Mathematical Physics   Electron Capture: a More Complete Equation

Authors: Antonio Puccini

The Electron Capture(EC) is a peculiar phenomenon that unstable atoms can use to become more stable. During EC, an electron(e) in an atom's inner shell is drawn into the nucleus where it combines with a proton(P), forming a neutron(N) and a neutrino(): P + e  N + (1). Electrons are usually captured from the inner K layer, leaving 'holes' process or Auger’s es. Such a capture may also leave the nucleus in an excited state, causing it to release γ rays. This emission of highly energetic electro-magnetic radiation(EMR), generally originates the production of pairs of light particles: γ  e + e+(2), or:γ   + ῡ(3), where ῡ is an anti-neutrino. Yet, if this phenomenon of materialization of the EMR that accompanies the EC, manifesting in the production of lepton pairs(described in this case by the Eq.3), was represented in the equation describing the EC, we could better justify that  appeared ex abrupto in Eq.(1). Therefore, taking into account also the EMR(γ) emitted at the time of the EC, and inserting it in Eq.(1) on the side of the captured e, we have: P + e + γ  P + e + ῡe.+ e  N + e(4), that is:P + e + ῡe.+ e ↔ N + e(5). However, as the e mass is considered  2eV, Eq,(1) and (5) show a conspicuous mass gap problem, since according to Pauli and Fermi the  proposed to compensate for the mass gap of the N decay must have the same mass of e. Unless one wishes to hypothesize the existence of the neutral electron(e°). In this case, Eq.(5) should be rewritten as follows: P + e + ē° + e° ↔ N + e°(6).