1.4 The Tools of the Trade!

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1.4 The Tools of the Trade!

Two things are required for material analysis:

• excitation mechanism for originating characteristic signature (radiation)

• radiation detection and identification system (spectroscopy)

For dating techniques you need either:

• measurement of activity A(t)

• counting of radioactive atoms N(t)

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Accelerators for Excitation Processes

Required 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

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Technical Principle of the cyclotron

Period T for particle

with mass m and charge q in magnetic field B:

Ion Source

T m

= q B ⋅ ⋅

⋅ 2 π

Energy of particle in cyclotron of radius R:

E m v q B R

= ⋅ = ⋅ m ⋅

⋅ 1

2 2

2

2 2 2

∆V

Acceleration across Voltage gap ∆V between the Dees: ∆E=q· ∆V

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

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Technical Principle of the Van de Graaff

potential: with Q charge and C capacity Energy: E = 1

2 with up to

U Q C

m v q U

U V E q eV q MeV

= = =

⋅ = ⋅

≤ ⋅ = ⋅

2

10000000 10

7

10 ; :

Sufficient energy for necessary excitation mechanisms!

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The single-ended Van de Graaff

1. charging system 2. Belt

3. Terminal charge pick-up

4. High pressure N₂/CO₂ gas vessel 5. Ion source

6. Acceleration tube 7. Vacuum tube

8. Generating voltmeter 9. Analyzing magnet 10. Target system

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The Tandem Accelerator

Advantage of ion-source at ground

Ion-source

V_term Terminal potential

Total energy: E=(1+q)V_term

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The smallest and the largest

Holifield tandem (ORNL) for

36Cl analysis Zürich tandem for ¹⁴C analysis

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Typical Accelerator Laboratory for Material Analysis and Dating

beam-

production

Material analysis

Mass analysis or dating

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Electron Beam Production

Release of electrons by filament heating,

-light-bulb-

extraction and acceleration through electric fields

E_e = 1 m v_{e e} = ⋅e U 2

2

negative potential

positive potential

Electron beam electron source

U

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Ion Beam Production by Sputter Source

Sputtering & charge exchange

E_ion≈100 keV Extraction and focusing

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Signatures through reaction processes

A(a,a)A A(a,a’)A*

A(a,b)B A(a,γ)C

(in-) elastic scattering

Ö characteristic particle energy Ö characteristic X-ray radiation Ö characteristic γ-ray radiation

nuclear reaction processes Ö characteristic γ-radiation

Ö characteristic particle break-up

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Some background

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

R

probability for incoming beam to hit a target nucleus with

radius R: σ ≈ πR²

Typical radius of nucleus ≈ 10^-12 m

cross section

^≈

area, unit barn:

1 barn = 1·10

^-24

cm

²

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Total probability for reaction ≈ Yield

If target has thickness d, and target material has

# nuclei/volume: n₀[part./cm³]

Y=σ·n

₀

·d

The yield gives the intensity of 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!

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Example:

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 5·10¹⁹part/cm³along 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 km

Y C cm part cm cm neutron

neutrons cm s

C cm s

S cm

C C s

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

( ) [ ] [ / ] [ ] . /

[ / ]

. [ ]

[ ] .

14 14 19 3

14 25 2 19 3 5

3 2

14 2

12 2

14 14 22

01 5 10 1

1 10 5 10 10 0 5

10 13 10 4 4 10

= ⋅ ⋅ = ⋅ ⋅ ⋅

= ⋅ ⋅ ⋅ ⋅ =

⋅

= ⋅

⋅ = ⋅

−

σ

a cosmic ray flux of 2.15

yields a total production rate of: 1.08 10 for entire surface area of earth:

production of: 1.4 10

3

15

[

¹⁴

C y ] = 102 . [ / ] g y

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Another Example

Estimate the number of

¹⁴

C

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

¹⁴

N(n,p)

¹⁴

C. The mummy contains 2·10

^{25 14}

N particles &

1.6·10

^{15 14}

C particles.

Cosmic ray flux at ground

level of ~1·10

⁴

particles/m

²

s.

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Estimate of ¹⁴ C production & ¹⁴ C content

Y C barn N N I particles m s t

Y C cm particles m s y

Y C cm particles cm s s

Y C

( ) [ ] ( ) mic[ ]

( ) . [ ] [ ] [ ]

( ) . [ ] [ ] . [ ]

( ) .

cos

14 14 2

14 24 2 25 4 2

14 24 2 25 2 7

14 11

01 10 2 10 10 3290

01 10 2 10 1 3290 315 10

2 07 10

= ⋅ ⋅ ⋅

= ⋅ ⋅ ⋅ ⋅ ⋅

= ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅

= ⋅

−

σ

particles are produced in the mummy.

Production: use standard production equation!

Content: use standard decay equation!

mummy!

in the contained

are

particles 10

075 .

1 )

3290 (

10 6

. 1 )

3290 (

) (

14 15

5730 3290 2 ln 15

0

C y

N

e y

N

e N

t N

y y t

⋅

=

⋅

=

⋅

=

⋅

−

⋅

− λ

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Absorption and Transmission

Absorption and transmission of the initial beam with intensity I₀ depends on the target thickness d and total interaction cross section

σ

_tot

= σ

_i

for all possible reactions between projectiles and target

material of cross section σ_i:

I(d) I

₀

I d I e n

d

i i

( ) = ⋅

= ⋅

− ⋅

∑

⁰

0

µ

µ σ

d

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Cosmic Ray Absorption in Atmosphere

I d I e

^d

n

_i

i

( ) = ⋅

⁰ ^{− ⋅}^µ

; ^µ = ⋅

⁰

∑ ^σ

How many of the 2.15·10³/cm² neutrons produced at 12 km height will reach the surface of the earth assuming an average nitrogen density of 5·10¹⁹part/cm³and an interaction cross section of 0.1 barn?

I km e

I km

n

N cm cm cm

n

( ) .

[ / ] . [ ] . [ ]

12 215 10

12 53

3 510^{19 14} ³ 0 110 ²⁴ ² 1 2 10⁶

= ⋅ ⋅

=

− ⋅ ⋅ ⋅ ⁻ ⋅ ⋅

[n / cm s]

2 2

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Interaction processes between projectile and target material

•

atomic excitation processes Ö X-ray-visible light

(Coulomb Interaction between projectile and atomic electrons): σ_i ≈[kbarn]

• elastic scattering processes

^Ö

char. particle energies

(mechanical momentum without energy transfer): σ_i ≈ [barn]

• inelastic scattering processes

^Ö

char. γ-radiation

(mechanical momentum and energy transfer): σ_i ≈ [barn]

• radiative capture reactions

^Ö

char. γ-radiation

(Coulomb Interaction between projectile and atomic nucleus): σ_i ≈ [µbarn]

• nuclear reaction processes

^Ö

char. particle radiation

(Strong Interaction between projectile and atomic nucleus): σ_i ≈ [mbarn]

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Radiation Detectors

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:

• Scintillator X-ray, γ-ray, and neutron radiation

• Solid State Detector particle- and γ-ray radiation

• Ionisation Chamber particle radiation

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Example: NaI scintillator

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

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

• electrons are multiplied in photo multiplier and converted to an electrical signal

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Ionization chamber and 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.

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