Difference between revisions of "Doppler Broadening"

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=Theory of Dopler Broadening=
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Spent fuel casket density: 
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== Photon emmision along direction of fission fragment velocit==
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<math>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</math>
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=Theory of Doppler Broadening=
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== Photon emmision along direction of fission fragment velocity==
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<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<br>
 
where <math>E_{photon}</math> is the Doppler-shifted <math>\gamma</math>-ray energy which was measured<br>
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<math>cos\theta_{photon}^i</math>=-<math>cos\theta_{i}</math> for an excited fragment in det-1= angle between momentum of fragment i and the emitted photon<br>
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<math>cos\theta_{photon1}</math>=-<math>cos\theta_{1}</math> for an excited fragment in det-1<br>
 
<math>cos\theta_{photon2}</math>=-<math>cos\theta_{2}</math> for an excited fragment in det-2<br>
 
<math>cos\theta_{photon2}</math>=-<math>cos\theta_{2}</math> for an excited fragment in det-2<br>
  
  
 
<math>\theta_i</math> is the polar emission angle of excited fragment and <math>\beta_i</math> the fragment velocity<br>
 
<math>\theta_i</math> is the polar emission angle of excited fragment and <math>\beta_i</math> the fragment velocity<br>
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<math>\beta_i</math>=0.04634<math>\sqrt{\frac{E_i[MeV]}{A_i[u]}}</math><br>
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'''Our Calculations'''<br>
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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>
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We obtained  the following results for different angles between the direction of the fission fragment propagation and the direction of the gamma emission<br>
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(i) <math>\theta</math>=<math>0^0</math><br>
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<math>E_{shift}</math>=2532.02 keV<br>
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(ii) <math>\theta</math>=<math>90^0</math><br>
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<math>E_{shift}</math>=2618.43 keV<br>
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(iii) <math>\theta</math>=<math>180^0</math><br>
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<math>E_{shift}</math>=2704.83 keV<br>
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FWHM(for energy 2617 keV)=2.5 keV(experimental data)<br>
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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==
 
== Photon emission off fission fragment velocity axis==
  
 
= Cf-252 Fission =
 
= 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.
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[[Image:Cf-252_FF_Egamma_Table.gif]][[Image:Cf-252_FF_Egamma_Table1.jpg]]
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[[Image:Cf-252_FF_Egamma_Table2.jpg]][[Image:Cf-252_FF_Egamma_Table3.jpg]]
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==Photon Spectra from Cf-252 ==
 
==Photon Spectra from Cf-252 ==
  
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[[June 15,2007 Cf-252 measurements with HpGe & neutron sensitive scintillators in coincidence]]<br>
 
[[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 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]]

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

[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.

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.

Cf-252 FF Egamma Table.gifCf-252 FF Egamma Table1.jpg Cf-252 FF Egamma Table2.jpgCf-252 FF Egamma Table3.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
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

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