Ground State of Two-Electron Atoms
Ground State of Two-Electron Atoms
复制标题
二电子原子的基态
DOI：
10.1103/physrev.112.1649
复制
发表时间：
1958
期刊：
影响因子：
--
通讯作者：
C. Pekeris
中科院分区：
文献类型：
--
作者：
C. Pekeris
开发了一种求解双电子原子波动方程的新方法。波函数被展开为三个周界坐标中的三重正交集。从波动方程中可以得到展开式系数的显式递推关系，而这些系数行列式的消失为能量特征值和特征向量提供了条件。使用迭代方法在 Z= 1 到 10 的 WEIZAC 上求解行列式。由于行列式的元素是整数，并且每行平均只有约 20 个元素是非零的，因此在超过 WEIZAC 快速存储器的容量之前，可以达到 214 的数量级。获得的基态非相对论能量特征值低于之前发布的所有 Z 从 1 到 10 的能量特征值。就氦气而言，我们的非相对论能量值精确到 0.01 cm−1 以内，比 Kinoshita 计算的值低 0.40 cm−1。根据获得的波函数，对 Z= 1 到 10 的质量极化和相对论校正进行评估。使用 Kabir、Salpeter 和 Sucher 计算的兰姆位移值，我们获得氦气的电离势为 198 310.67 cm− 1，而 Herzberg 的电离势值为 198 310.8 2±0.15 cm− 1。还与可用的电离势进行了比较。 Z 其他值的实验数据。通过使用我们的磁带存储，氦的非相对论能量值的精度可以提高到大约 0.001 cm−1，如果未来实验值和计算的辐射校正的改进能够保证这一点。
A new method is developed for solving the wave equation for two-electron atoms. The wave function is expanded into a triple orthogonal set in three perimetric coordinates. From the wave equation one obtains an explicit recursion relation for the coefficients in the expansion, and the vanishing of the determinant of these coefficients provides the condition for the energy eigenvalues and for the eigenvectors. The determinant was solved on WEIZAC for Z= 1 to 10, using an iteration method. Since the elements of the determinant are integers, and only an average of about 20 per row are nonvanishing, it has been possible to go to an order of 214 before exceeding the capacity of the fast memory of WEIZAC. The nonrelativistic energy eigenvalues obtained for the ground state are lower than any previously published for all Z from 1 to 10. In the case of helium, our nonrelativistic energy value is accurate to within 0.01 cm− 1 and is 0.40 cm− 1 lower than the value computed by Kinoshita. From the wave functions obtained, the mass-polarization and the relativistic corrections were evaluated for Z= 1 to 10. Using the values of the Lamb shift computed by Kabir, Salpeter, and Sucher, we obtain an ionization potential for helium of 198 310.67 cm− 1 as against Herzberg's value of 198 310.8 2±0.15 cm− 1. Comparison is also made with the available experimental data for the other values of Z. By the use of our magnetic tape storage, the accuracy of the nonrelativistic energy value for helium could be pushed to about 0.001 cm− 1, should future improvements in the experimental values and in the computed radiative corrections warrant it.