Zur Begründung der GAMOWschen Zerfallstheorie. I

This is the first of two papers dealing with the theory of decaying systems in the frame of nonrelativistic time‐dependent elastic scattering theory. We show that the essential feature of the cross section corresponding to the physical possibility of the formation of decaying systems is a maximum of the derivative of the phase shift. This arises because of the intimate connection of this derivative with the scattering delay time of the scattered particles. If this sort of behaviour of the scattering cross section meets with a slowly varying energy distribution of the incoming particles, compound systems are formed which eventually decay according to an exponential decay law. Whether the cross section has itself a maximum also in this energy region appears to be not at all important. The validity of an exponential decay law is established by a rather careful examination of the approximations necessary to obtain mathematically convenient expressions for the discussion of the wave functions describing the particles. The commensurability of such notions as unscattered particles and form elastically respectively compound elastically scattered particles is thoroughly investigated, too.