Gamow factor relation to cross section in fusion
Posted: Sat Oct 22, 2016 4:43 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?
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?