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Journal of Physical Studies 15(4), Article 4002 [15 pages] (2011)
DOI: https://doi.org/10.30970/jps.15.4002 CALCULATIONS OF PENETRABILITY OF BARRIERS IN THE PROTON DECAY PROBLEM: THE FULLY QUANTUM APPROACH AND INITIAL CONDITION OF DECAYS. P. Maydanyuk, S. V. Belchikov Institute for Nuclear Research, Kyiv, UA--03680, Ukraine |
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We develop a new fully quantum method for determining the widths of nuclear decay by proton emission where multiple internal reflections of the wave packet describing the tunneling process inside a proton-nucleus radial barrier are taken into account. The exact solutions for the amplitudes of wave function, penetrability $T$ and reflection $R$, are found for an $n$-step barrier (at arbitrary $n$) which approximates the realistic barrier. In contrast to the semiclassical approach and the two-potential approach we establish by this method an essential dependence of the penetrability on the starting point $R_{\rm min}$ in the internal well where the proton starts to move outside (for example, for $^{157}_{73}{\rm Ta}$ the penetrability is changed up to 200 times; the accuracy being $|T+R-1| < 1.5 \cdot 10^{-15}$). We impose a new condition: in the beginning of the proton decay the proton starts to move outside from the minimum of the well. Such a condition provides the minimal calculated half-life and gives stable basis for predictions. However, the half-lives calculated by such an approach turn out to be a little closer to experimental data in comparison with the semiclassical half-lives. The estimated influence of the external barrier region on the half-lives is up to 1.5 times.
PACS number(s): 03.65.Xp, 23.50.+z, 27.70.+q