Coulomb photoproduction ofπ 0 at high energy andπ 0 lifetime

Abstract

A discussion is presented of the possibility of determining the lifetime of theπ0 using the photoproduction ofπ0 in a Coulomb field as suggested by Primakoff. It is first shown how the competition with the coherent nuclear production makes it necessary to use a rather high photon energy. Even at 1 GeV, however, the Coulomb photoproduction dominates over the coherent nuclear one only in a very narrow cone around the forward direction; this cone has an angle of ∼3° forτ=5·10−17 s and only 2° forτ=5·10−16 s. Assuming that the difficult technical problems connected with these small angles may be solved, it is still necessary to prove that, at these small angles the incoherent production is not dominant. Indeed, though the incoherent production is certainly smaller than the coherent nuclear one by a factor ofA (=mass number), the incoherent cross section does not have the factor sin2θ which affects both the Coulomb and the nuclear coherent cross sections. A calculation of the incoherent photoproduction ofπ0 at small angles is therefore made using a multipole expansion and sum rules. It is shown that, for lead, the incoherent cross section at small angles is at most of the same order of magnitude of the nuclear coherent one so that it does not dominate the picture. For light nuclei the competition between incoherent and coherent nuclear production at small angles is more unfavourable and depends rather critically on the properties of the individual nucleus chosen. It is concluded that heavy nuclei are the most suited for this experiment and that, at 1 GeV, only lifetimes shorter than some units times 10−16 may possibly be measured by this method.