بسم الله الرحمن الرحيم ” وقل رب زدنى علماً “ صدق الله العظيم

Applications of Gamma Ray Spectroscopy 1) Study of the Nuclear Structure. 2) Identification of the Radioactive Isotope. 3) Measuring the Absorbed Doses. 4)Determination of the Interaction Cross Section.

Gamma-ray Spectrum 1- Measurements method 2- Measurements analysis ( Detector Efficiencies)

Detection system diagram Detector High-voltage power supply Pre-amplifier Amplifier Multichannel analyzer Source

The energy distribution in the spectrum Double escape peak Single escape peak Full energy peak E MeV E MeV E N( C )

The Detector ’ s Efficiencies The total efficiency (  T ). The geometrical efficiency (  g ). The intrinsic efficiency (  i ). The full energy peak efficiency (  p ). The intrinsic peak efficiency (  ip ). The photo-fraction (P). The single escape peak efficiency (  se ). The double escape peak efficiency (  De ).

1) Experimental method 2) The empirical method 3) Monte Carlo method 4) Direct Statistical Calculation method The different methods of Calculations

The probability fraction (p), that, the photon is recorded in the detector is given by: - By using this fact, the efficiency can be calculated by: - where  is linear attenuation coefficient (interaction probability in cm) d is the path length inside the detector Direct Statistical Calculation method where  is the subtended solid angle between the source and the detector



 h L R The Cylindrical Detector at R   : - The polar angle

 h L R The azimuthal angle

 h L R The paths inside the detector    x

11  1

11  1  2 22

22  2  3 33

33  3  4 44

The efficiency of the geometrical volumetric source is: - The self-absorption factor must take in account so - : The plane source efficiency is: -

Efficiencies’ Attenuation Coefficient  Photoelectric Effect (  ) Compton Scattering (  ) Pair Productions (  )

3) The intrinsic efficiency (  i ): - 2) The geometrical efficiency (  g ): - where  is calculated by: 1) The total efficiency (  T ): - The total attenuation coefficient (  T ) is used to done that:

4) full energy peak efficiency (  p ) The condition for the photon to be recorded under the peak is given by:- E is the deposited energy in the detector, h 0 is the incident photon energy,  is the peak full width at half maximum.

Photoelectric Effect (  ) The electron binding energy can be neglected w. r. t. the incident photon energy, so it’s deposited completely in the peak area i.e. The photoelectric effect contributes totally in the peak efficiency 

Compton Scattering (  ) A part of incident photon energy is deposited and the residual part with the scattered photon. The deposited energy isn’t enough to the photon is recorded under the peak!!!! But, there is a probability of the scattered photon makes other interactions and the photon is recorded under the peak f (if we assume that, the detector considers all the events as one interaction) That is mean that, we study the successive interactions in details

  Compton Scattered Photon Energy h 1 h 0 is the incident photon energy, h 1 is the scattered photon energy,  = h 0 / m 0 c 2 and m 0 c 2 is the electron rest mass

Angular Distribution d  /d  Klein and Nishina derived a differential cross section formula for polarized incident photon : where  is the angle between the electric vector of the incident photon and the scattered electric vector, r 0 is the classical electron radius and d  is the element of the solid angle for the scattered photon.

Scattered photon energy and direction From Klein - Nishina formula, We can deduced mean scattered photon energy and the average angle cosine. The mean scattered photon energy : - where F n is energy reduction factor: where Z n = 1+2  n

Average cosine angle by substituting by in Compton scattered photon energy formula, We can get the average angle cosine as:

Where f m is the average fraction of the Compton scattering and is given by: Where P in is the probability of the scattered photon to interact in the main free path. and m is the allowed scattering number Compton scattering Contribution f m

and The allowed scattering number m: The allowed scattering number depends on the lateral and longitudinal limitations of the detector and is given by: Where,  d is the average covered path of a ray inside the detector,  R is average lateral displacement inside the detector. and where  0 is the average incident angle.

RR h L dd 22 00 R 11 33 00 1/  3 1/  2  1/  1

where are the average annihilated photon energy and given by: - and Whereas, the probability of the photon recorded under the peak from the pair production is g n and given by: Pair Production Effect (  )

The peak efficiency attenuation coefficient (  p )

5)The intrinsic peak efficiency (  ip ): - 6) The photo-fraction ( P ): - 7) The Single Escape Peak Efficiency (  se ): - 8) Double Escape Peak Efficiency (  De ):-

Comparisons

Variation of intrinsic peak efficiency for disc source S = cm with 8  4  NaI cylindrical detector at h =15 cm with energy Pst: present work ref (11): Monte Carlo. ref (84): Monte Carlo.

Variation of total efficiency for spherical source with 2  2  NaI cylindrical detector at h = 5 cm with energy Pst: present work ref (76): Monte Carlo.

Variation of relative peak efficiency for block source A=2.27cm, B=0.755 cm and height H = 1.18 cm with 108 cm 3 Ge cylindrical detector at h = cm with energy Pst: present work ref (43): empirical

Variation of peak efficiency for annular source S 1 =2.95 cm, S 2 = cm and height H = 3 cm with cm 3 Ge cylindrical detector at h = 5 cm with energy Pst: present work ref (72): Monte Carlo

﴿ وما أوتيتم من العلم إلا قليلاً ﴾ بسم الله الرحمن الرحيم صدق الله العظيم