Doppler Broadening

Spent fuel casket density:

Theory of Doppler Broadening

Photon emmision along direction of fission fragment velocity

$E_{shift} = E_{photon} \frac{1-\beta \cos(\theta_{photon}^i)}{\sqrt{1-\beta_i^2}}$ = amount of energy the gamma ray was shifted by

where $E_{photon}$ is the Doppler-shifted $\gamma$-ray energy which was measured

$cos\theta_{photon1}$=-$cos\theta_{1}$ for an excited fragment in det-1
$cos\theta_{photon2}$=-$cos\theta_{2}$ for an excited fragment in det-2

$\theta_i$ is the polar emission angle of excited fragment and $\beta_i$ the fragment velocity

$\beta_i$=0.04634$\sqrt{\frac{E_i[MeV]}{A_i[u]}}$

Our Calculations

For example for energy E=2617 keV and the fragment velocity v=$10^9$ cm/s(speed of light c=3x$10^{10}$ cm/s, $\beta$=0.033, $\sqrt{1-\beta^2}$=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) $\theta$=$0^0$

$E_{shift}$=2532.02 keV

(ii) $\theta$=$90^0$

$E_{shift}$=2618.43 keV

(iii) $\theta$=$180^0$

$E_{shift}$=2704.83 keV

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

Energy difference $E_{shift180^0}$-$E_{shift90^0}$=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