Resonance states of atomic anions

We study destabilization of an atom in its ground state with decrease of its nuclear charge. By analytic continuation from bound to resonance states, we obtain complex energies of unstable atomic anions with nuclear charge which is less than the minimum "critical" charge necessary to bind N electrons. We use an extrapolating scheme with a simple model potential for the electron which is loosely bound outside the atomic core. Results for O^-- and S^-- are in good agreement with earlier estimates. Alternatively, we use the Hylleraas-basis variational technique with three complex nonlinear parameters to find accurately the energy of two-electron atoms as the nuclear charge decreases. Results are used to check the less accurate one-electron model.

Draft of a possible paper, pdf

Reformatted paper, TeX and PDF.

Revised and shortened version that was finally accepted, TeX and PDF.

Final version, PDF file from the journal.

Mathematica programs and results of calculations

Variational calculations of the energy for helium isoelectronic series as a function of the nuclear charge on Hylleraas basis set:

• Fixed and real variational parameters a, b, c.
• With variational parameters a, b, c found as a complex stationary point.
• Results of computations using the above program (a list of {Z, Re a, Im a, Re b, Im b, Re c, Im c, Re E, Im E, accuracy}) for N=0, N=1, N=2, N=3, N=4 (incomplete), N=5 (incomplete).
• Calculating for larger basis sets with variational parameters a, b, c found as a complex stationary point for smaller basis set (they are read from a file).
• Finding the singularity.
• Finding the critical charge by minimizing lambda-functional.
• Results of finding the critical charge by minimizing lambda-functional.

Used subroutines:

• Hylleraas integrals, matrix, and mapping of indexes.
• Interpolating by an algebraic function (to take into account square-root singularities).
• Printing results in Fortran-like format.

Back to Results of work in Purdue University.

Designed by A. Sergeev.