nuclear engineering - What is the minimum amount of fissile mass required to acheive criticality?

Wikipedia gives the following definition for critical mass.

A critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction.

No mention is made of a neutron moderator in this definition. If critical mass is defined like this, then that should allow infinite moderator material to be used if doing so would lead to the minimum amount of fissile material.

My question: What is the universally minimum amount of fissile mass needed to achieve a critical configuration (allowing a neutron moderator and no restriction on the moderator) for something like Uranium-235 and what would its configuration be?

Uranium-235 has a bare sphere critical mass (BSCM) of around $52 kg$, which is the mass of a critical sphere containing only the fissile material where no neutrons are reflected back into the sphere after leaving the surface. Wikipedia has a good illustration of a bare sphere versus a sphere surrounded by a moderator.

Image: First item is a BSCM illustration, 2nd item is a critical sphere that uses less fissile mass than the BSCM due to the introduction of a neutron moderator blanket

This example illustrates how a critical configuration can be made with U-235 that uses less than the BSCM, or $52 kg$. It is possible, although unlikely, that the above sphere surrounded by a moderator could be the configuration that answers my question. Alternatives would include a homogenous mixture of the moderator and the fissile material, a mixture of the two that varies radially, or something I have not thought of.

The hard part is showing that the particular fissile material/moderator mix can not be improved by any small change. It would also be necessary to show that it can not be improved by adding more than 1 type of moderator (I suspect this could be done with a reasonably short argument).

Technical mumbo junbo

Everything I write here is just a suggestion, answer however you want to or can

Both the moderator and fissile material have a certain density. I would make the simplifying assumption that the density of a homogenous mixture of the fuel and moderator would be a linear combination of their specific volumes, with the understanding that this is not true in real life. Changing the mix changes the macroscopic cross section of both. It might help to note that the BSCM almost exactly determines the macroscopic cross section of the pure fissile material, one over the macroscopic cross section is the path length, which is on the same order of magnitude of the radius. Generally fast and thermal scattering from U-235 is small compared to the fission cross section.

I would use 2 neutron energy groups, and assume either diffusion or immediate absorption after scattering to thermal energies. In fact, I would just assume immediate absorption. At that point, all you would need is the scatter to absorption ratio and microscopic cross section at both thermal and fast energies for the moderator and fissile material, in addition to the densities of course. Even then some type of calculus of variations may be necessary (if you're looking for a radially varying mixture) in addition to the fact that it would be hard to describe the fast group without a fairly complicated form of neutron transport. The BSCM is comparatively simple since it has a constant number density of the fissile material and even that is actually pretty complicated.

Answer

I'm not an expert in critical mass calculation, but the minimum critical mass for U-235 must be less than (or equal to) 780 g as shown in "Mass Estimates of Very Small Reactor Cores Fueled by Uranium-235, U-233 and Cm-245" for a solution type core.