Maxwell-Boltzmann distribution.

[Nucengable]

Any one has some links, papers... anything describes the maxwell-boltzmann distribution that characterize neutrons in thermal equilibrium with the reactor core material at specific temperature...?
I want to get a crude estimation of energy-dependence neutrons flux for energies below 1 eV.

 

[Astronuc]

Neutrons slow down in the water (in an LWR) which in a PWR has an inlet temperature of about 275 to 293°C, and an exit temperature of about 300 to 327°C (up to 330°C in the hot channel). In a BWR, the inlet is about 274°C and the exit temperature is at saturation of the core pressure, so the temperature is about 274 to 276°C. BWRs can use spectral shift in which flow is reduced to increase voiding, and that leads to under-moderation which hardens the spectrum which allows for resonance capture in U-238.

The fuel is hotter, typically about 400°C on the pellet periphery, and with a centerline temperature of ~900 to 1400°C depending on the linear power. The average fuel temperature is in between ~700 to 800°C.

The moderator to fuel volume is about 1:1 give or take.

 

[wizwom]

http://tannerm.com/maxwell_boltzmann.htm
As Astronuc notes, the temperatures vary quite a bit - [STRIKE]fuel pellets in a working reactor reach close to the melting point of UO₂ at the center of the pellets (by design)[/STRIKE], and the coolant enters at 275°C (548 K) and exits at 319°C (592 K) in an ACR (for example), the moderator is maintained much cooler.
Furthermore, the neutrons are born at very high speeds - typically ~2 MeV; a significant portion of the neutrons will be fast.
http://www.neimagazine.com/journals/Power/NEI/September_2004/attachments/NEISept04p26-35.pdf is a fuel bundle description for various reactors; choose the data for your type and run the numbers.

But, if you were to assume a homogenous reactor at the mean temperature, you would have an order of magnitude estimate. A Westinghouse bundle, for instance, is 214mmx214mm, and has 264 8.19mm dia fuel rods; if it was fully loaded, it would be 30% fuel - but the flow channel is only 60%, the other 10% is the gap and wall. Call it .3 * 1000K, .6 * 570K, .1 * 620K so mean temperature is ~700K.