Gamow factor relation to cross section in fusion

It may be difficult to separate "theory" from "application," but let''s see if this helps facilitate the discussion.
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Grigory_Heaton
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Gamow factor relation to cross section in fusion

Post by Grigory_Heaton » Sat Oct 22, 2016 8:43 pm

I've been trying to figure out how to put these two together for awhile now but haven't found any conclusive information online or in the FAQs here.

In an Astronomy class I came across the Gamow factor formula (https://en.wikipedia.org/wiki/Gamow_factor), which is used to calculate the probability of a particle tunneling past the electrostatic barrier given a certain energy, allowing nuclear fusion to occur. I know that it in proton-proton fusion, this probability is very inaccurate, since diprotons also have to beta decay into dueterium very quickly to avoid falling apart into protons again. However, this shouldn't be the case for D-D fusion, since the product is energetic He-4 that is stable at rest but decays into the final products in most cases. In addition to this, D-T fusion has a much higher cross section for fusion than D-D, even though the Gamow factor would only predict a slight change in fusion probability due to the reduced mass term changing.

So my question is: How useful is the Gamow factor in calculating fusion probabilities? Why are the actual cross sections much different in some cases? Is it due to another probability existing of the particles actually fusing after one particle tunnels past the electrostatic barrier, like in proton fusion?

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Richard Hull
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Re: Gamow factor relation to cross section in fusion

Post by Richard Hull » Sat Oct 22, 2016 9:32 pm

Proton-proton fusion is virtually impossible. This might occur only in stars to any net value.

D-D fusion is also difficult but really doable via tunneling as the reality of experimental results shows. Most importantly D-D fusion almost never results on 4He fusion!! It is the rarist of the rare fusion in D-D fusion. All D-D fusion is known to go to one of two equally probable fusions. D+D = T + P or D+D = 3He + n About once in every 20,000 D-D fusions D+ D = 4He + gamma is seen. This is what we observe on earth in man produced fusion reactions.

When one has quintillions of billions of tons of H or P in a gravitationally locked ball, (stars), and about 4-20 billion years to burn, what we see on the sun today is the result of a 4 billion year burn....A mix of heliological eons of what probabilities, be they high or low, can do. This maybe why we can't seem to do fusion.......We don't have the right stuff and or concepts.

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
Retired now...Doing only what I want and not what I should...every day is a saturday.

Grigory_Heaton
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Re: Gamow factor relation to cross section in fusion

Post by Grigory_Heaton » Sat Oct 22, 2016 10:05 pm

As far as I understand it, proton fusion is so difficult because the diproton has to decay into deuterium in the incredibly short timespan before the diproton falls apart into two protons again, which makes the Gamow factor inaccurate for calculating the fusion likelihood. But this doesn't happen with D-D fusion since once the highly energetic He-4 is formed, it always decays into one of the three D-D fusion products and never back into two deuterons. Because of this I lean towards thinking the Gamow factor would be accurate for calculating D-D/D-T fusion probabilities, but then that doesn't mesh with cross section data for D-T fusion. Because of that, I'm wondering if it doesn't work for D-D either.

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Richard Hull
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Re: Gamow factor relation to cross section in fusion

Post by Richard Hull » Sat Oct 22, 2016 10:30 pm

4He, once formed in a D-D fusion reaction, is one of the most stable of the gases! It can't then decay to the other three, spontaneously or it never was 4He! The three reactions I stated above are the only reactions we observe on earth. In the guts of a star it is all guesswork as no one has instrumented it.

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
Retired now...Doing only what I want and not what I should...every day is a saturday.

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