SOME CALCULATIONS ON THE GROUND AND LOWEST-TRIPLET STATE OF HELIUM IN THE FIXED-NUCLEUS APPROXIMATION
SOME CALCULATIONS ON THE GROUND AND LOWEST-TRIPLET STATE OF HELIUM IN THE FIXED-NUCLEUS APPROXIMATION
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DOI：
10.1103/physreva.49.4520
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发表时间：
1994-06-01
影响因子：
2.9
通讯作者：
SUTCLIFFE, BT
中科院分区：
文献类型：
--
作者：
COX, H;SMITH, SJ;SUTCLIFFE, BT
Pekeris [Phys.Rev.112，1649（1958）; 115，1216（1959）]为双电子原子的薛定谔方程发展的级数解方法，被Frost等人[J.Chem.Phys.41，482（1964）]推广到处理具有库仑相互作用的任何三个粒子。波函数在三个圆周坐标系中的三重正交集合中展开。从薛定谔方程得到展开式中系数的显式递推关系，这些系数的行列式的消失提供了能量本征值和本征向量的条件。用计算机代数系统MAPLE求解薛定谔方程，代数地产生矩阵元。用C语言编写的程序实现了特定原子的替换和对角化。由于行列式是稀疏的，因此可以像Pekeris那样在不使用过多内存或计算机CPU时间的情况下达到1078的数量级。通过使用一个非线性变分参数的表达用于删除的能量，非相对论能量，在固定核近似下，已获得。对于基态单线态11 S态，这是Frankowski和Pekeris [Phys.Rev.146，46（1966）; 150，366（E）（1966）]，对于Z从1到10使用对数项，并且对于三重态2（3）S，已经获得了精确到小数点后12位的能量，除了Z = 2之外，低于任何以前公布的，所有Z从3到10。
The series solution method developed by Pekeris [Phys. Rev. 112, 1649 (1958); 115, 1216 (1959)] for the Schrodinger equation for two-electron atoms, as generalized by Frost et al. [J. Chem. Phys. 41, 482 (1964)] to handle any three particles with a Coulomb interaction has been used. The wave function is expanded in a triple orthogonal set in three perimetric coordinates. From the Schrodinger equation an explicit recursion relation for the coefficients in the expansion is obtained, and the vanishing of the determinant of these coefficients provides the condition for the energy eigenvalues and for the eigenvectors. The Schrodinger equation is solved and the matrix elements are produced algebraically by using the computer algebra system MAPLE. The substitutions for a particular atom and diagonalization were performed by a program written iu the C language. Since the determinant is sparse, it is possible to go to the order of 1078 as Pekeris did without using excessive memory or computer CPU time. By using a nonlinear variational parameter in the expression used to remove the energy, nonrelativistic energies, within the fixed-nucleus approximation, have been obtained. For the ground-state singlet 1 1S state this is of the accuracy claimed by Frankowski and Pekeris [Phys. Rev. 146, 46 (1966); 150, 366(E) (1966)] using logarithmic terms for Z from 1 to 10, and for the triplet 2(3)S state, energies have been obtained to 12 decimal places of accuracy, which, with the exception of Z = 2, are lower than any previously published, for all Z from 3 to 10.