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Physics/Coulomb Barrier of two nuclei


QUESTION: What is the coulomb barrier between lithium-7 and helium-4? Can you show me how to calculate it? What is the minimum energy that the helium-4 nucleus must have in order to overcome this barrier?

ANSWER: Due to quantum tunneling, usually how these things happen in standard astrophyics, means that the Coulomb barrier (yes, it's capitalized since Coulomb is a proper last name) doesn't exactly limit the fusion rate.  The height of the barrier where you're truly above it is determined by the radii of the two nuclei (typically approximated by 1.2fm*A^1/3 where 1fm = 10^-15 m and A = the combined protons and neutron number in the nucleus) and the formula for Coulomb energy where that's determined by kq1q2/r.  k is almost exactly 9 billion in SI units, q1 and q2 are the charges of the colliding nuclei, and r is the combined radius as previously described (both radii added).  Simple enough.  :)

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QUESTION: Why are the results from calculation using the method above different from what I get from this online calculator?
Try using lithium-7 and helium-4 and you will notice that the results are different.

I don't know why they have a negative number for their Coulomb barrier at all, but not every online calculator is accurate.  I suggest you actually refer to the wiki entry on this, I've reviewed it and it's accurate.  There are many other resources than that with a quick google search, but at least the calculator got the Q-value correct.


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Dr. Stephen O. Nelson


I can answer most basic physics questions, physics questions about science fiction and everyday observations of physics, etc. I'm also usually good for science fair advice (I'm the regional science fair director). I do not answer homework problems. I will occasionally point out where a homework solution went wrong, though. I'm usually good at explaining odd observations that seem counterintuitive, energy science, nuclear physics, nuclear astrophysics, and alternative theories of physics are my specialties.


I was a physics professor at the University of Texas of the Permian Basin, research in nuclear technology and nuclear astrophysics. My travelling science show saw over 20,000 students of all ages. I taught physics, nuclear chemistry, radiation safety, vacuum technology, and answer tons of questions as I tour schools encouraging students to consider careers in science. I moved on to a non-academic job with more research just recently.

Ph. D. from Duke University in physics, research in nuclear astrophysics reactions, gamma-ray astronomy technology, and advanced nuclear reactors.

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