Abstract
The proton emission from ground-state spherical nuclei is investigated exactly through the numerical solution of the time-dependent Schr\"odinger equation for initial single-proton quasistationary states. Contrary to common belief, it is shown that such calculations can be performed for any proton half-life ranging from ${10}^{\ensuremath{-}22}--20\mathrm{s},$ the longest proton lifetime observed at present. The important and careful choice of the initial metastable state is clarified. Applied to the calculation of the decay width of several ground-state spherical emitters, this method gives comparable results with the distorted wave-Born approximation and therefore justifies its use.
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