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Manuscript Title: ASYMPT: a program for calculating asymptotics of hyperspherical potential curves and adiabatic potentials.
Authors: A.G. Abrashkevich, I.V. Puzynin, S.I. Vinitsky
Program title: ASYMPT
Catalogue identifier: ADLL_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 125(2000)259
Programming language: Fortran.
Computer: SGI Origin2000, SGI Indigo2, IBM RS/6000 Model 320H, HP 9000/755, Intel Pentium Pro 200MHz PC.
Operating system: IRIX64 6.1/6.4, AIX 3.2.5, HP-UX 9.01, Linux 2.0.36.
RAM: 120K words
Word size: 64
Peripherals: disc.
Keywords: Atomic physics, Structure, Scattering, Electron, Two-electron systems, Hyperspherical Coordinates, Schrodinger equation, Adiabatic approach, Potential curves, Adiabatic potentials, Perturbation theory, Dipole asymptotics, Second-order corrections.
Classification: 2.1, 2.4.

Nature of problem:
The purpose of this program is to calculate asymptotics of hyperspherical potential curves and adiabatic potentials with an accuracy of O(rho**-2) within the hyperspherical adiabatic approach [3,4]. Corrections to matrix elements of potential coupling are calculated as well. The program finds also the matching points between the numerical and asymptotic adiabatic curves within the given accuracy. The adiabatic potential asymptotics can be used for the calculation of the energy levels and radial wave functions of doubly excited states of two-electron systems in the adiabatic and coupled-channel approximations and also in scattering calculations.

Solution method:
In order to compute the asymptotics of hyperspherical potential curves and adiabatic potentials with an accuracy of O(rho**-2) the corresponding secular equation is solved. The matrix elements of the equivalent operator corresponding to the perturbation rho**-2 are calculated in the basis of the Coulomb parabolic functions in the body-fixed frame. The asymptotics of potential curves and adiabatic potentials are calculated within an accuracy of O(rho**-2) using the eigenvalues of the corresponding secular equation. Zeroth-order asymptotic wave-functions are used to calculate the relevant corrections to the potential matrix elements.

Restrictions:
The computer memory requirements depend on: (a) the maximum value of the total orbital momentum considered; and (b) the number of maximum threshold required. Restrictions due to dimension sizes may be easily alleviated by altering PARAMETER statements (see Long Write-Up and listing for details).

Unusual features:
The program uses the subprograms: RS [1], SPLINE and SEVAL [2].

Running time:
The test run which accompanies this paper took 0.4 s on the SGI Origin2000.

References:
[1] B.T. Smith, J.M. Boyle, B.S. Garbow, Y. Ikebe, V.C. Klema and C.B. Moler, Matrix Eigensystem Routines - EISPACK Guide, (Springer-Verlag, New York, 1974); B.S. Garbow, J.M. Boyle, J.J. Dongarra and C.B. Moler, Matrix Eigensystem Routines - EISPACK Guide Extension, (Springer-Verlag, New York, 1977). Routines from the EISPACK library are freely available from the NETLIB at URL: http://www.netlib.org/eispack/.
[2] G.E. Forsythe, M.A. Malcolm and C.B. Moler, Computer Methods for Mathematical Computations (Englewood Cliffs, Prentice Hall, New Jersey, 1977).
[3] J. Macek, J. Phys. B1, 831 (1968); U. Fano, Rep. Progr. Phys. 46, 97 (1983); C.D. Lin, Adv. Atom. Mol. Phys. 22, 77 (1986).
[4] A.G. Abrashkevich, D.G. Abrashkevich, I.V. Puzynin and S.I. Vinitsky, J. Phys. B24 (1991) 1615; A.G. Abrashkevich, D.G. Abrashkevich, M.S. Kaschiev, I.V. Puzynin and S.I. Vinitsky, Phys. Rev. A 45 (1992) 5274; A.G. Abrashkevich and M. Shapiro, Phys. Rev. A50 (1994) 1205.