Why are fusion and fission reactions stochastic?

It may be difficult to separate "theory" from "application," but let''s see if this helps facilitate the discussion.
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RobertMendelsohn
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Why are fusion and fission reactions stochastic?

Post by RobertMendelsohn »

Does anyone know the physics of why most (all?) types of nuclear reactions are random in nature? More specifically, the cross sections are a statistical approach (rather than a deterministic) approach to modelling various nuclear processes, and the fusion (or fission) products are also described by probabilities (and distributions). Why is this?

It makes sense experimentally, because it is observed in this way, but why do probabilistic models model nuclear reactions well? Are there external factors that influence this? For instance, in looking at fission products, the distribution gets broader with increasing neutron energy; if an experiment had very carefully controlled variables (temperature, magnetic fields, spin polarization, monochromatic, etc.) would a deterministic pattern emerge?

What accounts for the probabilistic nature of nuclear processes?

Hoping to have an enlightening discussion of theory. Math and scientific paper references welcome.
Frank Sanns
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Re: Why are fusion and fission reactions stochastic?

Post by Frank Sanns »

The short answer is tunneling. Energy barriers, velocities, mass, time. Lots of variables and lots of statistical probabilities.
Achiever's madness; when enough is still not enough. ---FS
We have to stop looking at the world through our physical eyes. The universe is NOT what we see. It is the quantum world that is real. The rest is just an electron illusion. ---FS
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Liam David
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Re: Why are fusion and fission reactions stochastic?

Post by Liam David »

All physics at the nano scale is essentially probabilistic in nature. At larger scales and with more particles, that randomness gets smeared out into average values that are well-described by non-probabilistic models (ignoring statistical mechanics here).

A good place to start if you're into the math is Griffiths Quantum Mechanics, which is essentially the de-facto undergrad quantum textbook. For a simple model of tunneling that works as a first approximation for both fission and fusion, see chapter 8 on the WKB approximation.

The distribution of products is related to scattering theory, which is introduced in chapter 11.

Here's a pdf: https://www.fisica.net/mecanica-quantic ... hanics.pdf
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Richard Hull
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Re: Why are fusion and fission reactions stochastic?

Post by Richard Hull »

At least fission, once a single isotope of U235 fuel is in hand is flawlessly controllable with great ease. Why? It is like burning coal. The energy is stored in the nucleus to the point that merely bringing sub critical components close together, not touching in any way, using zero net energy will release megawatts of truly stored energy. Fission ash is what it is due to all the afore mention reasons, the high energy nuclear willow the wisp (quantum physics)

Having the ideal fusion fuels on hand by the metric ton means you only have a bulk storage problem, not an intrinsically stored energy situation. You need applied electrical energy from fission, coal, natural gas, hydro, solar or wind power like we use here, in tightly controlled conditions, and with as little as 400 watts you are doing fusion at a billion to one net loss, but you are doing fusion! The fuel resists with all its electrostatic might to not fuse and not produce or release energy at every instance. Again, Quantum physics and the role of the dice within that sub nuclear scale.

The good thing about fusion is you might get only two reaction ash products or even only one. The reason being you start with not many nucleons in the fuel and what comes out is very limited as you are at the first rungs of the elemental ladder.

Not so at the end of the periodic table where two massive nuclei have 470 nucleons to smash, split, mix and scatter. Quantum mechanics really has a field day here making a giant pot pie of radioactive debris that boggles the mind.

The idea of fine tuning either energy scheme with magnetics, spin controls or other draconian control efforts seems a bridge too far just to make "happy and healthy debris". However, for those that can experiment with the concept....."let the experiment be done"!

Richard Hull
Progress may have been a good thing once, but it just went on too long. - Yogi Berra
Fusion is the energy of the future....and it always will be
The more complex the idea put forward by the poor amateur, the more likely it will never see embodiment
RobertMendelsohn
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Re: Why are fusion and fission reactions stochastic?

Post by RobertMendelsohn »

Thank you all for your answers! I haven't read Griffiths in a few years, and admittedly my QM/QED is a bit weak.

Let me further clarify a question; we use probabilistic models to describe mortality (i.e. for life insurance or actuarial purposes) even though the individual events (deaths) are often extremely deterministic events (if we had all data (EKG etc.) available to us), but there are so many factors as well as so many events that the ensemble is described through statistical methods.

By analogy, is it the case that these nuclear processes are modeled as probabilistic events because they are thought to be intrinsically random processes, or because of a similar ensemble/too-many-factors reason that means that probabilistic models can fit the experimental data?

I'm sorry if this verges on meta-physics about the model vs. the reality of the process, but I'm really trying to rigorously grasp whether there are hidden/neglected variables that really do effect the cross section, reaction channels etc. Who has the most complete theoretical picture of these processes?

Thank you all for some stimulating ideas.
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Liam David
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Re: Why are fusion and fission reactions stochastic?

Post by Liam David »

Our most fundamental theories are quantum field theories (QFT), which are intrinsically stochastic. I haven't studied QFT, so to avoid putting my foot in my mouth, I'll backtrack to basic QM, which nonetheless encapsulates most of the fundamental ideas.

An ensemble of particles is described by a wavefunction (Psi). We don't know intrinsically what it is, but we know that the probability density of some observable (i.e. outcome of some measurement) is dependent on Psi Psi* = |PsiI^2. This "fact" is merely an assumption (proposed by Born) that has worked so far and has no deeper origin in our theories. Some physicists are uncomfortable with the intrinsically random nature of these models, leading to hidden variable theories (largely ruled out by the Bell inqeualities and associated experiments) or deterministic addons like Bohmian mechanics. It seems like the randomness is fundamental and not the result of unknowns and unknown-unknowns as we assume for life insurance purposes.

We can compute cross-sections for fusion theoretically using the standard Schrodinger equation, provided we have a model of the strong force potential at small radii (we often don't and assume a square well of some fudged depth that gives results matching experiment). Things get more complicated when we have to factor in angular momentum, spin, center-of-mass and center-of-charge differences, which can give rise to effects such as D-D anisotropy or the resonance peak in the p-B cross-section. These are factors that are often ignored to make the math easier, but the key is that we know we're ignoring them, unlike with the unknown-unknowns which it seems like you're most interested in.

The bottom line is that it seems likely that the randomness is intrinsic. Short of a more fundamental theory than QFT, we can only speculate.
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Richard Hull
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Re: Why are fusion and fission reactions stochastic?

Post by Richard Hull »

Great and thoughtful reply, Liam! The key is always bound not only in the understanding of the various areas in the physics and the math, but the history of when things were brought forth between 1900 and the late 1950s.

When I was in college the FET was a new thing, a weak thing with a hint at being a true voltage controlled device replacing the far more familiar vacuum tube. Transistors were strictly current controlled devices, not pretty. All solid state devices are the result of quantum physics. No need to dig deep there at the engineering level. Just the basics and acceptance of "holes" being current carriers need be absorbed.

My ilk learned tubes and transistors. I get together with fellow engineers of my age and we have endless amazement of what we have seen in advancements in electronics due to the application of an ever advancing quantum physics in the solid state. Countless quadrillions of atoms in a semiconductor (solid state) make quantum uncertainties merge into reliable entities.

Among the greatest of improvements I use now is the FET with an Rds-on of .028 ohm with an input impedance of pure voltage field control demanding nano-amps of current. I am amused that the thousands of FET cells all connected in parallel within its substrate have advanced only marginally since my college days. It is the monkeying with the silly-con that makes the little chip in the 50v, 80 amp FET so potent to rival the contact resistance and zero dissipation of a gold contact relay at the behest of a 50 nanoamp input current to start a 3 horse power motor. The limits remain voltage and frequency handling of such power devices due to the huge capacitance of those thousands of parallel connected FETs and arc over in such densities.

If there is a real world reliable application of QED it is the solid state biz! There are so many atoms that the roll of the quantum dice within make the "house" a winner 100% of the time!

Solid state fusion!!?? Any one ever load palladium or thorium with a D-T mix? I haven't heard of it. Deuterium? Yes. That is what started the much debated concept of CF. The instant anyone of some caliber and chops in academia or even the industrial research area mentions "let's try tritium", the operation gets zero traction and all thoughts of experiment end!

There are intermetallic hydrides known... Th7Ni3H28.

https://www.sciencedirect.com/science/a ... 8875900028



Richard Hull
Progress may have been a good thing once, but it just went on too long. - Yogi Berra
Fusion is the energy of the future....and it always will be
The more complex the idea put forward by the poor amateur, the more likely it will never see embodiment
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Dennis P Brown
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Re: Why are fusion and fission reactions stochastic?

Post by Dennis P Brown »

The experimental answer. The reason we use probabilistic mathematics is because it works. End of discussion.

Just joking - quantum is all in the math. So mathematically, the complex wave functions are used (these are wave functions that use 'i' (the negative square root of 1)in their arguments.) These functions best describe quantum systems behavior and after taking their complex conjugate's (that converts them into the actual measured values we see) these function act like probability functions.

The critical idea to understand is that there is no underlying mechanical process in any quantum system. This is not classical physics. Nature isn't hiding anything - this is just the way the universe works and complex wave functions give correct answers. There are NO hidden variables or processes - quantum is reality - attempts to make it into a classical system always fails. Understand the application of the math and the insights into the quantum world becomes far more clear.

I'll just add a few thoughts: the nucleus is a very difficult breast to understand using quantum mechanics. You have many charges concentrated within a very tiny area. Worse, the strong force involved also treats non-charged (or semi-noncharged) particles the same. No theory can account perfectly but many do give good answers. But this is very difficult physics and poorly understood due to the multibody problem and the three very different force carriers that cause so much to occur within the nucleus (strong (gluon 'leakage'), weak, electro-magnetic.)

When anyone cites 'deterministic' physics that is classical and will simply never work. That approach is profoundly misleading and guaranteed to lead one down a rabbit hole of useless ideas. Also, most nuclear reactions are not just probability - many have very good reasons they occur and are well understood. The issue is for 'natural' radioactive decay - this is probabilistic - but certainly the half-lives are not random. These often are understood and many can be predicted. But in no case can one can pick a specific atomic nucleus and say when that particular one will exactly decay.
Last edited by Dennis P Brown on Wed Feb 16, 2022 6:16 am, edited 2 times in total.
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Richard Hull
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Re: Why are fusion and fission reactions stochastic?

Post by Richard Hull »

I always love the fact that 100% of the uranium in our ore was made as stellar debris long before our solar nebula formed over 4.5 billion years ago.
Let us just for grins and googlers, say our earthly U was made 8.93 billion years ago when two neutron stars merged and exploded. A partial mass from this explosion accreted 4.5 billion years ago and half of all the U from the explosion that made up our solar nebula is now lead. The inner rocky planets are the holder of much of the uranium atoms, being closer to the sun just after its ignition burst wave threw all the lighter gases off at higher velocities to make the gas giants. (Mercury might just hold the bulk of the solar system's minable uranium!)

Anyway, another 4.5 billion years after earth's formation, the earth contains only 9 billion year old uranium and most of that original is minable lead. Still, if we refine U ore today, the pure Uranium product we grab is pure uranium, "fresh" uranium starting a new half life all over again. All pure uranium gathered any where at any time is "fresh" uranium, "new" Uranium even though all of its atoms were formed over 9 Billion years ago. Wow!

In short there is no old uranium It is all just a collection of uranium atoms that have not decayed. When refined to 99.9% pure, it will decay starting right now as if just made via those two neutron stars exploding.

This is what makes it all so fascinating about natural long period radioactivity. A totally random process. Yet all Uranium atoms are doomed! Tons of them that are here on earth are the survivors of two half lives, some will go on to live through 100 more half lives. (over half a trillion years)....Long before then, they will all be either scattered by our solar nova or swallowed by our dying sun having gobbled up the earth only a few billion years from today.

Example: I have a 1uCi source of Thallium 204 with a half life of 3.8 years. I bought it in 1981, 41 years ago. It still can produce a lowly 350 counts per minute over background! Some of those Tl 204 puppies are still alive in the kennel and each one is just as likely to decay as all there dead brethren were when first produced, starting today! They are all as fresh as a daisy right now. Within the next 3.8 years half will have died off, just as did the 2.22 million that died each minute when my source was measured as being 1uCi in activity when produced in 1981.

Food for thought indeed.

Richard Hull
Progress may have been a good thing once, but it just went on too long. - Yogi Berra
Fusion is the energy of the future....and it always will be
The more complex the idea put forward by the poor amateur, the more likely it will never see embodiment
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Re: Why are fusion and fission reactions stochastic?

Post by RobertMendelsohn »

Thank you all for very interesting and stimulating responses!
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