Doppler Broadening

Spent fuel casket density:

Theory of Doppler Broadening

Photon emmision along direction of fission fragment velocity

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

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

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

[math]\displaystyle{ \beta_i }[/math]=0.04634[math]\displaystyle{ \sqrt{\frac{E_i[MeV]}{A_i[u]}} }[/math]

Our Calculations

For example for energy E=2617 keV and the fragment velocity v=[math]\displaystyle{ 10^9 }[/math] cm/s(speed of light c=3x[math]\displaystyle{ 10^{10} }[/math] cm/s, [math]\displaystyle{ \beta }[/math]=0.033, [math]\displaystyle{ \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]\displaystyle{ \theta }[/math]=[math]\displaystyle{ 0^0 }[/math]

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

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

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

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

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

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

Energy difference [math]\displaystyle{ E_{shift180^0} }[/math]-[math]\displaystyle{ 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