Lifetime of the Neutral Pion

As Primakoff has noted, the phenomenological coupling constant of the neutral pion with the electromagnetic field can be investigated by considering the photoproduction of neutral pions in an external Coulomb field. This is the inverse of the usual two-photon decay (one of the photons being provided by the external field). The relationship between the cross section and the free lifetime of the ${\pi }^0$ is derived. Although the total cross section is small, it is found at high energy that the differential cross section is strongly peaked near the forward direction. The peak cross section is proportional to the fourth power of the photon energy. It is this feature which makes possible an experimental determination of the lifetime by the photoproduction method to an accuracy of about ten percent. A minimum photon energy of one Gev is required to avoid uncertainties in the nuclear form factor. A higher photon energy would be necessary only if the ${\pi }^0$ mean life is greater than 5×${10}^{-17\mathrm{}}$ sec. The backgrounds to be expected from nuclear photoproduction are estimated and found to be sufficiently small. In particular, the interference between the coherent nuclear ${\pi }^0$ photoproduction and the Primakoff process is not excessive.