Record 4 of 40


Author(s):
 Elout MO; Goodson DZ; Elliston CD; Huang SW; Sergeev AV; Watson DK

Title:
 Improving the convergence and estimating the accuracy of summation approximants of 1/D expansions for Coulombic systems

Source:
 JOURNAL OF MATHEMATICAL PHYSICS 1998, Vol 39, Iss 10, pp 51125122

Addresses:
 Elout MO, So Methodist Univ, Dept Chem, Dallas, TX 75275 USA. So Methodist Univ, Dept Chem, Dallas, TX 75275 USA. Univ Oklahoma, Dept Phys & Astron, Norman, OK 73019 USA. SI Vavilov State Opt Inst, St Petersburg 199034, Russia.

KeywordsPlus:
 LARGEDIMENSION LIMIT; PERTURBATIONTHEORY; ELECTRONICSTRUCTURE; 2ELECTRON ATOMS; SCHRODINGEREQUATION; QUANTUMMECHANICS; MAGNETICFIELD; EXCITEDSTATES; HYDROGENATOM; HELIUM

Abstract:
 The convergence of largeorder expansions in delta = 1/D, where D is the dimensionality of coordinate space, for energies E(delta) of Coulomb systems is strongly affected by singularities at delta = 1 and Pade'Borel approximants with modifications that that completely remove the singularities at delta = 1 and remove the dominant singularity at delta = 0 are demonstrated. A renormalization of the interelectron repulsion is found to move the dominant singularity of the Borel function F(delta) = Sigma(j)E(j)'/ j!, where Ej' are the the expansion coefficients of the energy with singularity structure removed at d51, farther from the origin and thereby accelerate summation convergence. The groundstate energies of He and H2(+) are used as test cases. The new methods give significant improvement over previous summation methods. Shifted Borel summation using Fm(delta) = Sigma(j)E(j)'/Gamma(j + 1  m) is considered. The standard deviation of results calculated with different values of the shift parameter m is proposed as a measure of summation accuracy. (C) 1998 American Institute of Physics. [S00222488(98)042108].

Times Cited:
 0

Source item page count:
 11

Publication Date:
 OCT

IDS No.:
 124NC

29char source abbrev:
 J MATH PHYSNY
