New Neutron State in Transition-Metal Hydrides and Cold Fusion Phenomenon
Hideo Kozima
cf-lab.kozima@pdx.edu
The
Cold fusion phenomenon (CFP) has been studied for more than 13 years without a
consistent explanation based on modern physics. Relying on theories to infer
the nature of neutron wave functions at the excited bound levels that are less
than 1 eV from zero, we have shown that CFP in transition metal hydrides and
deuterides is explained by the formation of neutron valence bands consisting of
excited neutron states in metal nuclei mediated by occluded hydrogen
(deuterium).[1]
Two
experimental data sets [2,3] show that it is very difficult to measure neutrons
with very low energies around several eV due to the large background, low
counting rates, uncertainty of the neutron detector efficiency and difficulty
in detecting low-energy neutrons (<500 keV). Fortunately, recent work on the
parity violation measurements with medium and heavy nuclides have shown the
existence of resonance levels down to 10 eV in absorption and transmission
spectra of neutrons.[4] From these experimental data sets, it is reasonable to
expect the presence of excited levels near zero with a long tail outside the
nucleus..
Using
two methods, we can determine possible wave functions of neutrons in excited
states at and below zero energy (the separation level): wave functions
suggested by neutron scattering cross sections [5] and wave packets of neutrons
in excited bound levels in a semi-classical model by Weisskopf.[6] The wave
function of the neutron with an energy E = –∣ε∣ is expressed as follows;
χ(r) = C×exp(–r√(2m∣ε∣)/ħ) (1)
where
C is a constant. This shows that a neutron level near zero has a slow
damping exponential function extended out into space outside the nucleus.
Therefore,
we may extrapolate the density of excited neutron levels determined by the
experiment [2] to the energy domain near zero. We assume the existence of
excited neutron levels (single particle or wave-packet type) around zero with
wave functions extending out of a nucleus into outside space as (1) These
decrease exponentially with a decay parameter κ = √(2m∣ε∣)/ħ. The value ofκ
with the neutron mass m = mn = 1.67×10–27 kg for ∣ε∣ below 100 eV is easily calculated and
givesκ= 7 (A –1), the
e-folding length r1/e = 0.14 A for ∣ε∣= 0.1 eV.
This
value shows that the wave function of the neutron at excited levels near zero
down to 0.1 eV extends far into space where proton or deuteron wave functions
of occluded hydrogen isotopes overlap with it in transition metal hydrides,
e.g. PdH. The lattice constant a = 3.89 A (Pd metal) and the static Pd-H
distance is 1.95 A (octahedral) and 1.68 A (tetrahedral sites) using a
for Pd.
When these neutrons with energies close
to zero have wave functions largely extended out beyond the nuclear domain,
they interact with occluded protons (or deuterons) through the nuclear force.
The wave functions of the occluded protons (and deuterons) are represented as
wave functions localized at interstitial sites [7] or Bloch functions of band
states [8]. In either case, the wave functions have the possibility to spread
out to lattice points where there are lattice nuclei with neutrons at excited
levels near zero described above.
As
a result, two neutrons in different adjacent lattice nuclei interact with each
other through their interactions with the same proton (or deuteron) of the occluded
hydrogen (or deuterium). This interaction results in neutron Bloch waves with a
band structure in its energy spectrum.
RESULTS
The
states of the neutron Bloch waves at band bottoms have almost the same energy
and slightly different wave vectors, in general. Therefore, there appears local
coherence [9] of neutron Bloch waves where they are reflected at a boundary
(and/or surface) region of the crystal. Then, if there are many neutrons in the
band excited from the ground states of lattice nuclei somehow, the density of
neutrons in the boundary layer becomes very large. This results in the
formation of stable neutron drops [10] composed of many neutrons and a few
protons similar to the Coulomb lattice in neutron star matter.[11]
The
scenario of the CFP will be described as follows. The background (ambient)
thermal neutrons enter into a neutron band above zero (neutron conduction band)
when they are trapped in a sample of the transition metal hydrides or
deuterides.[12] Their density in the boundary (surface) region of a crystal
becomes high due to the local coherence but may not be sufficient to form
neutron drops. The neutrons in the neutron conduction band, however, can react
with nuclei in the boundary region and the reactions can be called the trigger
reactions. The nuclear products of the trigger reactions induce
breeding reactions resulting in multiplication of the number of neutrons in the
conduction band and also excitation of neutrons in lattice nuclei. This causes
the formation of neutron valence bands. The neutron drops thus formed from
neutrons in the valence bands in boundary layers effectively induce CFP.
ACKNOWLEDGEMENT
The
author would like to express his thanks to John Dash of PSU for correcting the
English of this paper. He is also thankful to Motoe Suzuki and Tsuneo Nakagawa
of Japan Atomic Energy Research Institute for the information about the paper
in reference [4]. This work is supported by a grant from the New York
Community Trust and . by the Professional Development Fund for part-time
faculty of PSU.
[1]
H. Kozima, "Excited States of Nucleons in a Nucleus and Cold
Fusion Phenomenon in Transition‑Metal Hydrides and Deuterides" Proc, ICCF9 (May 19-24, 2002, Beijing, China) (to be published).
[2] K. Tsukada, S. Tanaka,
M. Maruyama, and Y. Tomita, “Energy Dependence of the Nuclear Level Density
below the Neutron Binding Energy” Nuclear Physics 78, 369 – 384 (1966)
[3]
K. Shibata, T. Nakagawa, H. Sugano and H. Kawasaki, "Curves and Tables of
Neutron Cross Sections in JENDL-3.2", JAERI-Data/Code 97-003, Japan
Atomic Energy Research Institute, 1997.
[4]
D.A. Smith, J.D. Boweman, B.E. Crawford, C.A. Grossmann, et al. "Parity
Violation in Neutron Resonances of Palladium" Phys. Rev.C65,
035503-1 – 9 (2002).
[5]
L.D. Landau and E.M. Lifshitz, Quantum Mechanics, Second Edition,
Pergamon Press, Oxford, 1965. Section 131.
[6]
V.F. Weisskopf, “Compound Nucleus and Nuclear Resonances” Helv. Phys. Acta
23, 187 – 200 (1950).
[7]
M.R. Chowdhury and D.K. Ross, “A Neutron Scattering Study of the Vibrational
Modes of Hydrogen in the β-Phases of Pd-H, Pd-10Ag-H and
Pd-20Ag-H” Solid State Comm. 13, 229 – 234 (1973).
[8]
R. Nieminen, “Hydrogen Atoms band Together” Nature 356, 289 – 291 (1992).
[9]
H. Kozima, K. Arai, M. Fujii, H. Kudoh, K. Yoshimoto and K. Kaki, "Nuclear
Reactions in Surface Layers of Deuterium-Loaded Solids", Fusion
Technology 36, 337 – 345 (1999).
[10]
H. Kozima, "Neutron Drop: Condensation of Neutrons in Metal Hydrides and
Deuterides", Fusion Technol. 37, 253 – 258 (2000).
[11] J.W.
Negele and D. Vautherin, "Neutron Star Matter at Sub-nuclear
Densities" Nuclear Physics A207, 298 – 320 (1973).
[12] H. Kozima, "Neutron Band in
Solids", J. Phys. Soc. Japan 67, 3310 – 3311 (1998)