The Decay Process: An Exactly Soluble Example and its Implications
There is agreement on the exponential decay law for unstable states in a certain range of times but not on what happens for very long or very short times. In particular for the latter a paradox appears from the contradictory results of two very straightforward calculations. To understand the matter better we consider s-states limited by a δ function radial potential of infinite height at a distance r = a. At time t = 0 we lower the height of the δ toa finite value b and obtain in an explicit analytic form the decay amplitude as a function of time in the full interval 0 ≤ t ≤ ∞. Our results support one of the calculations for very short times based on a schematic theory of nuclear reactions.
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