Calculation of Ratios of μ and π Masses to the e Mass for a Simplified Model with a Square-Well Potential

In the present paper, the feasibility of constructing a model of elementary and particles based on the Poincaré model of the electron 1] is examined with allowance for schemes of particle decay. The muon and pion in stopped states are considered as spherical resonators for virtual neutrino quanta excited inside an elastic lepton shell; the number of these quanta is determined by the scheme of the corresponding particle decay. In the model, the muon differs from the electron by two additional quanta of the neutrino field. The e, , and masses are calculated with the help of a single parameter. The ratio of and e masses is about (6c/e ²)^2/3, and the ratio of ° and e masses is (3/2)^2/3. The calculated e, , and ° masses are in the 0.547:105.71:134.963 ratios, which is in good agreement with the available experimental data. The calculated electromagnetic radius of the charged pion (±) = 0.5f is close to that calculated from the experimental data. The neutrino mass _e is found to be m( _e ) 0.02 eV.