Damping Effect in the Gamma-decay of a Neutral Pion

* If we further assume that .11"1/=0, ±1 for weak decay interactions, yo will decay through Y0-+ AO -+: nO, so· that YO. will not be observable since another observable decay mode YO-+p+n-(.d"l/=2) is highly forbidden. This assumption is an analogue of the selection rule .111= 0, ± 1 for electromagnetic interactions. found in the pseudoscalar meson theory with pseudoscalar coupling that the virtual nucleon pair formation is strongly damped by the inertia of the self-field of a nucleon. Consequently, at low energies, the s state meson scattering which occurs through the virtual nucleon pair formation is weakened and the p state scattering without the pair formation is relatively enhanced since the latter is almost undamped. This effect leads to a better qualitative undetstanding of the nature of pions in terms of the pseudOscalar meson theory with pseudoscalar coupling. Further it is also the case for the nuclear forces.2) Bearing in mind of these successes we shall estimate this effect on the gamma-decay of a neutral pion. The motivation of this work is for the foilowing reasons: (a) In pion reactions involving real nucleons such as pion-nucleon scattering and nuclear forces, the transition amplitudes are partially damped. On the other hand, the gamma-decay of a neutral pion will be totally damped since this process cannot take place without the virtual nucleon pair formation. The life-time of a neutral pion calculated by the lowest order perturbation theory is given by