The existence of a small hydrogen state, in effect a sub-ground
state, is the basis for various theories of cold fusion, and for
theorizing electron screening as the means of overcoming the Coulomb
barrier in order to achieve cold fusion. Numerous cold fusion
researchers have hypothesized such small states, and thus recognized
the need for such small neutral states. However, without formation
of an actual neutron, the difficulty with some of the states proposed
is a lack of adequate binding energy to approach the nucleus. The
presence of actual neutrons in the lattice in sufficient quantities
to match excess heat observed would cause clearly visible neutron
activation of even very small amounts of common elements, and also
cause high energy signatures of nuclear reactions with lattice elements.
The deflation fusion theory (as defined here: http://
www.mtaonline.net/hheffner/DeflationFusion2.pdf) solves these
problems by noting that a brief attosecond sub-orbital state, if
repeated frequently enough, can provide a high probability of lattice
spacing distance simultaneous tunneling by the combined neutral
species, i.e. by the ground state energy bound electron and nucleus.
The Hamiltonian of the electron in the deflated state remains
unchanged until joint wavefunction collapse occurs with another
nucleus, fusion occurs, and the total charge of the combined nucleus
suddenly becomes highly positive, thus driving the electron
Hamiltonian negative by millions of electron volts, due to the
initially extremely small size of the collapsed wavefunction.
One problem with this theory is the fact the ground state orbital of
hydrogen does not appear to accommodate a close radius orbital.
However, such an orbital might be feasible when relativistic effects
are considered. The importance of a relativistic treatment of
orbitals to the feasibility of a sub-ground state hydrogen is shown in:
Jan Naudts,"On the hydrino state of the relativistic hydrogen atom",
Aug, 2005,
http://arxiv.org/abs/physics/0507193v2
Naudts summarizes: "This paper starts with the Klein-Gordon equation,
with minimal coupling to the non-quantised electromagnetic field. In
case of a Coulomb potential this equation is the obvious relativistic
generalisation of the Schr¨odinger equation of the non relativistic
hydrogen atom, if spin of the electron is neglected. It has two sets
of eigenfunctions, one of which introduces small relativistic
corrections to the non-relativistic solutions. The other set of
solutions contains one eigenstate which describes a highly
relativistic particle with a binding energy which is a large fraction
of the rest mass energy. This is the hydrino state."
"Even if Dirac’s equation constitutes the basic theory then it is
still not clear whether non-integrability at the position of the
nucleus is more than a mathematical inconvenience. Indeed, the
nucleus of the hydrogen atom is not a point but its charge is smeared
over a distance of about 10−15 m. The solutions of the Klein-Gordon
equation or of the Dirac equation with smeared-out Coulomb potential
are expected not to diverge at the origin. Hence the problem of
square integrability is not a physical problem. The equations cannot
be solved analytically in this case. But there is no reason why the
hydrino solution should disappear. The main effect of smearing out
the Coulomb potential, besides regularisation of the wavefunction at
the origin, will be a small decrease of the binding energy."
Naudts concludes with: "The motion of the nucleus and the spins of
electron and of nucleus have been neglected. The electromagnetic
field should be treated in second quantisation. These modifications
will add a lot of technicality but will probably add only minor
corrections to the present treatment. As long as these more
sophisticated calculations are not accomplished, there are no serious
arguments from quantum mechanical theory to reject the existence of
the hydrino state."
If it had occurred to him, Naudts might have considered the fact the
Coulomb force on the electron is from up quarks, and that the
electron even in a ground state, though additionally in a highly
relativistic portion of that high kinetic energy ground state, can
interact with an up quark at extreme kinetic energies and very close
proximities, without an extensive overlapping "fuzzing out" of
either the quark or the electron, e.g. see:
http://www.mtaonline.net/~hheffner/FusionUpQuark.pdf
If Naudts had considered the magnetic binding due to spin coupling of
the electron and nucleus at short range then he might have found an
even smaller partial orbital feasible, or at least a very small
momentary state.
The existence of an alternate eigenstate, a high kinetic energy
eigenstate, is an indication of the possibility of the partial co-
existence of that state with the ordinary ground state of the
electron, the possibility of a degenerate state. When sampling the
electron, there is a finite probability of finding it in that small
state close to the nucleus. Though the mathematical tools may not
exist for analytically solving for a realistic description of the
deflated state, including spin coupling, it is increasingly clear
what ingredients must be accommodated for a rigorous theoretical
description of the deflated hydrogen state. It appears such a state
might ultimately be rigorously defined if sufficient aspects are
considered, and relativistic orbitals and spin coupling are clearly
key aspects in that regard.
Best regards,
Horace Heffner
http://www.mtaonline.net/~hheffner/
