Relativity and Electron Deep Orbits of the Hydrogen Atom

This work continues our previous works on electron deep orbits of the hydrogen atom. An introduction shows the importance of the deep orbits of hydrogen (H or D) for research in the LENR domain, and gives some general considerations on the Electron Deep Orbits (EDOs). In a first part we quickly recall the known criticism against the EDO and how we face it. In particular, a solution to fix all problems is to consider a modified Coulomb potential with finite value inside the nucleus. For this reason, we deeply analyzed the specific work of Maly and Va’vra on deep orbits as solutions of the Dirac equation, with such a modified Coulomb potential without singular point. Then, by using a more complete ansatz, we made numerous computations on the wavefunctions of these EDOs, allowing to confirm the approximate size of the mean radii of orbits and to find further properties. Moreover, we observed that the essential element for obtaining deep orbits solutions is special relativity. At a first glance, this fact results from an obvious algebraic property of the expression of energy levels obtained by the relativistic equations. Now, a comparative analysis of the relativistic and of the non-relativistic Schrodinger equation allows us to affirm that Special Relativity leads to the existence of EDOs because of the non-linear form of the relativistic expression for the total energy, which implies a relativistic non-linear correction to the Coulomb potential