A photon that has undergone Compton scattering has both changed its direction of

Question

A photon that has undergone Compton scattering has both changed its direction of flight and lost some energy. Pulse height analysis is used to reject these scattered photons during nuclear imaging. A pulse height window is symmetrically set around the photopeak of the pulse height spectrum. The full width of this window is usually expressed as a percentage of the photopeak energy. (a) Calculate the maximum angle through which a 140 keV photon can be scattered and still be accepted within a 20 percent offset window centered at 1.50 keV. (b) What are the maximum acceptable scattering angles for 140 keV and 364 keV photons if 20 percent windows centered at photopeak are used.

Explanation / Answer

Energy of the incident photon= 140 KeV = 140x 103x 1.6x 10-19 J= 2.24 x 10-14 J

Energy and wavelength are related as E=hc/

Incident wavelength 0= hc/E= 6.626 x 10-34 x 3x 108/2.24 x 10-14=8.874 x 10-12 m

Centre of acceptance window (Photopeak)= 150 KeV = 150x 103x 1.6x 10-19 J= 2.40 x 10-14 J

Range of 20% offset window= 150 KeV ± (150 x 0.2) = 120 KeV to 180 KeV = 1.92 x 10-14 J

to 2.88 x 10-14 J

Range of accepted wavelengths (min to max) = 6.902 x 10-12 m to 10.353 x 10-12 m= 0.06902 x 10-10 m to 0.10353 x 10-10

(Note that in Compton shift wavelength shift is only upward)

A) Maximum accepted wavelength max = 10.353 x 10-12 m

=Permissible shift in wavelength (max- 0) = 10.353 x 10-12 m - 8.874 x 10-12 m = 1.874 x 10-12 m (EQ -1)

Compton shift = (h/moc) x {1- cos ) (EQ -2)

mo- mass of electron = 9.1 x 10-31 kg; c= 3x 108 m/s

- scattering angle

(h/moc)= 2.43 x 10-12 m

Using value of obtained in (EQ -1) in (EQ -2)

= 76.77 (Angle of scattering for 140 KeV electrons)

B)

For 364 KeV electrons (Assuming Photopeak at 364 KeV)

Energy of the incident photon= 364 KeV = 364x 103x 1.6x 10-19 J= 5.824 x 10-14 J

Energy and wavelength are related as E=hc/

Incident wavelength 0= hc/E= 6.626 x 10-34 x 3x 108/5.824 x 10-14=3.413 x 10-12 m

Range of wavelength shift (20%)= 2.7304 x 10-12 m to 4.0956 x 10-12 m

Maximum accepted wavelength max = 4.0956 x 10-12 m

=Permissible shift in wavelength (max- 0) = 4.0956 x 10-12 m - 3.413 x 10-12 m = 0.682 x 10-12 m (EQ -3)

Compton shift = (h/moc) x {1- cos ) (EQ -4)

Using value of obtained in (EQ -3) in (EQ -4)

= 43.99

For 140 KeV electrons (Assuming Photopeak at 140 KeV)

Energy of the incident photon= 140 KeV = 140x 103x 1.6x 10-19 J= 2.24 x 10-14 J

Energy and wavelength are related as E=hc/

Incident wavelength 0= hc/E= 6.626 x 10-34 x 3x 108/5.824 x 10-14=8.874 x 10-12 m

Range of wavelength shift (20%)= 7.0992 x 10-12 m to 10.6488 x 10-12 m

Maximum accepted wavelength max = 10.6488 x 10-12 m

=Permissible shift in wavelength (max- 0) = 10.6488 x 10-12 m - 8.874 x 10-12 m = 1.7748 x 10-12 m (EQ -5)

Compton shift = (h/moc) x {1- cos ) (EQ -6)

Using value of obtained in (EQ -5) in (EQ -6)

= 74.36

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