Some calculations on the ground and lowest-triplet state of helium in the fixed-nucleus approximation
- Department of Mathematics, University of York, Heslington, York, YO15DD (United Kingdom)
- Department of Chemistry, University of York, Heslington, York, YO15DD (United Kingdom)
The series solution method developed by Pekeris [Phys. Rev. 112, 1649 (1958); 115, 1216 (1959)] for the Schroedinger equation for two-electron atoms, as generalized by Frost [ital et] [ital 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 triple orthogonal set in three [ital perimetric] coordinates. From the Schroedinger 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 Schroedinger 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 in 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 [sup 1][ital S] state, this is of the accuracy claimed by Frankowski and Pekeris [Phys. Rev. 146, 46 (1966); 150, 366(E) (1966)] using logarithmic terms for [ital Z] from 1 to 10, and for the triplet 2 [sup 3][ital S] state, energies have been obtained to 12 decimal places of accuracy, which, with the exception of [ital Z]=2, are lower than any previously published, for all [ital Z] from 3 to 10.
- OSTI ID:
- 7238702
- Journal Information:
- Physical Review A; (United States), Vol. 49:6; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
HELIUM
ELECTRONIC STRUCTURE
CALCULATION METHODS
EIGENVALUES
EIGENVECTORS
EXCITED STATES
GROUND STATES
SCHROEDINGER EQUATION
TRIPLETS
DIFFERENTIAL EQUATIONS
ELEMENTS
ENERGY LEVELS
EQUATIONS
FLUIDS
GASES
MULTIPLETS
NONMETALS
PARTIAL DIFFERENTIAL EQUATIONS
RARE GASES
WAVE EQUATIONS
664100* - Theory of Electronic Structure of Atoms & Molecules- (1992-)