# Question about Resonance Cross Sections

Hi All,

I have a question about resonance cross sections. I have been doing the design work on the reactor I want to propose for testing at Oak Ridge National Labs, and have run into a problem. It is an accelerator driven reactor transmuting thorium into uranium, then burning the uranium by accelerating particles into the thorium plated with beryllium (which converts into uranium) target.

The question is what particles to accelerate and what energy to accelerate those particles to. I want to make an efficient source of neutrons, and since I am a civilian, cannot use the transuranics like Californium-252. So, I'm exploring using helium or hydrogen as the accelerated particles to transmute the target. Now from a first cut analysis, I know that the coloumb repulsion will be enormous, and that most of the time the helium and hydrogen nucleii will scatter instead of getting captured by the target. (Assuming the charged particle beam is collimated and at a uniform energy. This is another big problem, but that is for another post)

After doing the analysis, I found the design would not close unless the helium or hydrogen nucleii impact the target at an energy where the capture cross section is significantly higher than the scattering cross section. This is where resonance cross sections come in and my confusion. From all my searching, it seems resonance cross sections exist for ALL particles, not just neutrons, but I haven't been able to find any math to be able to actually calculate them. From what I read from Google, resonance cross sections occur at energies that exactly match the impact energies where the product binding energy exactly equals the incoming kinetic energy of the particle.

So here are my questions.

1) How does one go about calculating the resonance cross sections of charged particles impacting targets?
(Or am I mistaken and charged particles do not have resonance cross sections?)
2) Where can I go to find the needed equations or data to calculate the cross sections?

Thanks

## Answers and Replies

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QuantumPion
Gold Member
The wiki article here has a good description of the various methods of generating neutrons. I'm not an expert on the theoretics side, but it is my understanding that not all nuclides have resonances for every interaction. I don't know much about the physics of resonances of charged particle interactions, I think that is more into quantum physics territory rather than nuclear engineering, you could try cross posting there.

What is the overall goal of your design? It seems to be an extremely roundabout and inefficient way of producing fissile material which can be generated much more easily using conventional methods.

Astronuc
Staff Emeritus
I have a question about resonance cross sections. I have been doing the design work on the reactor I want to propose for testing at Oak Ridge National Labs, and have run into a problem. It is an accelerator driven reactor transmuting thorium into uranium, then burning the uranium by accelerating particles into the thorium plated with beryllium (which converts into uranium) target.
It looks like folks are already exploring ADTRs.

High-current, high-energy accelerators or cyclotrons are able produce neutrons from heavy elements by spallation. A number of research facilities exist which explore this phenomenon, and there are plans for much larger ones. In this process, a beam of high-energy protons (usually >500 MeV) is directed at a high-atomic number target (e.g. tungsten, tantalum, depleted uranium, thorium, zirconium, lead, lead-bismuth, mercury) and up to one neutron can be produced per 25 MeV of the incident proton beam. (These numbers compare with 200-210 MeV released by the fission of one uranium-235 or plutonium-239 atomb.) A 1000 MeV beam will create 20-30 spallation neutrons per proton.
Ref: http://www.world-nuclear.org/info/Current-and-Future-Generation/Accelerator-driven-Nuclear-Energy/

Cross sections from proton irradiation of thorium at 800 MeV
http://arxiv.org/ftp/arxiv/papers/1305/1305.6638.pdf

This might be of interest. http://ojs.ujf.cas.cz/~krasa/ZNTT/SpallationReactions-text.pdf

As for operation of accelerators and production of special nuclear material, there are legal requirements concerning licensing and approval from US NRC and DOE.