Equation for neutrons in a nuclear reactor

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SUMMARY

The discussion centers on deriving the neutron diffusion equation as presented in Thorne and Blandford's "Modern Classical Physics," specifically from chapter 3, problem 21. The user seeks clarification on the correct formulation of the equation, including necessary terms and normalization factors. They express uncertainty about the completeness of their current equation and request guidance on accurately constructing it to reflect their specific conditions in a nuclear reactor context.

PREREQUISITES
  • Understanding of neutron diffusion theory
  • Familiarity with nuclear reactor physics
  • Knowledge of mathematical modeling techniques
  • Experience with Thorne and Blandford's "Modern Classical Physics"
NEXT STEPS
  • Study the derivation of the neutron diffusion equation in nuclear reactors
  • Research normalization techniques in mathematical physics
  • Explore boundary conditions relevant to neutron behavior in reactors
  • Examine case studies on neutron diffusion in various reactor types
USEFUL FOR

Students and professionals in nuclear engineering, physicists focusing on reactor design, and anyone involved in modeling neutron behavior in nuclear systems.

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Homework Statement
Neutron diffusion in nuclear reactor - deriving the equation of the slowing of the neutrons in momentum space and of their struggle to pass through the 238U resonance region without getting absorbed.
Relevant Equations
Boltzmann eq., Neutron transport eq., Neutron diffusion eq.
I am trying to solve a problem from Thorne and Blandford: Modern classical physics, chapter 3, problem 21: Neutron diffusion in nuclear reactor.
thorn_bland.JPG

I am struggling with how the equation, from which this should be calculated, should look like. I watched some videos where they did the derivation a such equation, however I don't know how to simplify it to fit my conditions. I think it should look roughly like this:
aaa.JPG

I'm not sure if there are supposed to be more terms or by what factors they should be multiplied, so is it somehow correct and I just need to add correct normalization, or am I completely wrong?
If someone could explain to me how to precisely create the equation from which I could get the desired relations, I would really appreciate it. Thanks!
 

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