PROGRAM SUMMARY
Title of program:
ASYMPT
Catalogue identifier:
ADLL
Ref. in CPC:
125(2000)259
Distribution format: gzip file
Operating system: IRIX64 6.1, 6.4, AIX 3.2.5, HP-UX 9.01,Linux 2.0.36
High speed store required:
120K words
Number of bits in a word:
64
Peripherals Required: disc
Number of lines in distributed program, including test data, etc:
2358
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.
Programming language used: Fortran
Computer:
SGI Origin2000 ,
SGI Indigo2 ,
IBM RS/6000 Model 320H ,
HP 9000/755 ,
Intel Pentium Pro 200MHz PC.
Nature of physical 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.
Method of solution
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 on the complexity of the problem
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 of the program
The program uses the subprograms: RS [1], SPLINE and SEVAL [2].
Typical 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.