Numerical Evaluation of the Fermi Beta-Distribution Function
Numerical Evaluation of the Fermi Beta-Distribution Function
复制标题
费米 Beta 分布函数的数值评估
DOI：
--
复制
发表时间：
1950
期刊：
影响因子：
--
通讯作者：
I. Feister
中科院分区：
文献类型：
--
作者：
I. Feister
在制作IJ谱的费米-居里图时，已经使用了各种近似来评估fCZ，）。然而，很可能这些近似值都不完全适用于Z和11的所有值。因此，现在正在准备对这一重要功能进行精确计算和制表。本文将feZ（1）的三个近似值与已为该表计算的fez（1）的一些代表值作了比较，并指出了这些近似值的精度和有效范围。由于通过r-函数的级数展开直接计算（2）是不方便的，因此为此目的已经使用了各种近似。在他最初的论文中，费米使用了Z=82.2的近似，他们估计可以用于所有轻元素，直到大约Cu，Z=29（假设TJ不>> 1）。因此该表达式的适用性也相当有限。Bethe和Bacher给出了一个更普遍有用的近似，并由Longmire和Brown将其转化为下面的方便形式。
In making a Fermi-Kurie plot of a IJ-spectrum various approximations have been used to evaluate fCZ, ,,). It is probable, however, that none of these approximations is completely adequate for all values of Z and 11. Hence an accurate computation and tabulation of this important function is now in preparation. Three approximations for feZ, ,,) are compared with some representative values of fez, 11) that have been cOlnputed for the proposed table, and the accuracy and range of validity of these approximations are indicated. Since the direct evaluation of (2) by means of a series expansion of the r-function is inconvenient, various approximations have been utilized for this purpose. In his original paper l Fermi used the following approximation for Z=82.2 which they estimated could be used for all light elements up to about Cu, Z=29 (provided TJ is not »1). Thus this expression also has quite limited applicability. A more generally useful approximation has been given by Bethe and BacherS and put in the following convenient form by Longmire and Brown 4