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it has been theoretically asserted@xcite , for surfaces of fully loaded metallic hydrides saturated with protons , that the collective electron and proton surface plasma modes give rise to the production of ultra - low momentum neutrons .
the reaction proceeds in accordance with the weak interaction model , @xmath0 wherein @xmath1 is an electron , @xmath2 is a `` dressed '' or heavy electron localized near the metal hydride surface , @xmath3 is a proton , @xmath4 is a neutron and @xmath5 is an electron neutrino .
the resulting hydride surface product ultra - low momentum neutrons have an extraordinarily high absorption cross section .
these neutrons in turn yield successive nuclear transmutations into higher and higher values of the atomic mass number @xmath6 . at appropriate values of @xmath6 , a resulting unstable nucleus may beta decay so that the values of the nuclear charge number @xmath7 then also rises . from such energy nuclear reaction kinetics ,
most of the periodic table of chemical elements may be produced , at least to some extent .
such nuclear transmutations do not require the high coulomb energy barrier penetration implicit in low energy fusion models .
it has been previously reported@xcite , for experimental electrolytic chemical cells employing metallic hydride electrodes , that a variety of nuclear transmutations have indeed been observed and that the resulting abundances of various nuclei have been reliably measured .
our purpose is to describe the experimental abundances of nuclear transmutations in strongly driven electro - chemical cells in terms of theoretical ultra - low momentum neutron absorption cross sections .    in sec.[potential ] , a simple neutron optical potential model for a spherical well is reviewed and the complex scattering lengths for describing the ultra - low momentum neutron absorption cross sections are derived@xcite . in sec.[transmutation ] , we discuss the experimental distribution in atomic mass number @xmath6 of the low energy nuclear reaction products measured in laboratory chemical cells@xcite . very remarkably , the product yield in a chemical cell is in some ways qualitatively similar to nuclear abundances found in our local solar system and galaxy@xcite . the local maxima and minima in these abundances are strongly correlated to the local maxima and minima in the ultra - low momentum neutron absorption cross sections .
this strong similarity serves as an indicator of the potential importance of ultra - low energy neutrons in nuclear reaction kinetics as briefly discussed in the concluding sec.[conc ] .
let us consider the following _ optical potential model _ for the effective ( added to a nucleus ) neutron amplitude @xmath8 .
the complex potential probed by the neutron has the form of a spherical well .
the well radius for a given atomic mass number @xmath6 is modeled by @xmath9 in detail , we assume a complex spherical step potential well @xmath10 from the scrdinger equation for the neutron amplitude @xmath11 one finds the scattering amplitude @xmath12 , @xmath13 and thereby the total neutron cross section @xmath14 in the ultra - low momentum limit , one may compute the neutron scattering strength @xmath15 the exact analytic form of the limiting eq.([potential6 ] ) is given by @xmath16 employing this optical potential model with @xmath17 , the total neutron cross section in the long wavelength limit may be analytically computed , @xmath18 as plotted in fig.[fig1 ] .
the peaks in the neutron cross section correspond to comfortably fitting the neutron wave within the spherical model optical potential wells of the nuclei .
the well radius @xmath19 varies with @xmath20 in accordance with eq.([potential1 ] ) .
while the model solved above refers the absorption of one neutron by one spherical nucleus , when the model is applied an ultra - low momentum neutron in a condensed matter electrode of a chemical cell , the very long neutron wave length spans many nuclei .
this gives rise to collective quantum coherent effects in the neutron - nuclei interaction .
the following experimental nuclear transmutations have been previously reported using light water solutions of one molar @xmath21 in electrolytic cells .
small plastic micro - spheres were coated with thin films of nickel which were then employed to construct electrodes .
the granular thin film structure of the electrodes allowed for large effective surface areas for the nickel hydride .
if there exists sufficiently large flux of protons moving through the nickel and if the surface of the nickel hydride film is saturated with hydrogen atoms and thereby protons , then nuclear transmutations could be measured to take place with a yield that is plotted as functions of @xmath6 .
the magnitude of the transmuted nuclear yields varies from one experimental run to to another .
the variations will depend on the isotopic composition of the metallic hydride cathode and anode , various ions found in solution and the nano - scale uniformity of the electrode fabrication processes .
however , the distribution of the yields versus atomic number appear to be understandable in terms of the total cross sections for neutron absorption in the ultra - low momentum limit , i.e. in terms of the above calculated neutron scattering strength .    in fig.[fig2 ] , we plot the reported transmutation yield versus atomic mass number for a moderately productive run@xcite employing a nickel cathode and compare the observed shape of the yield function and the shape of the ultra - low momentum neutron scattering strength . in fig.[fig3 ]
we plot the reported transmutation yield versus atomic mass number for a very productive run@xcite employing a nickel cathode and again compare the observed shape of the yield function and the shape of the ultra - low momentum neutron scattering strength .
similar experimental results@xcite@xcite@xcite@xcite have been found employing titanium hydride , palladium hydride , and layered pd - ni metallic hydride electrodes . in all such experimental runs ,
the agreement between the multi - peak transmutation yields and the neutron scattering strength is quite satisfactory .
let us conclude with some comments on the nature of the peaks in the theoretical neutron scattering strengths shown in fig.[fig1 ] . in varying the atomic mass number @xmath6 , we are in reality varying the radius @xmath22 of the optical potential well . when the neutron wavelength within the well reaches resonance with the radius of the well@xcite a peak appears in the scattering strength . if we associate resonant couplings with the ability of the neutron to be virtually trapped in a region neighboring the nucleus , then for intervals of atomic mass numbers about and under the resonant peaks we would expect to obtain neutron halo nuclei@xcite@xcite .
the spherical optical potential well@xcite predicts the halo nuclei stability valleys@xcite and thus the peaks in observed nuclear transmutation abundances .
finally , the neutrons yielding the abundances in our local solar system and galaxy have often been previously assumed to arise entirely from stellar nucleosynthetic processes and supernova explosions .
however , such assumptions may presently be regarded as suspect@xcite@xcite .
it appears entirely possible that ultra - low momentum neutron absorption may have an important role to play in the nuclear abundances not only in chemical cells but also in our local solar system and galaxy .
g. h. miley , g. narne , m. j. williams , j. a. patterson , j. nix , d. cravens , h. hora , `` quantitative observation of transmutation products occurring in thin - film coated microspheres during electrolysis '' , iccf-6 - _ progress in new hydrogen energy _ , m. okamoto editor , hokkaido , japan , ( 1997 ) .
low energy nuclear transmutations have been reported in experimental chemical electrolytic cells employing metallic hydride electrodes . assuming that the nuclear transmutations are induced by ultra - low momentum neutron absorption , the expected chemical cell nuclear abundances 
 are discussed on the basis of a neutron optical potential model . 
 the theoretical results are in satisfactory agreement with available experimental chemical cell data 
 . some implications of these laboratory nuclear transmutations for r- and s - process models of the neutron induced solar system and galactic nuclear abundance are briefly explored .