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Manuscript Title: A program to calculate the eigenfunctions of the random phase approximation for two electron systems.
Authors: M.J. Jamieson, I.H.K. Aldeen
Catalogue identifier: AAJD_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 20(1980)213
Programming language: Fortran.
Computer: IBM 360/370.
Operating system: IBM OS.
RAM: 122K words
Word size: 32
Keywords: Atomic physics, Structure, Random phase Approximation, Time dependent Hartree-fock theory, Eigenfunction, Eigenvalue, Two electron system, Numerov, Secant method.
Classification: 2.1.

Nature of problem:
Knowledge of the eigenfunctions and eigenvalues of the random phase approximation (RPA) or time-dependent Hartree-Fock (TDHF) theory is sufficient for calculations of one electron properties for closed shell systems correct to at least first order in correlation. The eigenfunctions of two electron systems satisfy a pair of second order eigenvalue differential equations coupled by an integral term. These eigenfunctions, characterized by a principal quantum number n and an angular momentum quantum number l, are evaluated by the program. The user need only specify n,l and supply data for a Hartree-Fock ground state orbital.

Solution method:
The integral coupling term is replaced by an exchange term satisfying a third differential equation. The resulting set of eigenvalue differential equations is solved by attempting to match forward and backward trial solutions; this leads to a nonlinear equation for the eigenvalue which is solved by the secant method. In case the NAG library is not available the specifications on the NAG routines used are given as comments at the end of the program.

For very large principal quantum numbers some dimensions must be increased. However, in such cases the user is encouraged to derive a formula asymptotic in n, if possible, for the properties of interest rather than solve the eigenvalue problem. Also l = 0.

Running time:
On the IBM 370/168 the eigenfunctions corresponding to a single nl pair, are obtained in 2.6 s.