A report for Debora Watson group (pdf files)

• Part I. Asymmetric stationary points in a helium effective potential
• Calculation of all asymmetric stationary points in the effective potential
• Summary of the computation of all asymmetric stationary points
• Choice of a proper stationary point
• The stationary point, frequencies, and normal-mode coordinates as functions of nuclear charge and mass of the first electron
• Plot of the effective potential for different lambda and mass m1
• Tables
• Asymmetric stationary points, frequencies, and transformation to normal modes for helium potentials
• Behavior of stationary points for helium potentials in the vicinity of the symmetry-breaking point
• Transformation to normal modes for helium potentials using prolate spheroidal coordinates
• Stationary points for helium effective potential, with increased mass of the first electron
• Transformation to normal modes for helium potential using prolate spheroidal coordinates, with variable mass of the first electron
• Part II
• Two-Coulomb-center approximation (the first electron is regarded infinitely heavy)
• Discussion
• Part III
• Exact expansion around the asymmetric stationary point
• Details of computations
• Large-n1 limit of the dimensional perturbation theory
• Tables
1. Summation of the shifted 1/(D+a)-series for the "frozen planetary" (6, 0, 0) state of helium using different shift parameters a
2. Summation of the large-D series for (n, 0, 0) states of helium
3. FORTRAN program for calculation of the large-D expansion for "frozen planetary" states of two-electron atoms
4. Summation of the large-D series for (3,0,1) and (6,1,0) states of helium and (n, 0, 0) states of the positive ion of lithium
5. Accuracy zero-order test: comparison of exact equilibrium distances and frequencies obtained by Mathematica with that obtained by complex*32 FORTRAN
6. Coefficients of the 1/D expansion of the energy for the ground state of He: comparison of complex*32-results with the results of D. Goodson (J. Chem. Phys. 1992, 97, 8481)
7. Accuracy test for asymmetric state (6,0,0): comparison of the 1/(D+11)-expansion coefficients calculated directly with that obtained by re-expansion of the 1/D-series
• Figures that were not embedded in the text
1. Dependence of the energy (real part) on 1/D for helium asymmetric states
2. Real part of the energy in the larger scale
3. Dependence of the width on 1/D for helium asymmetric states
4. Poles of PA for the function Sqrt(-E'(delta'))
5. Energy as a function of the variable n1/D
6. D-dependence of the energy for Li+ ion
7. D-dependence of the width for Li+ ion
8. Poles of PA for the energy function of (600) state
9. Poles of PA for the Borel function of (600) state
10. Poles of PA for the Borel function of (000) state

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Designed by A. Sergeev.