Detection of energetic particles and gamma rays

The interaction of radiation with matter

Peter Dendooven

KVIdendooven@kvi.nl

Basic Detection Techniques 2009-2010http://www.astro.rug.nl/~peletier/DetectionTechniques.html

2

Contents

• Interaction of radiation with matter– high-energy photons

– charged particles• heavy charged particles

• electrons

– neutral particles• neutrons

• neutrinos

• General radiation detection concepts– pulse mode operation

– energy spectrum

– detector efficiency

– timing

• Radiation detectors– semiconductor detectors

• operation principle

• examples (silicon, germanium)

• other materials

– scintillation detectors• principle

• organic scintillators

• inorganic scintillators

• photosensors

– gas detectors• ionisation

• proportional

• Geiger

3

Radiation categories

charged particles

heavy charged particles

fast electrons

neutral particles

high-energy photons

neutrons

neutrinos

“Coulomb”

“easily stopped” transfer

4

Nomenclature high-energy photons

• high-energy photons = energy higher than ionisationenergies, so rougly >1 keV (!<1 nm)

• in principle:

– X-rays: atomic transitions

• up to ~115 keV for uranium

– "-rays: nuclear transitions

• from few eV to many MeV

• other sources of high-energy photons

– bremsstrahlung

– synchrotron radiation

– annihilation radiation

• to keep things simple: “"-rays”

5

High-energy photons: 3 major interactions

• photo-electric effect

• Compton scattering

• pair production

1921

Arthur H. Compton

1927Nobel prizes in physics

6

Attenuation of gamma rays (1/2)

!

I(x) = I0 e"µ x

x

dx

0

I0 I(x)

!

dI

dx" I

!

dI(x)

dx= "µ I(x)

µ: linear attenuation coefficient

all-or-nothing processes:

7

Attenuation of gamma rays (2/2)

mean free path

!

" =x e

-µx dx

0

#

$e

-µx dx

0

#

$=

1

µ

compound or mixture

mass attenuation coefficient

half-thickness

!

µ" #µ

"

!

µ 1

cm

"

# $

%

& ' , (

g

cm3

"

# $

%

& ' ) µ(

cm2

g

"

# $

%

& '

!

µ

"

#

$ % &

' (

c

= wi

i

) µ

"

#

$ %

&

' (

i

wi: weight fraction of element i

!

I(x) = I0 e" ln 2

x

d1/2

!

d1/ 2 =ln2

µcm or

g

cm2

"

# $

%

& '

8

Interaction cross section

number of “interactions” proportional with: N [/s]

– beam intensity I [/s]

– number of “reaction partners” encountered n t (#t’) [/cm2]

beam, I

t

target, n atoms/cm3

N = $ I t’

$= cross section [cm2]

1 barn (b) = 10-24 cm2

9

• interaction with whole atom

• K-electron most probable

• energy deposition:

– (Eb: electron binding energy) % E" > Eb

– electron cloud is “rearranged”:• X-rays

• Auger electrons

– photo-electron preferentially emitted in a forward direction

Photo-electric effect

!

Ee" = E # " E

b

"

!

E "

!

Ee"

10

Photo-electric cross section in lead

absorption edges

11

Compton scattering (1/2)

!

" E # =E #

1+E #

m0c

21$ cos %( )

m0c2 : electron rest mass (511 keV)

& : scattering angle

!

E "

!

" E #

e-

12

Compton scattering (2/2)

angular distribution: Klein-Nishina formula

!

d"

d#($) =

1

2re

2% E &

E &

'

( ) )

*

+ , ,

2

E &

% E &+

% E &

E &

- sin2 $'

( ) )

*

+ , ,

cm2

sr

.

/ 0

1

2 3

!

d"

d#($) =

1

2re

2 1

1+%(1& cos$)

'

( )

*

+ ,

2

1+ cos2 $ +%2(1& cos$)2

1+%(1& cos$)

'

( )

*

+ ,

cm2

sr

-

. /

0

1 2

re: classical electron radius = 2.82 x 10-13 cm

!

" =E #

m0c

2

13

Compton scattering

14

Compton scattering

15

Compton scattering

16

Pair production

• nucleus for momentum conservation

• requires E" > 2 m0c2 = 1022 keV

• kinetic energy (e– + e+) = E" - 1022 keV

• e+ annihilates with an electron

– two 511 keV annihilation photons

– emitted back-to-back

17

Dependence on atomic number and energy

Z : atomic number

photo-electric effect

Compton scattering

pair production

type of interaction attenuation coefficient comment

!

" # Z4.5

E $

-3.5

!

"# Z E $

-1

(0.1 to 10 MeV)

!

" # Z2 E $ %1022 keV( )

!

" # Z2 ln(E $ )

dominates for low energies

and heavy elements

dominates from ~0.5 to 5 MeV

(for most elements)

E close to 1 MeV

E >> 1 MeV

dominates for high

energies and heavy

elements

18

Total "-ray attenuation

µ = ' + $ + (

19

Half-thickness

20

Relative importance

21

Heavy charged particles

• protons, alpha particles, atomic ions

• primary interaction through Coulomb forces

(only at low energy, nuclear reactions are important for energy loss)

• Coulomb scattering by atomic electrons

– maximum energy transfer (head-on collision)

for 10 MeV proton: )Emax * 20 keV

% energy loss in very many small steps

– Coulomb force has infinite range, so interaction with many electrons

simultaneously

% continuous, gradual, energy loss

!

"Emax

# E4m

M

m: electron mass

M: mass heavy particle

22

Heavy charged particles

• Coulomb interaction leads to:

– electron capture/loss by projectile

– exitation projectile

– exitation and ionisation of target atoms

• basis for detection

• kinetic energy is tranferred to +-rays, X-rays, Auger electrons, ...

• many-faceted and complicated process

• paths are essentially straight because

– M >> me

% per interaction a small deflection

– interactions in all directions

23

Stopping power

• stopping power # energy loss per unit of amount of material

• linear stopping power

• specific stopping power

!

S = "dE

dx e.g.

MeV

cm

#

$ %

&

' (

!

S = "dE

d(#x) e.g.

MeV

g cm2

$

% &

'

( )

x

dx

0

E0 E(x)

24

Bethe-Bloch formula

incoming particle: ,: v/c

v: velocity

ze: charge

absorber material: n: electron density (electrons/cm3)

I: average excitation and ionisation potential

~10 Z eV

electron: e: charge

m0: rest mass

!

"dE

dx=

e

4#$0

%

& '

(

) *

2

4# (ze)2 n

m0c2 +2

ln2m0c

2 +2

I" ln 1"+2( ) "+2

,

- .

/

0 1

25

Bethe-Bloch formula

!

"dE

dx= 0.31 MeV cm

2

z2

#2

$ Z

Aln

2m0c

2 #2

I" ln 1"#2( ) "#2

%

& '

(

) *

!

n " N Z "N

A # Z

A

N: atomic density (atoms/cm3)

Z: atomic number

NA: Avogadro constant

-: density (g/cm3)

A: atomic weight

!

"dE

dx=

e

4#$0

%

& '

(

) *

2

4# (ze)2 n

m0c2 +2

ln2m0c

2 +2

I" ln 1"+2( ) "+2

,

- .

/

0 1

26

Stopping power dependencies

non-relativistic Bethe-Bloch

[...] changes slowly

!

"dE

dx#

z2 n

v2

different energy

!

"dE

dx#

1

v2#

1

E

!

"dE

dx# z

2different particle(same velocity)

!

"dE

dx# ndifferent material

!

"dE

dx=

e

4#$0

%

& '

(

) *

2

4# (ze)2 n

m0v2ln

2m0v2

I

+

, -

.

/ 0

27

Bragg-Kleeman rule

stopping power per atom of compounds/mixtures is additive

!

1

Nc

dE

dx

"

# $

%

& '

c

= Wi

1

Nii

( dE

dx

"

# $

%

& '

i

Nc, Ni: atomic density of compound, component

Wi: atomic fraction of component i

28

Stopping power example #1

protons in aluminum

slow-m

oving io

ns

captu

re e

lect

rons

29

Stopping power example #2

about same energy loss minima

% minimum ionizing particle

~2 MeV/(g/cm2) in light materials

30

The Bragg peak

stopping power vs. distance travelled

basis for hadron (e.g. proton) therapy

31

Electrons

electron mass is small

% Coulomb interaction causes:

• large relative energy loss per interaction

• large deviations in path

% large accelerations cause energy loss

due to electromagnetic radiation: bremsstrahlung

% distance travelled >> projected range

% backscattering (low E and high Z)

32

Electron energy loss

!

dE

dx=

dE

dx

"

# $

%

& ' c

+dE

dx

"

# $

%

& ' r

!

"dE

dx

#

$ %

&

' ( c

=e

4)*0

#

$ %

&

' (

2

2) e2 n

m0c2 +2

lnm0v2 E

2I2(1"+2)" (ln2) 2 1"+2 "1++2#

$ %

& ' ( + (1"+2) +

1

81" 1"+2# $ %

& ' (

2,

- .

/

0 1

!

"dE

dx

#

$ %

&

' ( r

=e

4)*0

#

$ %

&

' (

2

e2 n (Z + 1) E

137 m0

2c44 ln

2E

m0c2"

4

3

+

, -

.

/ 0

!

(dE dx)r

(dE dx)c

"E[ MeV] Z

700

c: collisional

r: radiative

33

Electron collisional vs. radiative energy loss

34

Electron stopping power

minimum ionizing particle:

~0.5 to ~5 MeV: 1-2 MeV/(g/cm2)

35

Range of a charged particle

# distance travelled before stopping

!

R = "dE

dx

#

$ %

&

' (

"1

dE

E0

0

)

of more practical use: projected range

(= “range”)

charged particle track

projected range

range

36

Straggling

energy loss is a stochastic process

% energy straggling

% range straggling

% angular straggling

range

37

Range example: hydrogen, helium ions

38

Electron range: examples

39

Cherenkov radiation (1/2)

• a charged particle travelling faster than the speed of light in a

medium emits light, so-called Cherenkov radiation

!

v >c

n

!

" n > 1

!

" #v

c

n: refractive index

• energy threshold

!

Eth

= m0c

2 "1+ 1+1

n2 "1

#

$

% %

&

'

( ( m0c

2: electron rest mass

40

Cherenkov threshold energy

41

Cherenkov radiation (2/2)

• Cherenkov photons are emitted under a fixed angle

!

cos" =1

# n

• yield per unit wavelength . 1/!2

(breaks down at short ! as n%1)

“electromagnetic shock wave”

42

Cherenkov light yield

!

d2N

dE dx" 370 z2 sin2

#(E) 1

eV

1

cmze: charge of particle

43

Cherenkov radiation: example

spent nuclear fuel under water at the La Hague reprocessing plant

44

Neutrons

• no Coulomb interaction, only strong interaction

• short range & atomic nucleus is small:

% interaction probability << than charged particles/photons (~108)

• as the result of an interaction:

– neutron disappears, creating secondary radiation

• mostly heavy charged particles (p,d,t,/) (basis for detection)

– scattering in which energy and direction are significantly changed

• can give rise to recoil nuclei (basis for detection)

% attenuation of a collimated beam is exponential

45

Neutrons

type of interaction depends mostly on the neutron energy

– fast neutrons (> ~0.5 eV)

• elastic scattering (most effective on light nuclei), gives recoil nuclei

• inelastic scattering, gives recoil nuclei

• scattering results in neutron energy loss (neutron is moderated)

• neutron capture (resulting in the emission of charges particles (p,d,t,/))

– resonant

– slow neutrons

• elastic scattering

– small energy loss, so no good for detection, but thermalizes neutrons

(~25 meV at room temperature)

• eventually captured by nucleus followed by gamma ray: (n,")

– most effectively by B, Cd, In, Gd

46

Neutrinos

• no electromagnetic or strong interaction, only weak interaction

% very small interaction probability

e.g. cross section ~ 10-43 cm2

1 cm3 of material contains ~1024 protons

interaction probability ~10-43 x 1024 ~ 10-19 /cm

1019 cm (10 light-years) required for a good capture probability

• neutrino interaction results in secondary radiation,

which is then detected

• interaction possibilities and probabilities are different for the

3 neutrino flavours: electron-, muon-, and tau-neutrino

!

" e + p# n + e+

47

Neutrino detection schemes

• inverse beta-decay– detect e+ (annihilation) and/or Y (radiochemical detection)

• neutrino capture by a nucleus (Homestake experiment)

– detection of 37Ar

• water-Cherenkov detection: scattering off electrons

– all neutrino flavours but with different cross sections

– detected via Cerenkov radiation from the scattered electrons (E0 > 5 MeV)

– Cherenkov cone tells incoming direction and particle type

– e.g. (Super)-Kamiokande

• heavy water: 3 options, all 3 neutrino flavours can be detected

– scattering off electrons (all 3 flavours, different cross sections)

– 0e + d % p + p + e– detect e– via Cherenkov, only 0e

– 0e + d % 0e + n + p deuteron break-up, detect neutron, all 3 flavors,

same cross section

– e.g. SNO (Sudbury Neutrino Observatory)

!

" e+

Z

AX # e

++

Z$1

AY

!

"e+

17

37Cl # e

$+

18

37Ar

!

" + e#$ " + e

#

48

Super-Kamiokande

• 1 000 m underground

• 41.4 m tall, 39.3 m diameter

• 50 000 tonnes ultra-pure water

• 11 146 20” and 1 885 8” photomultiplier tubes

49

Sudbury Neutrino Observatory

• 2 km underground

• 1 000 tonnes of heavy water

• 6-metre radius acrylic vessel

• 9 600 photomultiplier tubes