Latest revision as of 07:48, 7 December 2008

Spent fuel casket density:

Theory of Doppler Broadening

Photon emmision along direction of fission fragment velocity

= 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.

Photon emission off fission fragment velocity axis

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.

Photon Spectra from 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

@@ Line 1: / Line 1: @@
-=Theory of Dopler Broadening=
+Spent fuel casket density:
-== Photon emmision along direction of fission fragment velocit==
+=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
@@ Line 13: / Line 15: @@
 <math>\theta_i</math> is the polar emission angle of excited fragment and <math>\beta_i</math> the fragment velocity<br>
-<math>\beta_i</math>=0.04634<math>\sqrt{\frac{E_i[MeV]}{A_i[u]}}</math>
+<math>\beta_i</math>=0.04634<math>\sqrt{\frac{E_i[MeV]}{A_i[u]}}</math><br>
+'''Our Calculations'''<br>
+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)<br>
+We obtained  the following results for different angles between the direction of the fission fragment propagation and the direction of the gamma emission<br>
+(i) <math>\theta</math>=<math>0^0</math><br>
+<math>E_{shift}</math>=2532.02 keV<br>
+(ii) <math>\theta</math>=<math>90^0</math><br>
+<math>E_{shift}</math>=2618.43 keV<br>
+(iii) <math>\theta</math>=<math>180^0</math><br>
+<math>E_{shift}</math>=2704.83 keV<br>
+FWHM(for energy 2617 keV)=2.5 keV(experimental data)<br>
+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.<br>
 == Photon emission off fission fragment velocity axis==
 = Cf-252 Fission =
-==Photon Spectra from Cf-252 ==
+The table below from http://www-aix.gsi.de/~wolle/ identifies gamma energies (in keV) for several fission fragments of Cf-252.
+[[Image:Cf-252_FF_Egamma_Table.gif]][[Image:Cf-252_FF_Egamma_Table1.jpg]]
+[[Image:Cf-252_FF_Egamma_Table2.jpg]][[Image:Cf-252_FF_Egamma_Table3.jpg]]
-[[Image:photon_spectrum.jpg]]
+==Photon Spectra from 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]]<br>
 [[June 19,2007 Cf-252 measurements with HpGe & neutron sensitive scintillators in coincidence]]<br>
-[[June 19,2007 Cf-252 measurements of gamma-spectrum using HpGe ungated]]
+[[June 19,2007 Cf-252 measurements of gamma-spectrum using HpGe ungated]]<br>
+[[June 19, gamma-singles spectra of a Cf-252 source]]<br>
+[[June 25,2007 Cf-252 measurements of gamma-spectrum using HpGe ungated]]<br>
+[[June 25,2007 Cf-252 measurements of total gamma-spectrum using HpGe ungated]]<br>
+[[June 27,2007 Cf-252 measurements with HpGe detector and BC408]]<br>
+[[July 3,2007 Cf-252 without lead container measurements with HpGe & fast plastic scintillators in coincidence]]<br>
+[[July 6, 2007 Neutron Capture in lead]]<br>
+[[July 10, 2007 Division of gated to ungated spectra of Cf-252]]<br>
+[[July 11, 2007 Experimental setup]]<br>
+[[Results and Discussion]]<br>
+== Measurements at the IAC ==
+[[Image:HuntsIACgraphs.pdf]]<br>
+[[Image:promptg02_cf252_IAC.pdf]]
+=Details of Cf-252 Source=
+The manufacturers description of the source [[Image:CF-252-Description.pdf]]<br>
+Gamma and Neutron activity curves[[Image:CF-252-gamma-n-activitycurves.pdf]]

Difference between revisions of "Doppler Broadening"