ACC Neutron Current Question: Calculating Net Neutron Flux and Direction

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SUMMARY

The discussion focuses on calculating net neutron flux and direction through a unit area of the xy plane using the equation J(Ω) = ∫n(Ω)vΩdΩ. The neutron density function is defined as n(Ω) = (1/4π)(1-cosθ), with the neutron speed specified as 2200 m/s. The main point of confusion revolves around the interpretation of Ω as a unit vector in spherical coordinates, particularly in the context of integrating over a solid angle. The participant ultimately resolves their query regarding the integration process.

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doublemint
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Hello!

J(Ω) = ∫n(Ω)vΩ

This is a neutron current question. It wants me to figure out the net neutron flux (and direction) through a unit area of the xy plane. It gives an equation for n(Ω) = (1/4π)(1-cosθ), but I am trying to figure out what Ω is inside the intergrand because that is where the direction comes from.
I know it is the unit vector, but what is it?? Since I am integrating over a solid angle, the vector should be in spherical coordinate notation? I feel like I should know this, but I am just confusing myself in the process of figuring it out.
Any help is appreciated!

n(Ω) - expected neutron density
v - neutron speed - 2200m/s
dΩ - solid angle

DM
 
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