论文标题
允许$β$ -DECAY的交换更正
Exchange correction for allowed $β$-decay
论文作者
论文摘要
我们研究了最终原子的结合电子与允许的$β$ - 初始核的交换效果之间的交换效果。电子波函数是通过狄拉克 - 哈特里 - 平台自洽的方法获得的，我们通过修改自符合方法的最后一次迭代来确保连续性和结合电子状态之间的正交性。我们表明，正交性在计算交换校正中起着至关重要的作用。施加正交性后，我们发现与以前的结果相比，幅度和能量依赖性有很大差异。我们认为，我们的发现可以解决$β$频谱的低能区域的先前预测和实验测量之间的不匹配。首先，我们计算低能$β$过渡的交换效果，以$^{14} $ c，$^{45} $ ca，$^{63} $ ni和$^{241} $ pu，最近在文献中进行了调查。接下来，我们计算大量$β$发射器的总交换更正，$ z $从$ 1 $到$ 102 $。从系统的研究中，我们发现，对于超低能量，即$ 5 $ eV，总交换效果的$ z $依赖性受$ s_ {1/2} $和$ p_ {1/2} $ orbitals关闭的影响。我们还表明，高于$ 2s_ {1/2} $轨道的轨道的贡献对于正确计算总效果至关重要，尤其是对于低能和繁重的$β$发射器。最后，我们提供了每个原子数的总交换校正的分析表达，以便于实验研究。
We investigate the exchange effect between the final atom's bound electrons and those emitted in the allowed $β$-decay of the initial nucleus. The electron wave functions are obtained with the Dirac-Hartree-Fock-Slater self-consistent method, and we ensure the orthogonality between the continuum and bound electron states, in the potential of the final atom, by modifying the last iteration of the self-consistent method. We show that orthogonality plays an essential role in calculating the exchange correction. After imposing the orthogonality, we found considerable differences in magnitude and energy dependence compared to previous results. We argue that our findings can solve the mismatch between the previous predictions and experimental measurements in the low-energy region of the $β$ spectrum. First, we calculate the exchange effect for the low-energy $β$ transitions in $^{14}$C, $^{45}$Ca, $^{63}$Ni, and $^{241}$Pu, recently investigated in the literature. Next, we compute the total exchange correction for a large number of $β$ emitters, with $Z$ from $1$ to $102$. From the systematic study, we found that for ultra-low energy, i.e., $5$ eV, the $Z$ dependence of total exchange effect is affected by $s_{1/2}$ and $p_{1/2}$ orbitals closure. We also show that the contributions from orbitals higher than $2s_{1/2}$ orbital are essential for correctly calculating the total effect, especially for low energies and heavy $β$ emitters. Finally, we provide an analytical expression of the total exchange correction for each atomic number for easy implementation in experimental investigations.
