Gamma-Ray Spectra

_ +

The photomultiplier records the (UV) light emitted during electronic recombination in the scintillator. Therefore, the spectrum collected in the scintillation detector combines the characteristics of the emitter as well as absorptive processes in the scintillator.

Radiation Absorption

The radiation energy is being absorbed through several mechanisms.

major mechanisms:

a) photoelectric effect b) Compton scattering c) pair production

other mechanisms:

d) coherent scattering e) photodisintegration f) edge absorption

Photoelectric Effect

E = h  K = h   The energy of the photon is used to ionize the atom (work function) and the kinetic energy of the photoelectron.

Traveling with considerable kinetic energy, photoelectrons ionize a number of atoms.

Absorption Cross-Section

( in Photoelectric Effect )

The probability of absorption is proportional to the total absorption cross-section  [cm -1 ] 100  ph    2  10  8 8  e 2  m 0 c 2 3  2 3    S 



Z  0 .

3  h   7 2 10 1.0

0.1

0.01

0.1

h  1.0

[MeV] 10.0

Absorption coefficient is NaI.

Z – atomic number h  – photon energy (keV) S – function of h  and Z S   0 .

18  0 .

28 log 1000  Z 2 h 

Angular distribution

The number of photoelectrons ejected into angle d  making an angle  with the incoming photons is dn   1  sin  2 cos    4 d  150  120   = 0 90   = 0.5

60  30  2 1 0 1 2 0  where   v c

Compton Scattering

Conservation of momentum and conservation of energy lead to h  h  ’  • the energy of the scattered photon h  '  1  h  m 0 c 2 h   1  cos   • the energy of the electron K  h 2  2 m 0 c 2   1 h    1 cos   cos    Compton shift:    h m 0 c  1  cos  

Absorption Cross-Section

( in Compton scattering )

 C  [cm -1 ]  3  4  0   9  51   3  93   1  2 2   5   3 3  10  4  3  2  2    2 ln  1  2      ( Klein – Nishina equation (1929) ) 100 10 1.0

0.1

0.01

0.1

h  1.0

[MeV] 10.0

Absorption coefficient is NaI.

where   h  m 0 c 2 Thompson scattering cross-section by electrons  0  8   3 e 4 m 2 0 c 4

Angular distribution

The differential form of the Klein – Nishina equation gives the angular distribution of the scattered photons 90  120  60  150  ~0 keV 100 keV 30  20 MeV 20 MeV 0 

Pair Production

h  > 1.02 MeV e e + Almost the entire energy of the photon is used for the relativistic energy of the pair.

The recoil of the nucleus satisfies the momentum conservation.

Absorption Cross-Section

( in pair production )

Approximate value valid up to 15 MeV  [cm -1 ] 100  pp   0 Z 2 28 ln 9 2   218 17 10 1.0

0.1

0.01

0.1

h  1.0

[MeV] 10.0

Absorption coefficient is NaI.

where   h  m 0 c 2 Thompson scattering cross-section by electrons  0  8   3 e 4 m 2 0 c 4

e + h 

Positron-Electron Annihilation

h  e -

e

+

+ e

-

= 2h

 Usually annihilation takes place at low kinetic energy of the particles.

Conservation of momentum favors the emission of two (511 keV) photons emitted in the opposite directions.

Coherent Scattering

Coherent scattering results from the interference of photons scattered from a number of scattering centers.

Cross-sections for coherent scattering are small, therefore it is an unimportant mechanism of absorption for radiation detection.

Photodisintegration

The absorption of photons associated with photodisintegration occurs above precise energy thresholds causing removal of a nucleon from the nucleus 9 Be + h   8 Be + 1 n (1.66 MeV) 2 H + h   1 H + 1 n (2.22 MeV) 1 n Photodisintegration is used for calibration.

High energy photons (>20MeV) used to produce neutron beams..

Absorption Edges

 [cm -1 ] 100 10 Photoelectric effect and Compton scattering are in resonance with the absorption edges.

1.0

0.1

0.01

0.1

h  1.0

[MeV] 10.0

Absorption coefficient is NaI.

The absorption edges correspond to the characteristic X-ray emission of the scintillator.

Cts

Spectral Features

- The photopeak

22 Na 0.5

1.0

1.5

2.0

MeV The excitation and recombination (photoelectric effect and Compton scattering), taking place within the “life-time” of the photocathode emission, result in the main

photopeak

.

Statistic fluctuations broaden the peak, according to approximately normal distribution.

Spectral Features

- the escape peak

Cts Iodine escape peak 22 Na 0.5

1.0

1.5

2.0

MeV Some ionized atoms do not recombine in the time of the photopeak. The de-excitation becomes a delayed event and the absorption of the secondary X-ray radiation produces the

escape peak

.

Cts

Spectral Features

- Compton continuum

22 Na Compton continuum 0.5

1.0

1.5

2.0

MeV The dissipation of Compton electron energy does not contribute to the photopeak. The energy of Compton electrons ranges from zero up to the maximum that the original photons could transfer. The band with a high-energy edge called the

Compton continuum

results from the dissipation of the Compton electron energy.

Spectral Features

- backscattered peak

Cts backscattered peak 22 Na 0.5

1.0

1.5

2.0

MeV Often the scattering of the original radiation from the shielding produces a

backscatter peak

of energy lower than that of the photopeak.

Spectral Features

sum peak

Cts sum peak 22 Na 0.5

1.0

1.5

2.0

MeV There is positive probability for the absorption of two photons from the source within a short time interval resulting in the

sum peak

.

Spectral Features

- pair production peaks

Pair production (above 1.02 MeV) adds peaks at h  -1.02 MeV (both particles escape from the scintillator) h  -0.511 MeV (one particle escapes from the scintillator) 0.511 MeV positron annihilation takes place outside the scintillator.