Nuclear Quantum Theory: Neutrons as Waves in Diffusion & Transport

[madhisoka]

Hi , in the classical course " nuclear reactor theory we treated neutrons as particles. can we treat neutrons as waves when it comes to diffusion or transport equation ? neutrons flux/ cross-sections ? I googled it and I didn't find enough info. Like there a lot of common terms between quantum mechanics theory and reactor theory.

 

[Astronuc]

Quantum mechanics is used on the level of individual interactions between neutrons and nuclei. In addition to experiment, QM is used to determine microscopic cross-sections, particularly for resonance scattering and absorption. In diffusion and transport theory, we use the macroscopic cross-sections (product of atomic density and microscopic cross-sections) and fluxes (and currents), so we don't explicitly use QM. The flux (or current) treat neutrons as a large population of which some fraction in each energy range will undergo some reaction, e.g., absorption or scattering. Scattering means that a fraction of one energy group will move into another energy group, usually downward for neutrons not in kinetic (thermal) equilibrium with their environment.

One sees discussions of QM in textbooks on nuclear physics, e.g., Kenneth Crane's Introductory Nuclear Physics, Chapter 11, Nuclear Reactions, and Chapter 12, Neutron Physics, or John Lamarsh's, Nuclear Reactor Theory, Chapter 2.

 

[madhisoka]

Quantum mechanics is used on the level of individual interactions between neutrons and nuclei. In addition to experiment, QM is used to determine microscopic cross-sections, particularly for resonance scattering and absorption. In diffusion and transport theory, we use the macroscopic cross-sections (product of atomic density and microscopic cross-sections) and fluxes (and currents), so we don't explicitly use QM. The flux (or current) treat neutrons as a large population of which some fraction in each energy range will undergo some reaction, e.g., absorption or scattering. Scattering means that a fraction of one energy group will move into another energy group, usually downward for neutrons not in kinetic (thermal) equilibrium with their environment.

One sees discussions of QM in textbooks on nuclear physics, e.g., Kenneth Crane's Introductory Nuclear Physics, Chapter 11, Nuclear Reactions, and Chapter 12, Neutron Physics, or John Lamarsh's, Nuclear Reactor Theory, Chapter 2.

thank you sir for the great info. in James Duderstadt book we treat neutrons as particle why don't we treat them as a wave ? does that make a difference ? is it worth the effort to do some kind of quantum mechanics neutrons research stuff " noticing that I am a nuclear engineering student "
https://www.amazon.com/Nuclear-Reactor-Analysis-James-Duderstadt/dp/0471223638

 

[Astronuc]

thank you sir for the great info. in James Duderstadt book we treat neutrons as particle why don't we treat them as a wave ? does that make a difference ? is it worth the effort to do some kind of quantum mechanics neutrons research stuff " noticing that I am a nuclear engineering student "

Is one referring to Duderstadt and Hamilton, Nuclear Reactor Analysis, or some other text?

D&H gives a superficial mention of QM in Chapter 2, however, it is not necessary for a nuclear engineer to know QM at the level at which microscopic cross-sections are developed, since that is already done. At most, one must know how to do lattice calculations and then how to use the results in core simulations codes.

At the points of specific neutron-nuclei interactions, that research is more the role of a nuclear physicist. I'm of the opinion that it is useful for a nuclear engineer to understand the physics.

 

[madhisoka]

Is one referring to Duderstadt and Hamilton, Nuclear Reactor Analysis, or some other text?

D&H gives a superficial mention of QM in Chapter 2, however, it is not necessary for a nuclear engineer to know QM at the level at which microscopic cross-sections are developed, since that is already done. At most, one must know how to do lattice calculations and then how to use the results in core simulations codes.

At the points of specific neutron-nuclei interactions, that research is more the role of a nuclear physicist. I'm of the opinion that it is useful for a nuclear engineer to understand the physics.

Everything is worth it when it comes to science but do I have to put some time and effort in such a field or its just waste of time ? and I will end up circling in a closed loop ?

 

[Astronuc]

Everything is worth it when it comes to science but do I have to put some time and effort in such a field or its just waste of time ? and I will end up circling in a closed loop ?

One should ask a professor who has research or development experience in neutron reaction cross-sections to see what opportunities there are to explore QM applied to cross-sections. Otherwise, it is nice to know, but not necessary for typical lattice physics or core design work. I can ask some folks at work if they see some opportunities.

 

[madhisoka]

One should ask a professor who has research or development experience in neutron reaction cross-sections to see what opportunities there are to explore QM applied to cross-sections. Otherwise, it is nice to know, but not necessary for typical lattice physics or core design work. I can ask some folks at work if they see some opportunities.

Thank you sir, yes please do because all my profs are either thermal hydraulics researchers or materials science ones

 

[pierce15]

Astronuc I'm curious... if you don't mind me asking are you working in private sector? I am wondering the extent to which you can pursue your own research/projects in the nuclear private sector.

 

[Astronuc]

Astronuc I'm curious... if you don't mind me asking are you working in private sector?

I work for a government-sponsored research organization, mainly in the areas of nuclear materials and analysis. I worked in private industry for 26+ years.

I am wondering the extent to which you can pursue your own research/projects in the nuclear private sector.

What kind of projects? Small projects, particularly those that can be realized in the short term, i.e., have immediate application are feasible. More complicated projects are more difficult to accomplish. Opportunities often depend on one's reputation and breadth of contacts.

 

[pierce15]

I work for a government-sponsored research organization, mainly in the areas of nuclear materials and analysis. I worked in private industry for 26+ years.

What kind of projects? Small projects, particularly those that can be realized in the short term, i.e., have immediate application are feasible. More complicated projects are more difficult to accomplish. Opportunities often depend on one's reputation and breadth of contacts.

Thanks for the reply, that's pretty useful information.

 

[Astronuc]

Thank you sir, yes please do because all my profs are either thermal hydraulics researchers or materials science ones

I talked with a colleague, and he mentioned that he doesn't encounter any QM in his work. However, he suggested that QM is addressed in cross-section development, possibly in the NJOY code. I believe QM treatment is used in the development of various cross section libraries that lattice codes use. Usually, those involved in core design only need to know how to set up the lattice code and core simulator, and that does not require knowledge of QM.

The folks who establish cross-section data/libraries may use QM. Those who develop the software to process cross-section data use some QM treatment.

I found the following reference, but not all information is available. One, or rather, one's university would have to purchase a rather expensive books or set of books on nuclear reactor theory.

At high energies, the wavelengths of neutrons are small, and it is reasonable to treat scattering as classical collisions between particles. At thermal energies, however, the wavelengths of neutrons approach the size of molecules and the sapceing of the crystalline lattices. Scattering becomes a quantum mechanical problem. The theory for this was worked out in the late 1950s and is described in detail by Williams (1966). This theory was reduced to practice for the US Evaluated Nuclear Data File (ENDF) in the 1960s, mainly by researchers at General Atomi (Koppel and Houston 1978). This theoretical basis remains largely valid today except for the improvements in scope and detail allowed by modern computing machines (MacFarlane 1994; Mattes and Keinert 2005).

Ref: https://books.google.com/books?id=pu9BWuf2gdkC&pg=191#v=onepage&q&f=false

Unfortunately, the book preview doesn't show the references.

 

[madhisoka]

d in cross-section development, possibly in the NJ

I talked with a colleague, and he mentioned that he doesn't encounter any QM in his work. However, he suggested that QM is addressed in cross-section development, possibly in the NJOY code. I believe QM treatment is used in the development of various cross section libraries that lattice codes use. Usually, those involved in core design only need to know how to set up the lattice code and core simulator, and that does not require knowledge of QM.

The folks who establish cross-section data/libraries may use QM. Those who develop the software to process cross-section data use some QM treatment.

I found the following reference, but not all information is available. One, or rather, one's university would have to purchase a rather expensive books or set of books on nuclear reactor theory.Ref: https://books.google.com/books?id=pu9BWuf2gdkC&pg=191#v=onepage&q&f=false

Unfortunately, the book preview doesn't show the references.

Thank you sir for the info I got 2 questions. First one according to what was mentioned in that book neutrons at thermal energies can become quantum mechanical problem we as nuclear engineers are mostly interested in thermal neutrons therefore understanding quantum mechanics behaviour may help a lot right ? , second question which is kida naive from your own legendary experience sir do you think that it's worth the time to get into such a research ?