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The Wayback Machine - https://web.archive.org/web/20060912013620/http://burro.cwru.edu/Academics/Astr221/StarPhys/coulomb.html
Overcoming the Coulomb Barrier
Remember the problem with
fusing hydrogen nuclei -- the coulomb barrier
Protons have positive charge. Like charges repel -- the
electromagnetic force.
We need to overcome this repulsion to have the
nuclei fuse.
How do we do this? Energetic
nuclei!How do we make energetic
nuclei?
The Maxwell-Boltzmann Distribution
Particles at a given temperature will have a distribution
of speeds (and therefore a distribution in energies):
This is a probability distribution. The
probability of a particle having a given energy E is
And, in this distribution, particles have a most
probable velocity and an average velocity:
So to overcome the Coulomb barrier, particles must
have sufficient (thermal) kinetic energy to exceed the Coulomb repulsion.
Let's see:
Whoops.
Well, things aren't that bad. There is a high energy tail
to the distribution. But this alone isn't enough. We need to look to quantum
mechanics.
Quantum Mechanical Tunneling about
as close as you can get to magic...
The Heisenberg Uncertainty Principle:It is not possible to know both
a particle's momentum and
position to unlimited accuracy. In
other words,
So a particle of a given (insufficient) energy just might
find itself inside the nucleus even though classical mechanics say it has
no business being there. Wow...
So combining the high energy tail of the M-B distribution
and the possibility of QM tunneling (which rises as energy rises), we get
the Gamov peak:
So particles with 3-10 keV of energy (which there are plenty
of in the Sun's core) can overcome the Coulomb barrier.
Voila! Nuclear
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