Photonic Decay Rates and Nuclear-Coulomb-Field Coherent Production Processes

The relationship between the $A\to B+\gamma$ photonic decay process and the "inverse" nuclear-Coulomb-field coherent production process $B+Z\to B+{\gamma }^{\prime }+Z\to A+Z$ [$Z\equiv \mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h}-Z \mathrm{nucleus}$, ${\gamma }^{\prime }\equiv \mathrm{exchanged}\mathrm{virtual}\mathrm{Coulomb}\mathrm{photon}$] is studied in some detail for arbitrary particles ($A, B$). A procedure is described for the determination of the rate of $A\to B+\gamma$ from measurement of the differential cross section for $A$-particle coherent production by a $B$ particle incident on a high-$Z$ nucleus. A numerical application of the formulas derived is worked out in the case $K^{-}+Z\to K^{*-}+Z$, and it is estimated that a $K^{-}$ energy in the range 3-15 BeV is required for a successful determination of the rate of $K^{*-}\to K^{-}+\gamma$.