Pion Form Factor Contribution in Vacuum Polarization corrections for 1s energy level in different Pionic-Hydrogen Atoms

The 1s energy level vacuum polarization correctionsof pionic hydrogen atom induced by a potential including form factor are compared with those obtained by using pion point potential. Without form factor of nucleus and pion the correction increases very slowly for low Z atoms and increases fastly for higher Z. The finite size of the nucleus increases the correction with Z in case of exponential distribution, while in case of Gaussian distribution the increase is lower. For Fermi distribution there is a fast increase at low values of Z and faslty decreases with higher values of Z. The effect of form factor of pion on the correction is very clear for low Z nuclei and then becomes nearly constant for higher values Z.