Difference between revisions of "Anisotropic n's vs. isotropic ones"

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==Motivation: there are a lot of source of isotropic neutrons===
 
==Motivation: there are a lot of source of isotropic neutrons===
  
#Winhold and Halpern, Phys.Rev. 103 4, 990 (1956).
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1. Winhold and Halpern, Phys.Rev. 103 4, 990 (1956).
  
:'''The observation were consistent with the assumption that'''
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:The observation were consistent with the assumption that
:'''anisotropic fission is due solely to photons with-in about'''
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:anisotropic fission is due solely to photons with-in about
:'''3 MeV of the fission threshold".'''
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:3 MeV of the fission threshold".
  
  
:'''The photons in the giant resonance region were found'''
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:The photons in the giant resonance region were found
:'''to produce essentially isotropic fission'''
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:to produce essentially isotropic fission
  
  
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# A lot of other papers.
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2. A lot of other papers.
  
# Isotropic neutrons from (<math>\gamma</math>,n) channel and (<math>\gamma</math>,2n) channel
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3. Isotropic neutrons from (<math>\gamma</math>,n) channel and (<math>\gamma</math>,2n) channel
  
 
==Anisotropic n's vs. isotropic ones==
 
==Anisotropic n's vs. isotropic ones==

Revision as of 20:51, 26 June 2011

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Motivation: there are a lot of source of isotropic neutrons=

1. Winhold and Halpern, Phys.Rev. 103 4, 990 (1956).

The observation were consistent with the assumption that
anisotropic fission is due solely to photons with-in about
3 MeV of the fission threshold".


The photons in the giant resonance region were found
to produce essentially isotropic fission


Winhold fig.4.png


2. A lot of other papers.

3. Isotropic neutrons from ([math]\gamma[/math],n) channel and ([math]\gamma[/math],2n) channel

Anisotropic n's vs. isotropic ones

Say, we have only anisotropic neutrons

[math]\Theta=90^o,\ \phi = 0^o:\ 100\ n's[/math]
[math]\Theta=90^o,\ \phi = 90^o:\ 125\ n's[/math]

So the calculated asymmetry would be:

[math]A = \frac{125}{100} = 1.25[/math]



Now, say, we have extra 200 isotropic neutrons

[math]\Theta=90^o,\ \phi = 0^o:\ 100\ n's[/math]
[math]\Theta=90^o,\ \phi = 90^o:\ 100\ n's[/math]

So the calculated asymmetry would be:

[math]A = \frac{225}{200} = 1.12[/math]


That really reduce the measured asymmetry. If isotropic neutron's are much more than anisotropic ones we would not be able probably to see any asymmetry. Need to count isotropic and anisotropic neutrons.


Source of anisotropic neutrons:

  • ([math]\gamma[/math],f) channel due to photons with-in about 3 MeV of the fission threshold

Source of isotropic neutrons:

  • ([math]\gamma[/math],f) channel due to photons out of 3 MeV of the fission threshold
  • ([math]\gamma[/math],n) channel.
  • ([math]\gamma[/math],2n) channel.


U Photo-fission Cross Section

U235.sigma.01.png

U235.sigmaflux.01.png


Let's count isotropic and anisotropic neutrons

Assume most conservative:

Source of anisotropic neutrons:

  • ([math]\gamma[/math],f). In reality the number of anisotropic neutrons will reduce with increasing the energy of gammas.

Source of isotropic neutrons:

  • ([math]\gamma[/math],n) channel
  • ([math]\gamma[/math],2n) channel


We can calculate the relative number of neutrons from different channels using formulas:

[math]N_f = \frac{\int \sigma_f \Phi(E_{\gamma}) dE_{\gamma}}{\int \sigma_{tot} \Phi(E_{\gamma}) dE_{\gamma}}[/math]
[math]N_n = \frac{\int \sigma_n \Phi(E_{\gamma}) dE_{\gamma}}{\int \sigma_{tot} \Phi(E_{\gamma}) dE_{\gamma}}[/math]
[math]N_{2n} = \frac{\int \sigma_{2n} \Phi(E_{\gamma}) dE_{\gamma}}{\int \sigma_{tot} \Phi(E_{\gamma}) dE_{\gamma}}[/math]


Using root to approximate the sigma by appropriate polynomials and using Maple to estimate integrals I found:

[math]N_f = a1\ %[/math]
[math]N_n = a2\ %[/math]
[math]N_{2n} = a3\ %[/math]