Simulating Heavy Nuclei Reactions with Software: A Beginner's Guide

[jlefevre76]

Hey, is there software out there capable of simulating heavy nuclei? For instance, U235 or other fissile materials?

When I say simulating, I mean using all the appropriate equations (nuclear strong force fields represented, Schrodinger equations represented, etc). Mainly, I would want one that can simulate the nuclei being bombarded by photons.

Also, what's a good place to start in terms of reading material when it comes to understanding the behavior of nuclei? I have a basic textbook on nuclear physics, but I'm wondering mainly about the specific topic of the reaction of the nuclei to different wavelengths of light. I know photo-fission is a topic I've skimmed a paper on or two, but I'm wondering if there's ways of characterizing nuclei or modeling/simulating them using computers. I'm guessing if there is some kind of freeware available, it's not something I could just run on my laptop, but that's why I'm asking. I'm also asking because it's a little outside of my academic experience (though not outside of my basic understanding).

Anyway, let me know what's a good direction to start (preferably using resources on the internet if possible).

 

[Choppy]

Perhaps GEANT4 is what you're looking for?

 

[jlefevre76]

Hmmm, did I spell nuclei wrong? Whoops.

Anyway, to be honest, I'm not sure whether it would work. Can GEANT4 simulate the nucleons of a heavy nucleus (so, their 3D spatial probability functions) as they would appear at various average temperatures/energies, and then simulate the dynamics of the entire system as various EM waves of varying wavelengths pass through. Is that making sense yet, or am I not describing it well enough? As I mentioned, this is outside of my area, I'm a mechanical engineer by education, so if I'm not describing things correctly, feel free to correct me. Other than the Schrodinger equation (using electric fields for the protons and strong force fields for the protons and neutrons), I have to admit I'm not even sure how the governing equations change when you add an EM wave passing through. I would guess you would use the Maxwell equations for that part of it.

Anyway, anything out there that can reasonably simulate what I'm describing (if I've explained it well enough)?

 

[anorlunda]

A nucleus is a quantum system. You must use quantum mechanics to simulate it.

 

[eXorikos]

It is near impossible to simulate a nuclear like say U-235. That means simulating the interactions of 235 nucleons with one another. Have a look at the N-body systems to get a feel for how difficult this is. Imagine you would need to incorporate 3 forces as well.

A popular approach to do theoretical nuclear physics is the mean field approach, where a nucleon sees an average field of all the other nucleons. There are attempts at getting a working model of nuclei based on QCD, but this is this far only successful for light nuclei.

GEANT4 is a code that simulates the interactions of particles with matter, based on cross-sections that are measured. The code is developed by CERN as part of their accelerator program. It is one of the most accurate codes available.

 

[jlefevre76]

It is near impossible to simulate a nuclear like say U-235. That means simulating the interactions of 235 nucleons with one another. Have a look at the N-body systems to get a feel for how difficult this is. Imagine you would need to incorporate 3 forces as well.

That is sort of what I figured, 200+ nucleons would be hard to simulate, if I understand, it's a multibody problem + quantum dynamics problem, making it complex to simulate.

GEANT4 is a code that simulates the interactions of particles with matter, based on cross-sections that are measured. The code is developed by CERN as part of their accelerator program. It is one of the most accurate codes available.

So, as far as interactions of particles with matter, would it be appropriate for simulating photo-fission with fissile materials (I assume the material could be specified). I would also assume you could choose the particle types and energies, in this case, photons of various wavelengths.

Does it support multiple particles (perhaps of different types) simultaneously interacting with materials?

 

[Astronuc]

So, as far as interactions of particles with matter, would it be appropriate for simulating photo-fission with fissile materials (I assume the material could be specified). I would also assume you could choose the particle types and energies, in this case, photons of various wavelengths.

Does it support multiple particles (perhaps of different types) simultaneously interacting with materials?

The OP seemed to indicate an interest in simulation the behavior of the nucleons (protons and electrons) in a nucleus, rather than the interaction of radiation (gamma or neutrons) with a population of nuclei. Either way, one would have to do it statistically, since we cannot know the state of any given nucleus, and a gamma photon that could cause photo-fission could also result in pair production or photo-neutron emission.

The nucleus is a composite structure comprised of nucleons, which themselves are composite structures. Apparently there are QCD models within GEANT.
http://geant4.slac.stanford.edu/UPenn2011/HadPhys2.pdf
http://geant4.in2p3.fr/2013/resources/L12-HadronicPhysics.pdf

http://arxiv.org/pdf/1307.0996.pdf

http://www.fisica.uniud.it/~deangeli/test/g4aquila01.pdf

With regards to fission (I not sure if this answers the OP) - http://nuclear.llnl.gov/simulation/fission_v1.9.1/fission.pdf

Perhaps this thread needs to be moved to the HENP Physics forum.

Does it support multiple particles (perhaps of different types) simultaneously interacting with materials?

That would be improbable on a nuclear level, but certainly on the atomic level where one can have a broad spectrum of neutrons, charged particles and photons flying through a material.

In a nuclear reactor for example, solid materials have a density on the order of 10²⁸ to 10²⁹ atoms/m³, where neutrons, beta particles and gammas have particle fluxes on the order of 10¹⁷ to 10¹⁸ particles/m²-s.

 

[jlefevre76]

Perhaps this thread needs to be moved to the HENP Physics forum.

Thanks for the links, I will check them out when I have the time, especially the one related directly to fission. I have read papers that mention that photofission is possible, it's just not an efficient means of inducing fission (otherwise we'd already be using it). Sorry if this post should have gone elsewhere, this seemed the best place I knew of.

That would be improbable on a nuclear level, but certainly on the atomic level where one can have a broad spectrum of neutrons, charged particles and photons flying through a material.

In a nuclear reactor for example, solid materials have a density on the order of 10²⁸ to 10²⁹ atoms/m³, where neutrons, beta particles and gammas have particle fluxes on the order of 10¹⁷ to 10¹⁸ particles/m²-s.

Yeah, I remember from some of the papers I read just how particles are less likely to interact due to the vast spaces inbetween. I recall that material cross sections are measured in barns (not a typical cross sectional area), which if I remember, is basically a way of measuring how likely the particle will interact with the material. That's my basic understanding of it anyway. It would be great to simulate the full nucleus, but it doesn't sound like it's possible based on the high number of nucleons. I'm less interested in exploring particle interactions beyond the nucleons, and more interested in seeing which wavelengths or particle energies generally destabilize the nucleus of heavier elements. I know some research has been done in this area, but I just wanted to see some of the results for myself by running simulations.

Is there a way to find the resonant energies of a nucleus of a given composition, or would a simulation as I described be required? eXorikos mentioned field averaging and Astronuc mentioned "static" simulations, so I assume there exists some kind of software out there that is capable of doing what I described.

 

[Astronuc]

Yeah, I remember from some of the papers I read just how particles are less likely to interact due to the vast spaces in between. I recall that material cross sections are measured in barns (not a typical cross sectional area), which if I remember, is basically a way of measuring how likely the particle will interact with the material. That's my basic understanding of it anyway.

One's understanding is correct. One measures a cross-section which is related to the probability for given reaction producing a given outcome, e.g., neutron absorption leading to gamma emission (neutron capture), neutron emission (photoneutron), pair production, or fission (in transuranics).

I believe it is consequence of the limited gamma energies from fission and decay products, and the primary reaction in nuclear reactors is neutron- (thermal, epithermal or fast) induced fission. Gammas are produced with a spectrum of energies, generally below the threshold for photo-fission, but that's good because controlling nuclear reactors depends on having a fraction of neutrons having a long lifetime (seconds) between birth and the subsequent fission they cause. Also, the heavy elements probably wouldn't exist if photo-fission readily occurred, since they are born in supernovae where conditions are much more severe than we can reproduce on earth.

One must also appreciate that fission produces a lot of thermal energy, which we convert ultimately to mechanical and electrical energy, but it also means high temperatures in the core materials, and we generally have to maintain a narrow range of temperatures for a variety of technical reasons, such as structural integrity, control (requires dimensional stability and structural integrity), and retention of radioactive products.

It would be great to simulate the full nucleus, but it doesn't sound like it's possible based on the high number of nucleons. I'm less interested in exploring particle interactions beyond the nucleons, and more interested in seeing which wavelengths or particle energies generally destabilize the nucleus of heavier elements. I'm sure there's been research done on this, it would just be cool to simulate it for myself, and figure out how it works, etc.

One would use a Monte Carlo approach. Some nuclei undergo spontaneous fission, and it would be interesting to develop a model of why some radioisotopes undergo spontaneous fission, while others do not.

U-235 has a fairly long half-life, but shorter than the half-lives of Th-232 and U-238.

 

[jlefevre76]

Yeah, there are several papers on photofission:
https://scholar.google.com/scholar?hl=en&q=photofission&btnG=&as_sdt=1,45&as_sdtp=

I think they usually induce photofission by accelerating electrons at a target at high energies, then the target emits the photon onto the fissile target, that's my impression anyway. The gamma ray energies are quite high compared to what is emitted during standard fission processes, if I remember from crunching some of the numbers quite a while ago.

A Monte Carlo approach would not really solve this problem. Monte Carlo simulates the path of the neutrons as they are spontaneously emitted (then later absorbed by the fuel or its surroundings). I want to model EM waves passing over a nucleus of a given composition, and see how that affects the system dynamics of the nucleus. Specifically, the magnitude of the oscillations of the nucleus. I have heard an analogy between the nucleus of a heavy atom and a drop of water. Strong force would be like surface tension, holding the drop together, and the EM wave would represent a disturbance that might cause the droplet to split.

Anyway, I'm not sure that this can be modeled without using quantum dynamics, as the number of neutrons and protons directly determines the stability of the atom, meaning the "surface tension" changes depending on how well they mesh up together. One neutron too many or too few for a given element, and it destabilizes. Two neutrons too many and it might be better than one more, but worse than its most abundant isotope. So, I don't know if this can be realistically modeled given the high number of nucleons in a uranium atom. At least, the simulation couldn't be run on my computer at home, it would likely take years to complete. I'm thinking this is outside of my laptop's processing capability and I don't have access to software that would make it easy simulate.

 

[Astronuc]

A Monte Carlo approach would not really solve this problem. Monte Carlo simulates the path of the neutrons as they are spontaneously emitted (then later absorbed by the fuel or its surroundings). I want to model EM waves passing over a nucleus of a given composition, and see how that affects the system dynamics of the nucleus. Specifically, the magnitude of the oscillations of the nucleus. I have heard an analogy between the nucleus of a heavy atom and a drop of water. Strong force would be like surface tension, holding the drop together, and the EM wave would represent a disturbance that might cause the droplet to split.

One may be thinking of MCNP, a specific application of an MC method.

https://en.wikipedia.org/wiki/Monte_Carlo_method

http://pages.physics.cornell.edu/~s...ionalPhysics/LectureScans/CyrusMonteCarlo.pdf

 

[jlefevre76]

Yeah, I guess I'm thinking of a specific application of nuclear fission modeling that uses MC, I suppose that doesn't mean there isn't more than one.