Doppler Broadening

Spent fuel casket density:

Theory of Doppler Broadening

Photon emmision along direction of fission fragment velocity

[math]E_{shift} = E_{photon} \frac{1-\beta \cos(\theta_{photon}^i)}{\sqrt{1-\beta_i^2}}[/math] = 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[math]\sqrt{\frac{E_i[MeV]}{A_i[u]}}[/math]

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.

Cf-252 Fission

The table below from http://www-aix.gsi.de/~wolle/ identifies gamma energies (in keV) for several fission fragments of Cf-252.

Measurements in the Beam test lab with HpGe and BC408

June 15,2007 Cf-252 measurements with HpGe & neutron sensitive scintillators in coincidence
June 19,2007 Cf-252 measurements with HpGe & neutron sensitive scintillators in coincidence
June 19,2007 Cf-252 measurements of gamma-spectrum using HpGe ungated
June 19, gamma-singles spectra of a Cf-252 source
June 25,2007 Cf-252 measurements of gamma-spectrum using HpGe ungated
June 25,2007 Cf-252 measurements of total gamma-spectrum using HpGe ungated
June 27,2007 Cf-252 measurements with HpGe detector and BC408
July 3,2007 Cf-252 without lead container measurements with HpGe & fast plastic scintillators in coincidence
July 6, 2007 Neutron Capture in lead
July 10, 2007 Division of gated to ungated spectra of Cf-252
July 11, 2007 Experimental setup

Results and Discussion

Measurements at the IAC

File:HuntsIACgraphs.pdf
File:Promptg02 cf252 IAC.pdf

Details of Cf-252 Source

The manufacturers description of the source File:CF-252-Description.pdf
Gamma and Neutron activity curvesFile:CF-252-gamma-n-activitycurves.pdf