How do electrons impact the probability of fusion in a non-plasma fluid system?

[Aidan Davis]

Consider a system in which a non-plasma fluid (eg, gas, liquid, or supercritical fluid) consisting of a single isotope (for example, deuterium would be in the form of the D2 molecule) is struck with a small atom, stripped of all electrons. This atom also has a large amount of energy, enough to make fusion by tunneling significantly probable. The target would, of course, be neutral to the incoming positive charge at comparitively large distances. How would the electrons in the target molecule effect the probability of fusion? Would the Gamow-Sommerfeld factor apply fully here, or would the electrons inhibit fusion somehow? Or would they encourage it by allowing the fast positively charged atom to approach closer to the target nucleus without being repelled by coulomb forces?

 

[Aidan Davis]

I also need help please!

I have a guess but I'm no expert so here goes:
A nucleus involved in fusion must come within roughly one fermi of the other to fuse. The Gamow-Sommerfeld factor, derived in the context of fusion in the sun here:
http://www.astro.princeton.edu/~gk/A403/fusion.pdf ,gives the probability that, for two nuclei that are on a collision course with a certain total energy between them, fusion will occur due to quantum tunneling effects. The derivation assumes the energy level is low enough not to use the energy in other ways (eg, pair production).A modification to include the effect of electrons as they exist with the molecules in a non-plasma phase would treat the electrons as point charges at a set (but slightly varying) distance from the nucleus. In hydrogen, this is .25 Å. Consider a fast nucleus on a direct collision course with a target nucleus. At 1 Å, the coulomb force between two elementary charges is 23.077 nanoNewtons, varying by the inverse square law. Acting on a single particle! However, the repulsive force of the target nucleus cancels out this effect at long distances. Over 1 Å, this amount of force is provides just 14.4 eV, not compared to hundreds of KeV in the fast atom. So it seems it should be negligible, especially considering that beam-target fusion works fine in plasma targets containing electrons. But I can't find any data/studies/tests that confirm that this is a negligible effect.