arXiv 0906.47392009-06nucl-th

质子发射衰变问题中宽度的计算

Calculations of widths in the problem of decay by proton emission

Sergei P. Maydanyuk, Sergei V. Belchikov

备注：: 14 pages, 4 figures eps; content is changed

摘要：

本文发展了一种新的全量子方法，用于由质子发射确定核衰变的宽度，该方法考虑了描述质子-核径向势垒隧穿过程的波包的多次内反射。对于$n$阶势垒（任意$n$），得到了近似于实际势垒的波函数振幅、穿透率$T$和反射率$R$的精确解.与半经典方法和双势方法相比，我们通过这种方法建立了穿透性对质子开始向外移动的内部阱中的起始点$R_{\rm form}$的基本依赖性（例如，对于$^{157}_{73}{\rm Ta}$，穿透性变化高达200倍;精度为$|T+R-1| < 1.5 \cdot 10^{-15}$）。我们施加一个新的条件：在质子衰变的开始，质子开始从阱的最小值向外移动。这样的条件提供了最小的计算半衰期，并为预测提供了稳定的基础。然而，通过这种方法计算的半衰期与半经典半衰期相比更接近实验数据。外部屏障区域的影响估计为改变渗透性的1.5倍。

英文摘要：

We develop a new fully quantum method for determination of widths for nuclear decay by proton emission where multiple internal reflections of wave packet describing tunneling process inside proton--nucleus radial barrier are taken into account. Exact solutions for amplitudes of wave function, penetrability $T$ and reflection $R$ are found for $n$-step barrier (at arbitrary $n$) which approximates the realistic barrier. In contrast to semiclassical approach and two-potential approach, we establish by this method essential dependence of the penetrability on the starting point $R_{\rm form}$ in the internal well where proton starts to move outside (for example, for $^{157}_{73}{\rm Ta}$ the penetrability is changed up to 200 times; accuracy is $|T+R-1| < 1.5 \cdot 10^{-15}$). We impose a new condition: in the beginning of the proton decay the proton starts to move outside from minimum of the well. Such a condition provides 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. Estimated influence of the external barrier region is up to 1.5 times for changed penetrability.

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