$β$电子能谱：静态屏蔽库仑场和交换效应
$β$-electron spectrum: static screened Coulomb field and exchange effects
摘要：
我们考虑了$β$衰变中发射电子的能谱。精确的库仑狄拉克波函数描述的$β$ -电子在库仑场的子核。此外，改进的波函数，其中包括由于原子电子云的库仑场的屏蔽也被使用。因此，$β$ -电子之间的相互作用和由于子原子的字段内的非微扰的方法处理。示出了由于对$β$光谱的筛选而引起的修改，并且示出了这些效果是非常重要的。此外，解决的贡献的$β$光谱由于交换条款，并显示相应的效果可以是实质性的。高阶所产生的多极展开被认为是。在这项工作中获得的理论结果的比较已与最近的实验数据和观察到一个非常好的协议。
英文摘要：
We consider the energy spectrum of emitted electrons in $β$-decay. Exact Coulomb Dirac wave functions describing the $β$-electron in the Coulomb field of the daughter nucleus are used. Further, the improved wave functions which include the screening of the Coulomb field due to the atomic electron cloud are also used. Thus, the interaction between the $β$-electron and the field due to the daughter atom is treated within a nonperturbative approach. Are shown the modifications due to the screening on the $β$ spectra and shown that those effects are very important. In addition, are addressed the contributions to the $β$ spectra due to the exchange terms and shown that the corresponding effects can be substantial. Higher orders arising from the multipole expansion are considered. A comparison of the theoretical results obtained in this work has been made with recent experimental data and a very good agreement was observed.
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