Proton capture by Nickel nuclei obviously requires the overcoming of an electrostatic potential barrier which opposes the process. For Ni58(the more abundant Nickel isotope), the maximum potential energy Vmax occurs at a distance R between Ni and proton nuclei centers equal to the sum of their radii, that is R ≈ 6,1 fm. The Vmax value is given (in CGS units) by the expression Vmax=Zeˆ2/R , where Zeˆ2 is the product of the two nuclear charges: it results in Vmax=1,06*10ˆ-5erg=662 keV. The proton kinetic energy Ke can be easily estimated by the relation Ke=1/2 mvˆ2=3/2 kT, where k is Boltzmann’s constant and T is the temperature measured in Kelvin: also on assuming T=1000 K, Ke is only ≈0,9 eV. According to classical physics, a particle having an energy of about 1 eV cannot overcome such a very high potential barrier. Such an opportunity, in principle, is given by the quantum mechanical tunnel e¤ect: in this case, the incoming particle can penetrate into the nucleus by getting through the potential barrier. The tunneling probability of a single particle colliding with an atomic target has been calculated by Gamow . As shown by Evans , such a probability can be approximated as
where β=v/c is the ratio between the velocity v of the incoming particle and the velocity of light c: in our case, we obtain vˆ2=2Ke/m ≈ 2 * 10ˆ-9 cˆ2, and then β=v/c ≈ 4,47 *10ˆ-5 . Z and z are the charge values of Ni (Z = 28) and H (z = 1).
The tunneling probability becomes, as a consequence, P ≈ eˆ-28537 ≈ 3,5 * 10ˆ-12394, so small to make the capture of a single proton by a Nickel nucleus impossible. Nevertheless we have an experimental evidence of a large energy that can only arise from nuclear reactions between Nickel and Hydrogen, the only two elements existing in our apparatus. Furthermore, other attempts [11-15] have been made with Ni and H, obtaining analogous results, even if in a much smaller scale and without an easy and clear reproducibility.
In an attempt to explain the observed experimental effects, our attention has been attracted by a statement reported in  relative to a stellar gas where the electrons tend to cluster into spherical shells around nuclei, at distance rD known as Debye-Hückel radius. The .rst applications of the Debye-Hückel model  refer to electrolytic solutions for which it is possible to define a Debye length  with the following characteristic: if the distance between two charged ions is greater than rD , their electrostatic interactions are reduced by the presence of other ions attracted by the electric forces.
In our case, the proton-electron system might be shielded by the nuclear Coulomb potential, with the possibility of penetrating the Coulomb barrier.
Shielding effect would also explain the anomalous situation observed since 1938  in nuclear reactions, between accelerated protons and Ni63occurring at 3 MeV, below the expected 4,6 MeV threshold.
The effect of electron screening on low-energy fusion processes has been investigated by Assembaum et al : they report the increasing of the Coulomb barrier penetrability and calculate, for some reactions induced by protons (p+Li7 and p+B11) quantitative e¤ects, that look very relevant, though probably not sufficient to interpret our experimental results .
More recently, in a series of interesting papers [21-23], Raiola et al confirmed experimentally the significant increase of nuclear reactions cross sections in metals due to electron screening.