50 billion.

画像出典：http://commons.wikimedia.org/wiki/File:Melon_fly_(Bactrocera_cucurbitae)_03.jpg

22

Food Irradiation
 Purpose: extension of shelf life of food products,
sterilization, insecticides, etc.
 In Japan, the Shihoro Agricultural Cooperative in
Hokkaido irradiates potatoes only with Co-60 gamma
rays (To prevent germination).
gamma radiation
sourceImage source：http://www.ies.or.jp/publicity_j/mini_hyakka/21/mini21.html

23Flower breeding (Application of mutation)

Famous for his work with TIARA (Takasaki Ion Accelerator)

Ion beams with strong DNA-damaging effects are irradiated toincrease the probability of genetic mutations related to color andshape.

A new variety of chrysanthemum with gorgeous petals

Ion beams can be used to create a variety
with a spectacular atmosphere andvariegated petal shapes. Chrysanthemums
bred in this way are expected to open up
new applications such as celebrations andarrangements.

Image
image source: "Quantum Beam" for a family24Transmission imaging using neutron beams
Feature ①: High sensitivity to some light elements (hydrogen, lithium, etc.)
Feature ②: Easily permeable to heavy metals within a few centimeters⇒ Used for visualization of oil behavior inside engines, etc.

Explosives(Nitrogen)

Neutron

X-ray

Visualization of objects invisible by X-ray imaging(Light elements in heavy metals)
画像出典：ATOMICA「犯罪捜査における放射線利用」

25

Neutron imaging provides
clairvoyance to cultural properties
Transparency of the inside of a bronze sutra tube
for detection of organic materials such as paper and cloth inside a metal container
neutrons are more advantageous than X-rays!
Neutrons

X-raysImage source: "Fundamentals and Applications of Neutron Imaging Technology," Japan Radioisotope Association

26

Analysis of Japanese swords without
breaking them International joint research between Japan and Italy, including Hokkaido University
Scattering of low-energy neutrons to see heattreatment-induced strain in the blade edge of Japaneseswords and the presence of giant crystal grains in theblade.
FWHM of distribution of
FWHM of distribution of
FWHM of distribution of
crystal lattice plane spacing, w110 (nm)
0.005

0.003
0.002

0.002
0.001

0.000

0.000

0.000
10.24 cm

10.24 cm

Crystallite size (μm)

Crystallite size (μm)
5

5

4

4

4

3
2

3
2

10.24 cm

5

10.24 cm

10.24 cm

0.002

0.003

0.001

Crystallite size (μm)

10.24 cm

0.003

0.001
10.24 cm

Crystalgrain size ⇒

0.004

0.004

10.24 cm

Strainsize⇒

10.24 cm

0.004

crystal lattice plane spacing, w110 (nm)0.005

10.24 cm

crystal lattice plane spacing, w110 (nm)
0.005

3
2

1

1

1

0

0

0

10.24 cm

10.24 cm27

Volcano imaging using cosmic ray muons
Ultra-high energy
cosmic ray muons

To examine the tracks using
photographic dry plates, wirechambers, etc. to determine
from which direction and how
many muons were flown, and to
make images of the tracks.

Enables visualization and analysis of the interior of very large structures
image source：http://www.u-tokyo.ac.jp/ja/utokyo-research/feature-stories/a-window-into-the-earths-interior/28

Don’t we enable "x-ray the earth" with radiation (elementary
particles) that have a higher ability to penetrate matter?
We are doing! Earth Imaging with Cosmic Ray Neutrinos
IceCube, a super-sized detector in the Antarctic
icecap(like a supersized version of Kamiokande)
Antarctica

Data center

Inner
core

Detector
DOM

Outer
core

Neutrinos
through themantleMantleSky
TreeDeep Core

Crust

North
Pole
Neutrino through theinner core

The day is near when we will actually be able to see through the internal structure of the Earth!
image source：http://www.u-tokyo.ac.jp/ja/utokyo-research/feature-stories/a-window-into-the-earths-interior/

29

IceCube

Image source：https://www.pri.org/stories/2018-03-18/new-book-recounts-amazing-history-icecube-neutrino-observatory,
https://www.livescience.com/9164-world-largest-neutrino-observatory-built-south-pole.html

30

Research on the effects of cosmic rays on cosmic planetary materials

Europa, a satellite of Jupiter

Europa" environment simulation experimentusing the electron accelerator at Hokkaido
University

Collaboration with Exploration and
Observation Unit, Planetary SpaceGroup, Department of Space Science,
Faculty of Science

31

Particle accelerators (Using theelectron linear accelerator at
Hokkaido University as an example)

32

Purpose of accelerator: Generation of high-energy,
high-intensity, and highly directional radiation flux
① By supplying a flux (Quantum beam) of high intensity and high directionality,

Radiation generated by radioactive materials
Alpha rays

RI

Neutron beam

Radiation generated by accelerators
Accelerator

Beta rays
Gamma rays

radiation
radiation
radiation
radiation
radiation
radiation

Accelerating particles are used as they are, or secondary particles are
generated and used （a wide variety of radiation that can be generated）.

② "Seeing", "changing", and "curing" matter.

Atomic arrangement analysis
atomic motion analysis

Plant and semiconductor breedingsterilization of medical instruments

Cancer treatment
33

Japan’s large quantum beam facilities(Accelerators)

http://www.mext.go.jp/a_menu/shinkou/ryoushi/

Materials science, life and bio-science

Heavy ion

Particle physics and nuclear physics

Electron
X-ray
Synchrotron
radiation

Installer: JAEA
Location: Takasaki City,
Gunma Prefecture
Main Functions: Creation of
new materials and plants
with special properties using
ion beams!

Installer: RIKEN
Location: Harima Science Garden City, Hyogo
Prefecture
Main Functions: Investigate the function andstructure of materials with intense light!

ProtonNeutronMuon

ProtonHadronNeutrino

Installer: JAEA, KEK
Location: Tokai village, Ibaraki Prefecture
Main Functions: Using neutrons to investigate thestructure and function of matter and the natureof magnetic forces! Using a variety of otherparticles to explore the origin of matter!

RI beam factory
Heavy ion
Installer: RIKEN
Location: Wako City, Saitama Prefecture
Main Functions: Ion beam to explore theorigin of matter!

ElectronPositron
Meson
Installer: KEK
Location: Tsukuba City, Ibaraki Prefecture
Main Functions: To investigate the fineparticles that form matter by bombarding
them with electrons and positrons, and to getcloser to the origin of the universe!

34

Location of LINAC facility at Hokkaido
University
Faculty of Engineering, Hokkaido University
Electron Accelerator and Neutron
Experimental Facility

35Exterior view of the LINAC facility at Hokkaido University
One of the leading radiation controlled areas on campus. One of the largest accelerator facilities on campus, along with the Proton Therapy Center at Hokkaido University Hospital.

36

Control room in the basement: Accelerator operation,
remote control of experimental equipment, meetings, etc.

37

Electron LINAC （Linear Accelerator）：
Electron linear accelerator
Overhead view of accelerator room

Around the injector

Electron beam
3 m acceleration tube
(Transferred from AIST)RFWindow
Electrongun

3 MeV injector

Focusing
electromagnets(for use with existing
equipment)

3 m accelerator tube
(Made by Mitsubishi
Heavy Industries)

Wave
guide

Electron beam

3 MeV injector

Two accelerating tubes (about
6 m long) accelerate electrons
to near light speed (Energy:
approx. 32 MeV)

38

Principle of electron acceleration(Difficult to do with an electrostatic field) A method to generate an electric field with a potential difference of 32 MV.
Utilizes the fact that electrons interact with electric and magnetic fields. Uses electromagnetic waves (Radio waves (Microwaves)).

S-band (2856 MHz) microwave (15 MW total power input!)
Electron gun

Dummy load

 Waveguide (Black tube on previous slide)

Regular section

Buncher section

A traveling microwave wave is created in the accelerator tube. Electrons ride the traveling wave.

Electronic“Bunches"※ Red and blue arrows represent vectors of electric field.
39

Electronic LINAC performance: Summary
Overall performance (Current)Electron kinetic energy: 32 MeV
 Electron beam time-averaged current: 50 μA
 Electron beam power: 1.6 kW (= Energy x Current)

Performance of pulse operation (Current) Electron pulse width: 4 μs
 Pulse repetition rate: 50 pulses/second

At the maximum, the power (Current value) is doubled!

Annual operating performance: approx. 160
days
40

Using high-energy and high-intensity electron
beams, a large number of neutrons are producedby nuclear reactions!
Fast neutron source（～1 MeV）

Thermal neutron source（～25 meV）

Cold neutron
source（～5 meV）

Bending electromagnet

The instantaneous intensity of the LINAC
neutron source at Hokkaido University (1012
neutrons/sec) is comparable to the neutron
intensity of a research reactor.

Electron beam

41

Why do we need an accelerator?
 Different types of radiation interact with matters with different reaction crosssections, depending on their energy.
 The structure and motion of matters can be investigated by analyzing
various particles that cause various interactions.
↓ The use of primary particles with higher energy (Acceleration) will expand
the range of applications for “utilizing a wide energy band (Electron beams
and X-rays)” and “efficiently producing secondary and tertiary particles(Electron → X-ray → Neutron・Positron, Proton → Neutron).
 In order to "capture interactions in a shorter time" and "capture smaller
reactions," the incident beam intensity must be increased.
 In terms of controlling the type, energy, intensity, and shot
time of radiation, accelerators are effective in meeting theabove conditions.
 Large accelerator facilities are designed for high intensity and high energy.
 Small accelerator facilities are designed for ease of use and popularization.
42

Particle accelerator-based neutron
sources(Focusing on pulsed neutron
sources)43

Neutron generation and energy adjustment method(When the primary beam is an electron beam)TungstentargetLeadtargetBremsstrahlung X-ray

HighenergyneutronModerator

Water Intermediate

energyneutronElectron beam

Common uses of electron beams

Sterilization of medical instruments
Radiation chemical reactions, etc.

General uses of X-rays
X-ray Therap.
SPring-8, a large synchrotron
radiation facility, etc.

Lowenergyneutron 44

Major accelerator-driven neutron experimental facilities in Japan
Image from the website of the Japan Council of Accelerator Neutron Sources (JCANS)●●●■

Hokudai

Aomoriprefecture●■■

Tohokudai
●
■■

●
■■
Ibaraki ●prefecture ■●Kyodai■

Handai■ Materials, life and industrial
applications■ Medical sciences■ Particle and nuclear physics

Other,

J-PARC•(JAEA & KEK)●●●•
Riken■■■●

Meidai■■●

Kyodai ■■●Kyodai ■Sumiju Atex Co.

● Cold neutron source● Thermal neutron source /Epithermal neutron source● Fast neutron source

●●
■

•
•
•
•

National Institute of Advanced Industrial ●■Science and Technology (AIST)
Other, accelerator neutron sources
Other, reactor neutron sources
Other, laser neutron source
Other, RI neutron source
・・・

Various neutron sources andtheir applications inuniversities, national
laboratories, and privatecompanies45

Major pulsed neutron imaging
facilities in Japan
Faculty of Engineering, Hokkaido University HUNS

On demand
https://www.eng.hokudai.ac.jp/labo/QBMA/LINAC/
Neutron flux (max): 10⁴ n/cm²/s
Wavelength resolution (min):1%
Wavelength bandwidth (max): < 1.3 nm
Beam size (max): 10 cm x 10 cm
Beam divergence angle: 1/60 rad

J-PARC MLF BL22 RADEN （Mother-of-pearl）

World's highest
performance
Neutron flux (max): 10⁸n/cm²/s
Wavelength resolution (min): 0.20
Wavelength bandwidth (max): < 1.76 nm
Beam size (max): 30 cm x 30 cm
Beam divergence (min): 1/7500 rad

In addition to these, AISTANS is being maintained at AIST. 46

Neutron beamline configuration
Neutrongeneration

Neutronmoderator

Neutrontransport

Neutronutilization

Absorption
Choppers Reflective devices
Filters
Refractive devices (Gamma-ray
Collimators Polarization devices emission)

Transmission

Scattering
SampleNeutrongeneration
targetHigh energy
particle
accelerator(Proton andElectron)

Sample holders
High & low temperature apparatus
High voltage applying equipment
Magnetic field applying equipment

Neutronreflector

Neutron detectors
Gamma Detector
Monitor↓↓
Signal processing
Data processing
Data analysis
Data display
47

Large proton accelerator (more than several hundred MeV)
Spallation reaction~1017n/MW
Small proton accelerators (up to several tens of MeV)p（~11MeV） (Be,n) reaction
9Be
ｐ

n

~1015n/MW

Electron accelerator(e,γ) (γ,n) reaction

γ

γ
n

e

~1015n/MWXγγp（~3MeV） (Li,n) reaction
7Li
ｐ

n

~1014n/MWγ

48

Energy dependence of the number of neutrons produced per
number of primary particles for each reaction
1015
1014

J-PARC

Neutron yield (n/µC-)

1013

333 μA

100 μA

1012

Riken

1011
1010

Hokudai

109
108

Kyodai107

100 μA

106

1

10

33 μA

100

1000

10000

Incident primary particle energy (MeV)

The appropriate neutron-production reaction
depends on the specifications of the accelerators.49

Neutron energy spectrum

50Generated neutron spectrum
peaks at MeV

However, the energy required by material and life51
sciences is meV.

HUNS neutron source moderator system
Electron LINAC (Linear Accelerator)

Billiard“ collisions with hydrogen nuclei,
which are closest in mass to the neutron.

 33 MeV×33 μA = 1 kW electron pulse width ：3 μs
 electron pulse repetition ：50 Hz
Neutron generation

Polyethylene
premoderator (t 1.5 cm)

 Generation of synchrotron radiation X-rays bybremsstrahlung of electron beams
 Photonuclear reaction
Solid methane moderator
 Target material: Pb(12 cm×12 cm× t 5 cm)
 1.6×1012 per second

Neutron moderator
 Reflector-coupled moderator→ Polyethylene pre-moderator
 18 K solid methane moderator
 Cold neutron pulse width ：160 μs
Neutron reflector
 Graphite （80×80×80 cm3）

10 cm×10 cm
beam extraction

Lead target
Graphitereflector
52

Energy spectrum of supplied neutrons

Cold neutron

Neutron flux of about 104
n/cm2/s at 6 m from theneutron source (HUNS)

Thermal neutron

Epithermal neutron

53

Neutron transport and detection

54

Neutron pulse shape changed by the type ofneutron moderator (using J-PARC as an example)

55

Short pulse neutron source & neutron guide tube
for higher performance HUNS instruments

H. Sato et al., Phys. B 551 (2018) 452.

Graphite reflector
300 K polyethylene (PE)
(50 cm×50 cm×50 cm) main-moderator(t 3 cm, 9.5 cm×9.5 cm)
W+Pb target
Cd decoupler (t 0.8 mm)

TOF-imaging detector

Neutron21 cm

3.65Qc supermirror guide-tube(8 cm × 8 cm)

Samples0.67 m3.83 m1.50 m0.25

Total cross section / a. u.

Electron

Neutron scattering intensity

PE pre-moderator(t 1 cm)

0.20

Bragg edges are distinct.

0.15

3%

0.10
0.05
0.00

Achievement of wavelength
resolution comparable tothat of J-PARC

Improvement of researchcapability at Hokkaido
University

< 1%
0.39

0.40
0.41
0.42
0.43
Neutron wavelength / nm

0.44

56

Accelerator pulsed neutron source allows velocity(energy) analysis by time-of-flight (TOF) method
Neutron detector
L
Fast neutrons
Neutron flighttime analyzer

Slow neutrons

Trigger signal determining TOF = 0 （ from accelerator ）

2

1 h
1
1  L E = mv 2 = m
=
 

2
2  TOF 
2m  λ m : Mass of neutron2v : Velocity of neutron

L : Path Length from source to detector
TOF : Elapse time from neutron generationh : Plank’s constantPC

λ : Neutron wavelength

Because it's pretty slow,
it can be controlled
mechanically.
57

Wavelength-resolved neutron transmission
imaging using accelerator pulsed neutron source
and TOF method
Time of Flight（TOF: Time of Flight)
spectroscopy
Neutron velocity↓
Kinetic energy or
wavelength

13000 μs ~5000 μs ~2500 μs ~800 μs ~100 μs ~SamplePulsed white neutron beams~ 2 meV / 0.64 nm~ 13 meV / 0.25 nm~ 50 meV / 0.13 nm~ 500 meV / 0.04 nm~ 35 eV / 0.005 nm

TOF analysis type(High time resolution)neutron imaging
detector

58

Performance of TOF analyticalneutron imaging detectors
Pixel size GEM-type neutron imaging detector
KEK Uno group
Pixel size： 800 μm

Field ofview size

Photo by Prof.
MochikiField of vision ： 10 cm×10 cm

Mid-range spatial
resolution
Large area
High reliability

Neutron beam
High-speed camera type neutron image detector

MCP type neutron image detector

Tokyo City University
Mochiki group
Pixel size： 520 μm

UC Berkeley
Dr. A. S. Tremsin
Pixel size： 55 μm

Field of vision： 13 cm×13
cm

High spatial resolution
maximum area

Neutron color image intensifier (Toshiba) +High-speed CMOS video camera (NAC)

Field of vision ： 2.8 cm × 2.8 cm

Ultra-high spatial resolution59

Major reactions forneutron conversion & detectionn + 3He (0.0001% / 5333 barn)  3H + p
Isotope abundanceThermal neutron absorption cross-sectionn + 6Li (7.5% / 940 barn)  3H + α

n + 10B (20% / 3835 barn)  7Li + α

n + 155Gd (15% / 61100 barn)  156Gd + γ + e- (IC)n + 157Gd (16% / 259000 barn)  158Gd + γ + e- (IC)60

Neutron supermirror
Neutron focusing and miniaturization
Reflection of neutrons over a wideof neutron focusing andwavelength range by Ni-Ti multilayers
miniaturization of equipment

Neutron wavelength

2D detector

Sample position

Ellipsoidal
focusing mirror

2.5 m !

61

Nagneto-neutron lenses
SextuplemagnetMagnetic lensing with permanent magnets success ofneutron focusing experiment at Hokkaido Univ.
TOF synchronous (wide wavelength bandwidthtype) with no chromatic aberration to thedevelopment of pulsed sextupole magnets

Magnetic focusing
Neutron intensity multiplier100
exit y= 0(mm)exit y=-1(mm)With磁場あり
magnetic field
Without
magnetic field
磁場なし

10

λ＝５ [Å] λ＝７ [Å] λ＝９ [Å] λ＝１１ [Å]λ＝１３ [Å]

1

0

5

10
波長（Å）

15

20

62

Other examples of neutron devices（J-PARC MLF）
Chopper (Monochromator) Collimator (Divergence angle controller)
BL01

Wo. collimator

With collimator＋

Double disk chopper:
Variable aperture area.

63

Neutron utilization

64

Quantum beams" in mechanicalengineering!
Some specific examples will be presented later.
Neutron imaging analysis of space Space
propulsion thrusters by JAXA
engineering
Neutron imaging analysis of oil
 Thermal andbehavior inside an engine
fluid engineering Materials engineering Bionics
 Control engineering Fuel cells,lithium batteries
 Nuclear reactor engineering
Water behavior in fuelFatigue cracks in metallic materials synchrotron
radiation imaging analysis of fatigue cracks inmetallic materials (Prof. Nakamura)cells 4D neutron imaging
Analysis65Quantum beams" in Engineeringand Science!
Some specific examples will be presented later.
Neutron scattering (Applied) Physics
 (Applied) Chemistry atomic arrangement
analysis Biology
 Space and planetary science

DNA structure and sub-groove hydration water Materials engineering Architectural engineering
Hydrogen(Tetrahedral site)
 Soil engineering
Space probe Hayabusa brought back
 Environmental quantum beam linkage analysis of asteroid
material
engineering
Low Ca pyroxene

OlivinePlagioclase

High Ca pyroxene

Sub-groove

By X-ray fluorescenceanalysis image of elements
in pollen

66

The "quantum beam" is relevant to (almost) all
faculties at Hokkaido University!

Some specific examples will be presented later.

 Literature (Cultural property) Neutron imaging analysis
of paper in a sutra tube
 Law (Forensic science) Medicine and dentistry (Treatment
and diagnosis)
 Pharmaceutical sciences (Drug discovery /pharmaceutical)
 Agricultural science
Neutron-based pharmaceuticals ofradiopharmaceuticals for medical
diagnostic SPECT

4D neutron imaging analysisof root growth in soil

Process of 99mTc preparation

TargetMolybdenum solution

injection

Air transportation
2 daysNuclear reactor Molybdenum production facility
Target irradiation
4 to 10 days

Molybdenum
irradiation
1 to 2 days

Medicalinstitution
Manufacture and supply ofpharmaceutical products
2 to 3 days

Pharmaceutical manufacturer

67Non-destructive testing and development researchof aerospace equipment by neutron imaging

Turbine blade

Satellite thrusters

At the proton cyclotron facility of Sumiju Atex Co, inspection of
all space equipment by neutron imaging

68

Two-phase flow studies by neutron imaging
Visualization of water/nitrogen gas two-phaseflow in stainless steel pipe(a) Half water, (b) Slag flow, (c) Bubble flow, (d) Annular flow69

Time-dependent neutron magnetic fieldimaging analysis of electric vehicle motors
Neutron stroboscopes

Stroboscope of magnetic field(Visualize the magnetic field in thevertical direction)

3.5 cm

3.5 cm

SDGs／Cutting-edge research toward a carbon-neutral society

70Neutron imaging analysis forforensic applications
Using neutron resonanceabsorption, currency inspection
by elemental analysis

X-raysX線

Blasting
爆薬
powder（窒素）(Nitrogen)
Neutron
中性子

Zn

Cu
71

Equipment installed in the neutronlaboratory at Hokkaido University
Small-angle neutron scattering
instrument

Neutron beam

Neutron imaging system

Neutronbeam

72

We obtain microscopic information on the atomic
level of matter by analyzing the momentum
change of neutrons reacting with the matter!

Example: crystal structure analysis using diffraction(Bragg scattering)

Incident
wave

Diffracted
wave
Optical path
difference

Bragg diffraction by
crystalBragg diffraction
conditions

http://bb.phys.se.tmu.ac.jp/~bb/pukiwiki/index.php?Neutron_xray_1

When you want to know the face spacing d of a crystal lattice, you can examine the wavelength λ and thescattering angle 2θ (i.e., the momentum change) of the neutrons that caused the diffraction phenomenon
73(intensification).

Nano-structural analysis of steel, food, andbuilding materials by small-angle neutron
scattering
Quantum beam materials engineering laboratory A (Ohnuma laboratory)
Analyze the momentum change of scatteredneutrons at small angles to investigate thenanostructure of metallic materials and soft
matter!

Q2θ

2D detector
SampleExample of measured SAXS data

Size analysis of steel material nanoprecipitates,
analysis of aggregation state of food proteins, nanostructure analysis of building materials (cement), etc.

74Extensive analysis of automotive parts andcultural assets by neutron imaging

Neutron beam science and engineering laboratory (Kamiyama-Sato laboratory)

Visualization of interlayer distance of graphite
anode material for Lithium ion batteries
layer
spacing
層間隔 [nm]

Visualization of strain in heattreated parts of crankshafts
結晶格子面間隔

Variation of crystal latticespacing(nm)のばらつき (nm)0.005Stage11
Stage
ステージ1

0.004
0.003

ステージ2
Stage 2
Stage 3
ステージ3
ステージ4
Stage 4

0.002
0.001

Graphite
黒鉛

0.000

Visualization of the amount of different Visualization of
metals present in Japanese knives
crystallite size insteel plate welds
FerriteAustenite

Thickness
厚さ

（mm）
3.8

※ Applied to the studyof rails and Japaneseswords, etc.
Crystallite size（μm）
4.24
3.39
2.97

0.0

2.12
1.70

75

Reaction cross section between
neutrons and nuclei

76

Reaction cross section （barn = 10-24 cm2）

Total cross section of X-rays and one Al
atom （Scattering・Absorption）
http://www.nist.gov/pml/data/xcom/index.cfm
Absorbing
edge

104

1

Photoelectriceffect(Absorption)

10-4

Electron-positronpair generation（Positron generation
method)Thomson scattering(Coherent scattering)Compton scattering(Incoherent scattering)

10-8
10-3

Photon energy(MeV)
10-2

1

102

103

77

Interaction of γ-rays with matter Photoelectric effect: K-orbital or L-orbital
electrons absorb all of the energy of the γ-ray
and are ejected.
 Compton scattering: Orbital electrons thatcollide with γ-rays acquire part of the γ-ray
energy.
 Electron pair production: When the γ-ray energy
exceeds 1.022 MeV, electron-positron pairs areproduced.
 Due to these interactions, a γ-ray incident on amatter can give all (or part) of its energy to thematter.
78

Material analysis using X-ray-matterinteraction http://www.sci.u-hyogo.ac.jp/material/x-ray_optics/kago/presentations/
Incident X-rays
X-ray photoelectron
Photoelectron
spectroscopy (XPS)↓
Chemical state (Electronic state)

Reflected X-rays
Fluorescence X-ray analysis (XRF)↓
Fluorescence X-ray
Element type

Inelastic X-ray scattering

Elastic scattering X-ray

Compton scattering spectroscopy↓
Momentum of electron

X-ray diffraction↓
Periodic structure

Refracted x-ray

Refraction Contrast↓
High contrast imaging

X-ray transmission(Absorption)
X-ray absorption fine structure (XAFS)↓
Local structure, chemistry (electronic
structure)79

Total cross section of neutron and
one Al nucleus
http://wwwndc.jaea.go.jp/jendl/j40/J40_J.html

Low energy
regionAbsorption

Resonance
absorption

Resonancescattering(n,p)
reaction,(n,α)
reaction
etc.
Sourcesof softerrors80

Cross section / barn

Total cross-section in low-energy
regionData of Al nuclei calculated by "RITS" code developed by Hokkaido University
Coherent elastic scattering
干渉性弾性散乱Incoherent elastic scattering
非干渉性弾性散乱
Coherent inelastic scattering
干渉性非弾性散乱
Incoherent inelastic scattering
非干渉性非弾性散乱
吸収
Absorption
全断面積
Total cross section

2.5
2.0
1.5
1.0
0.5
0.0
0.001

Bragging edge

0.01
0.1
Neutron energy / eV181

Comparison of mean free paths ofelectrons, X-rays, and neutrons

Penetration Depth

1/μ（Mean free path = reciprocal of macroscopic total cross-section)

Roger Pynn, Neutron Scattering - A Primer, Los Alamos National Laboratory

Neutrons: hydrogen and heavy metals areequally reactive.
X-rays: Does not react with hydrogen.
Cannot penetrate heavy metals.
Neutron

1m
10 cm
1 cm
1 mm
0.1 mmX-rays

10 μm
1 μm

Electrons82

Scattering and absorption cross sectionsof major elements for thermal neutrons
Element

Scattering cross section（barn）

Absorption cross section（barn）

Applications in neutron engineering

H

82

0.33

Moderator (∵ light nuclei)
After neutron capture, high-energy γ rays
are also emitted

Li

1.37

71

Absorbers with low gamma ray effectafter neutron capture

B

5.24

767

Absorber
Emits alpha rays after neutron capture

Al

1.5

0.23

Transparent material (?)

Si

2.17

0.17

Fe

11.6

2.56

Scatterer

Co

5.6

37.18

Co-60 (gamma ray emitter) formation by
neutron capture

Cd

6.50

2520

Absorbing material, intense γ-ray emitter

Gd

180

49700

Absorber

Pb

11.1

0.17

Non-decelerating scatterer
Excellent gamma ray shielding material
83

Radiation safety at neutron
generating facilities(Once again, see and learn about
the site firsthand!)84

Principles of elemental analysis byneutron activation analysis

85

What is Neutron Activation
Analysis?
 Neutrons are captured by various nuclei, and γ
rays may be emitted from the nucleus that capture
the neutron. This is called the capture reaction((n,γ) reaction).
 Since the energy of γ rays emitted from aradionuclide has a unique value for each nuclide,the nuclide can be identified by measuring its
energy.
 Based on this principle, a sample is irradiated byneutrons to nondestructively qualify or quantify
the nuclides contained in the sample, which iscalled neutron activation analysis.
86Applications of neutron activation
analysis87

Neutron activation analysis (elemental analysis)that raised the possibility of Napoleon's"poisoning" theory.
 When neutrons are captured in
the nucleus, the matter isactivated (becomesradioactive).
 Analyzing the energy ofradiation (gamma rays) reveals
the type of nucleus (element).
 Suitable for cultural assets
because it does not break or
dissolve like normal chemical
analysis.
Napoleon's hair was found tocontain a large amount of arsenic!
Poisoning? !

Image source：http://www.revive.co.jp/magokoro/scrap_and_build/history-napoleon-revolution/

88

Analysis of particles brought back by Hayabusa
from the asteroid "Itokawa" through quantum
beam fusion collaboration
Low Ca pyroxene

Olivineplagioclase

High Ca pyroxene

image source: "Quantum Beam" for a family

Three-dimensional distributions ofolivine, pyroxene, and other minerals indust particles from the asteroid Itokawa
brought back from space were obtained.

 Analysis of 3D shape and 3Dinternal structure of particles by
X-ray CT imaging
 Crystal structure analysis ofminerals by X-ray diffraction(Bragg scattering) Elemental analysis by neutron
activation analysis
 Identification of minerals andmicrostructural analysis ofparticles by electron microscopy

Even if one analyticalmethod cannot give us acomplete picture, by
combining the power ofquantum beams, we caneven see the history of theformation of the solar
system!
89

Pulse height spectrum of NaI(Tl)scintillation detector

90

NaI(Tl) scintillator
 As a gamma (γ) ray measurement device, a scintillation detector
consisting of a sodium iodide (NaI) crystal containing a trace amountof thallium (Tl) is commonly called an NaI(Tl) scintillator.
 When a NaI(Tl) crystal is bombarded with γ-rays, the interaction(photoelectron effect, Compton scattering, and electron pair
production) causes secondary electrons to excite the NaI(Tl) crystal
material, and when the excited state returns to a steady state,
fluorescence, called scintillation, is produced.
 This light is captured and combined with a photomultiplier tube toconvert the radiation dose into a current pulse, which is used as aradiation measuring instrument.
 The intensity of the light is proportional to the energy lost bysecondary electrons in the crystal, which provides information on theenergy of the incident γ-rays.
 Scintillators have the advantages of (1) fast measurement due to shortscintillation decay time, and (2) energy measurement from the
proportional relationship between the amount of fluorescence andabsorbed energy.
91

Operating principle of NaI(Tl)scintillator
 When γ-rays strike the NaI crystal, secondary electrons are produced and theTl atoms emit fluorescence. Thallium (Tl), which emits fluorescence, is called
an activator.
 When the fluorescence by the Tl atom hits the photocathode of thephotomultiplier tube, photoelectrons are ejected due to the photoelectric effect,
which is multiplied by a number of dynodes to generate a pulse current in thecircuit.
 By counting the number of pulsed currents, the number of γ rays that enter the
NaI crystal can be measured.
Aluminum case

Light-shielding case

Magnetic seals

ReflecterElectrical signal
Amplified bypreamplifier &mainamplifier

DynodeGamma rays

fluorescence

Scintillator
Photocathode(Iodide single crystal)

Focusing electrode

Anode

92

Structure of NaI(Tl) scintillator
 NaI(Tl) scintillator in
Measuring container
combination with a
Photomultiplier tube
photomultiplier tube.
 The junction surface of the
Scintillator
NaI(Tl) scintillator andphotomultiplier tube has a
glass window.
Radioactive sample
 A cylindrical type with a
Photomultiplier tube
diameter of 5 cm x height
Cylindrical
Well-shapedof 5 cm or a well type withlarge geometric efficiency
FigureScintillator shapeis used.
93

Gamma-ray energy measurement
 The energy required to emit one photoelectron at thephotocathode of a photomultiplier tube is 120 eV.
When a γ-ray strikes the NaI(Tl) scintillator and all of
its energy is transferred to the NaI crystal, a numberof photoelectrons proportional to the γ-ray energy
are produced.
 As a result, a pulse current with intensity
proportional to the γ-ray energy flows through thecircuit, and the γ-ray energy can be determined bymeasuring the wave height of the pulse current
using a multi-channel pulse height analyzer (MCA).

94

MCA operation in γ-ray
spectrometry
512

Number of signals（ni）

Pulse height channel （i）

MCA: Multichannel Pulse Height Analyzer
510
508
506
504

4
2

Time
Discretize the pulse height voltage and countthe number of signals （ni） belonging to channel （i）.

Pulse height channel （i）

Plot the number of signals（ni）
in the pulse height channel （i）
95Total value per channel

Example of γ-ray spectra from a high-energyresolution Ge semiconductor detector （88Y）
1836 - 511×2 (keV)

Backs
cattering
Peak

Extinc
tion
γ-ray
peak

Doubleescapepeak

1836 - 511×1 (keV)

Singleescapepeak

898 keV γ線-rayコンプトン端Compton’s
edge

-ray
1836 keV γ線
コンプトン端Compton’s edge

Channel number The total absorption
peaks at 1836 keV and
898 keV are caused by
the photoelectric effect,
where all of the γ-ray
energy is absorbed by
the NaI crystal.
 Since only a part of theenergy of the γ-rays istransferred to the NaI
crystal due to Compton
scattering, etc., a
continuous spectrum ismeasured.
96Neutron irradiation experiments
 Irradiation samples• ?（Metal）

 Electron accelerator driven conditions:
10 pps for 15 minutes
 Attached to polyethylene moderator andplaced near neutron source

97Energy calibration and energy
resolution of NaI scintillation
detectors

98

Examples of pulse height spectra (Bothexamples measured in 3 minutes)
BackgroundCs-137

Na-22

Co-60

99

Calibration curves for pulse height channel and γray energy (to which we also add natural K-40
(1.46 MeV))

1.4

Nuclide Channel / ch γ-ray energy / MeV
Annihilation
消滅γ線
84
0.511
gamma rays
Cs-137
109
0.662
Co-60
189
1.17
Na-22
206
1.275
Co-60
215
1.33

γ-ray energy (MeV)

1.2
1.0
0.8
0.6
0.4

E (MeV) = 0.0063 ch - 0.019

0.2
0.0

0

50

100
150
Channel

200

250
100

γ-ray spectrum of Cs-137

Counts of γ-ray / cps

100

Cs-137
B.G.
Net

10
1
0.1
0.01
0.001

0.0

2.0
1.0
γ-ray energy / MeV

3.0
101

γ-ray spectrum of Cs-137(Display switched)30

Cs-137
B.G.
Net

Counts of γ-ray / cps

25
20
15
10
5
0

0.0

0.2

0.4
0.6
0.8
γ-ray energy / MeV

1.0
102

Evaluation of energy resolution(Fitting using Excel solver)
30

Experimental
Gaussian fitting

Counts of γ-ray / cps

25
20
15

ΔE/E = 7.77%@ 0.67 MeV

10
5
0

0.4

0.5

0.6
0.7
0.8
γ-ray energy / MeV

0.9

1.0
103

Backgrounds and how to deal with
them

104

Identification and Qualitative
Analysis
Element (nuclide) analysis

105

Measurement of γ-ray spectra of metal
samples and nuclide identification
 Measure the γ-ray spectrum of the mystery
metal sample using MCA and read the peak
center channel of all absorption peaks.
 Estimate the γ-ray energy of a metal sample
using an energy calibration curve.
 As a result, which of the following
radionuclides is considered to be induced in
the metal?
64Cu
65Zn

195mPt
198Au
203Hg

0.51 MeV
1.11 MeV
0.13 MeV
0.41 MeV
0.28 MeV106

Quantitative analysis
Estimation of neutron flux ⇔Quantitative determination ofelements107

Radioactivity in a sample inducedby neutron irradiation
 Average neutron flux in neutron moderator ：φ （1/cm2/s））
 Number of nuclei to be activated in the sample
placed in the neutron moderator ：N Effective activation cross section of its nuclei ：σ（cm2）
 Decay constants of radioactive nuclei ：λ （1/s）
 Radioactivity induced in the sample when only
time t1（s） has elapsed since the start ofirradiation. ：φNσ（1-exp（-λt1）） （1/s）
108

Example of calculation of time variation ofradioactivity of a sample
Figure for a sample containing
0.01 g of 197Au irradiated for 11days with a neutron flux of φ =108（1/cm2/s）

t1

t2

A(t1 ) = ϕNσ (1 − exp(− λt1 ))A(t 2 ) = A(t1 ) exp(− λt 2 )109

Let's estimate the neutron flux φA(t1 ) = ϕNσ (1 − exp(− λt1 ))A(t 2 ) = A(t1 ) exp(− λt 2 ) An irradiated gold foil weights 0.05 g.
Then what is the number of nuclei, N ?

Effective activation cross section of
197Au：
σthermal = 9.865×10-23（cm2）σresonance = 1.571×10-21（cm2） 198Au decay constant ： λ = 2.97×10-6（1/s）
 t1: s t2: s110

Estimation of thermal and epithermal
neutron fluxes using Cd filter
 If a Cd filter is attached to the gold foil, the neutron flux can be
estimated for higher energy neutrons than thermal neutrons.
 Subtracting this neutron flux from the flux without Cd, thethermal neutron flux can be derived.

111

Necessary precautions for accurate
radioactivity measurements γ-ray detection efficiency (with γ-ray
energy dependence)•••

Depends on the cross section of the photoelectric effect of the scintillator
Almost independent of the energy of the secondary electrons. (γ-ray scintillators
are often heavy elements, so the electrons stop almost entirely within the
scintillator.)
Absorption by window material and self-shielding of the sample must be
considered.

 Geometric detection efficiency
 γ-ray emission rate from the target
nuclide (γ-rays are not always emitted per
decay (transition)) Counting loss112

If the neutron flux φ is known, the N of an
identified element can be estimated （Elemental
determination）

A(t1 ) = ϕNσ (1 − exp(− λt1 ))A(t 2 ) = A(t1 ) exp(− λt 2 ) Since they have already been identified, σand λ are known.

113

Reference information onquantitative analysis

114

Cross-section of Au-197 (1)(JENDL-4.0)

115

Cross section of Au-197 (2)(JENDL-4.0)

116

Why φNσ（1-exp（-λt）） ?
dA(t )= −λA(t ) + λϕNσdt( )= 0Initial condition is A 0• First term on the right-hand side ： Decay ofradioactivity per second• Second term on the right-hand side ：Increase in radioactivity per second due toradiation capture• φNσ： Saturated radioactivity
117

Decay of radioactivity
 Radioactivity of the sample at any time after theend of irradiation ：A(0)（1/s）
 The radioactivity of the sample at the time t2（s）
elapsed from that point. ：A(0)exp（-λt2）（1/s）

dA(t )= −λA(t )dtInitial condition is A(0) at t = 0118