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.

The effects of nucleus form factors on the electromagnetically produced heavy lepton pairs

In this paper, the effects of different nucleus form factors to the cross-sections of electromagnetically produced heavy lepton pairs such as muons and tauons from the ultra-relativistic heavy ion collisions have been calculated. Nucleus form factors play important roles in the calculation of the cross-sections, because the Compton wavelengths of muon and tauon are comparable to the radius of the colliding ions. Some realistic form factors in these calculations have been used and compared the results among them. It has been shown that nucleus form factors reduce the cross-section calculations for muon and tauon pair production very strongly especially at RHIC energies.