On Jan 24, 2011, at 12:35 PM, [email protected] wrote:
Hi,
For what it's worth, I have attached a PDF file of a calculation of
the Casimir
binding energy of two touching protons assuming a "radius" of 0.87 fm.
Perhaps interestingly the resultant value is not a bad match for
nuclear binding
energy / nucleon.
Regards,
Robin van Spaandonk
http://rvanspaa.freehostia.com/Project.html<casimir-nucleus.pdf>
As noted in a recent posting, I provided a similar computation for
the Casimir effect in my relativistic computation of the deflated
state. The conclusion was similar, that the binding energy due to
the Casimir force is can be significant. The Casimir force is even
more significant to nuclear binding energy when you consider bindings
between neutrons and neutrons, neutrons and protons. It is similarly
significant between hadrons or quarks and a high energy small
wavelength electron in the nucleus. This is one of the reasons I
stated on page 16 of my "Cold Fusion Nuclear Reactions" paper: "In
addition there should be a kind of hadron version of the van der
Waals force between the hadrons, due to location uncertainty combined
with inter-hadron Coulomb colocation of quarks exposed on the
surfaces of the interacting hadrons. This is a form of a Casimir
force that results in some degree of bonding or attraction between
any two hadrons, including two neutrons, even if for a very short
half-life in the case of the di-neutron."
The fact the di-neutron does not stay bound, despite the large
additional magnetic binding energy, is a sign that the Casimir force
alone is not sufficient to account for all nuclear binding energy.
The conventional formula you use may be inappropriate for nuclear
charge densities, in either the proton or neutron (the neutron has
varying and typically non-zero charge density by radius, as I'm sure
you know). There are also some corrections required for the
spherical geometry of the attractants, and wavefunction overlap when
they are at less than 2R separation. From a nuclear perspective
there is also the fact the outer shell of the nucleus in effect
shields the inner shell, i.e. the virtual photons of all but very
small wavelengths are excluded from the interior of the nucleus,
reducing the Casimir force binding effect in the interior. This may
provide some explanation for the limits to the size of the nucleus.
The magnetic spin coupling forces between hadrons is also very large,
and far more complicated within large nuclei. I visualize the
nucleus to be built up in a manner as if by tinker toys, with the
neutrons providing the essential links between protons to overcome
the electrostatic repulsion.
Best regards,
Horace Heffner
http://www.mtaonline.net/~hheffner/
