A Study of $\tau^-$ and $\mu^-$ in the Field of Nuclei Using Neural Network Techniques

The rate of a heavy lepton (muon or tau) capture by nuclei as well as the heavy lepton to electron conversion rate can be calculated when the heavy lepton wavefunction is known. Analytical calculation of the wavefunction of any of these leptons around any nucleus is not feasible owning to their small Bohr radii, on the one hand, and to the finite nuclear extend on the other. A new numerical calculation algorithm is proposed hereby, which makes use of the concept of neural networks. The main advantage of this new technique is that the wave function is produced analytically as a sum of sigmoid functions.