1.5. The Tools of the Trade!

Two things are required for material analysis:

• excitation mechanism for originating characteristic signature (radiation)

• radiation detection and identificationsystem (spectroscopy)

For dating techniques you need either:

• measurement of activity A(t)• counting of radioactive atoms N(t)

Accelerators for Excitation ProcessesRequired energy transfer for atomic processes: E≅1 keV-5 MeV

Required energy transfer for nuclear processes: E ≅ 1 MeV-15 MeV

Two kind of accelerators are in use:

• cyclotron• Van de Graaff

Technical Principle of the Cyclotron

Ion Source

Period T for particle with mass m and charge qin magnetic field B:

Tm

q B=

⋅ ⋅⋅

2 π

Acceleration across Voltage gap ΔVbetween the Dees: ΔE=q· ΔV

ΔV

Energy of particle in cyclotron of radius R:

E m vq B R

m= ⋅ =

⋅ ⋅⋅

12 2

22 2 2

E < 20 MeV (relativistic effects)sufficient for material analysis.

Technical Principle of the Van de Graaff

potential: with Q charge and C capacity

Energy: E =12

with up to

UQC

m v q U

U V E q eV q MeV

= = =

⋅ = ⋅

≤ ⋅ = ⋅

2

710000000 10 10

;

:

Sufficient energy for necessary excitation mechanisms!

The single-ended Van de Graaff

1. charging system2. Belt3. Terminal charge pick-up4. High pressure N2/CO2 gas vessel5. Ion source

6. Acceleration tube7. Vacuum tube8. Generating voltmeter9. Analyzing magnet

10. Target system

The Tandem AcceleratorAdvantage of ion-sourceat ground

Ion-source

Total energy: E=(1+q)Vterm

VtermTerminal potential

The smallest and the largest

Zürich tandemfor 14C analysis

Holifield tandem(ORNL) for36Cl analysis

Typical Accelerator Laboratoryfor Material Analysis and Dating

beam-production

Material analysis

Massanalysisor dating

Eion≈100 keV

Ion Beam Production by Sputter SourceSputtering & charge exchange

Extraction and focusing

Signatures through reaction processes

(in-) elastic scatteringcharacteristic particle energycharacteristic X-ray radiationcharacteristic γ-ray radiation

nuclear reaction processescharacteristic g-radiationcharacteristic particle break-up

A(a,b)BA(a,γ)C

A(a,a)AA(a,a’)A*

Reaction Probability ⇒ Cross Section

The probability for a reaction to occur is the cross-section σ!

probability for incoming beamto hit a target nucleus with radius R: σ ≈ πR2

R

cross section ≈ area, unit barn: 1 barn = 1·10-24 cm2

Typical radius of nucleus ≈ 10-12 m

Interaction processes between projectile and target material

• atomic excitation processes X-ray-visible light(Coulomb Interaction between projectile and atomic electrons): σi ≈[kbarn]

• elastic scattering processes char. particle energies(mechanical momentum without energy transfer): σi ≈ [barn]

• inelastic scattering processes char. g-radiation(mechanical momentum and energy transfer): σi ≈ [barn]

• radiative capture reactions char. g-radiation(Coulomb Interaction between projectile and atomic nucleus): σi ≈ [mbarn]

• nuclear reaction processes char. particle radiation(Strong Interaction between projectile and atomic nucleus): σi ≈ [mbarn]

If target has thickness d, and target material has

# nuclei/volume: n0 [part./cm3]

Y=σ·n0·d

Total probability for reaction ≈ Yield

The yield gives the intensityof the characteristic signal

from the reaction process per incoming particle with the

cross section σ ! It also gives the number of reaction products

per incoming particle!

The cosmic ray bombardment of air produces the radioisotope 14C by the 14N(n,p)14C reaction. Calculate the number of produced 14C assuming an average 14N density of 5·1019 part/cm3

along the cosmic ray path length of 1.0 km, a reaction cross section of σ=0.1barn and a cosmic ray induced neutron flux of 2.15·103/cm2s.

Y C n N d barn part cm kmY C cm part cm cm neutron

neutrons cm sC cm s

S cmC C s

( ) ( ) . [ ] [ / ] [ ]( ) [ ] [ / ] [ ] . /

[ / ][ / ]

. [ ][ ] .

14 14 19 3

14 25 2 19 3 5

3 2

14 2

12 2

14 14 22

01 5 10 11 10 5 10 10 05

10

13 104 4 10

= ⋅ ⋅ = ⋅ ⋅ ⋅

= ⋅ ⋅ ⋅ ⋅ =

⋅

⋅

= ⋅

⋅ = ⋅

−

σ

a cosmic ray flux of 2.15yields a total production rate of: 1.08 10for entire surface area of earth:

production of: 1.4 10

3

15 [ ] . [ / ]14 102C y g y=

Example:

Another ExampleEstimate the number of 14C atoms produced in the mummy of Ramses II by 3290 years of cosmic ray bombardment!

Adopt a cross section of σ = 0.1 barn for 14N(n,p)14C.

The mummy contains2·1025 14N particles &1.6·1015 14C particles. Cosmic ray flux at ground

level of ~1·104 particles/m2s.

Estimate of 14C production & 14C content

Y C barn N N I particles m s tY C cm particles m s yY C cm particles cm s sY C

mic( ) [ ] ( ) [ ]( ) . [ ] [ ] [ ]( ) . [ ] [ ] . [ ]( ) .

cos14 14 2

14 24 2 25 4 2

14 24 2 25 2 7

14 11

01 10 2 10 10 329001 10 2 10 1 3290 315 102 07 10

= ⋅ ⋅ ⋅

= ⋅ ⋅ ⋅ ⋅ ⋅

= ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅

= ⋅

−

−

σ

particles are produced in the mummy.

Production: use standard production equation!

Content: use standard decay equation!

mummy! in the contained areparticles10075.1)3290(

106.1)3290(

)(

1415

32905730

2ln15

0

CyNeyN

eNtNy

y

t

⋅=

⋅⋅=

⋅=

⋅−

⋅− λ

Radiation Detectors

• Scintillator X-ray, γ-ray, and neutron radiation• Solid State Detector particle- and γ-ray radiation• Ionisation Chamber particle radiation

Radiation detectors are based on material which shows a high probability (cross section) for interacting with a particular kind of radiation (in a particular energy range)! The interaction process initiates an excitation or ionisation event in the material (e.g. atomic excitation, or solid state excitation) which results in light or particle emission which in turn can be used for generating an electrical pulse for analyzing and interpreting the event in the data acquisition electronics. There are three kind of detector materials:

Example: NaI scintillator

• Photons in the visible light range are created by excitation ofNaI material with radiation

• photons are absorbed on photo cathode and generate free electrons by photo-effect

• electrons are multiplied in photo multiplier and convertedto an electrical signal

Ionization chamberand semiconductor

detectors

Detectors are based on the principle of ionization along the track of energetic charged particle, production of ion-electron pairs, which are accelerated by attached electrical fields to anode or cathode pole of detector, charge pulse is converted in electrical pulse, pulse height corresponds to energy loss of initial energetic particle.

Summary

• Tools are needed to instigate the characteristicexcitation processes by energy transfer

• Tools are needed to analyze the characteristiclight or radiation signatures