Theory of Dopler Broadening

Photon emmision along direction of fission fragment velocit

= amount of energy the gamma ray was shifted by

where [math]E_{photon}[/math] is the Doppler-shifted [math]\gamma[/math]-ray energy which was measured

[math]cos\theta_{photon1}[/math]=-[math]cos\theta_{1}[/math] for an excited fragment in det-1
[math]cos\theta_{photon2}[/math]=-[math]cos\theta_{2}[/math] for an excited fragment in det-2

[math]\theta_i[/math] is the polar emission angle of excited fragment and [math]\beta_i[/math] the fragment velocity

[math]\beta_i[/math]=0.04634

Our Calculations

For example for energy E=2617 keV and the fragment velocity v=[math]10^9[/math] cm/s(speed of light c=3x[math]10^{10}[/math] cm/s, [math]\beta[/math]=0.033, [math]\sqrt{1-\beta^2}[/math]=0.999455352)
We obtained the following results for different angles between the direction of the fission fragment propagation and the direction of the gamma emission

(i) [math]\theta[/math]=[math]0^0[/math]

[math]E_{shift}[/math]=2532.02 keV

(ii) [math]\theta[/math]=[math]90^0[/math]

[math]E_{shift}[/math]=2618.43 keV

(iii) [math]\theta[/math]=[math]180^0[/math]

[math]E_{shift}[/math]=2704.83 keV

FWHM(for energy 2617 keV)=2.5 keV(experimental data)

Energy difference [math]E_{shift180^0}[/math]-[math]E_{shift90^0}[/math]=172.8 keV. This result shows us that we do not have Doppler Shift.