ASYMPT                   Library "JINRLIB"                       

    Authors: A.Abrashkevich, I.V.Puzynin, S.I.Vinitsky               You are 
    Language: Fortran                                                
    Operating system: IRIX64 6.1,6.4, AIX 3.2.5,                     visitor here.
                      HP-UX 9.01, Linux 2.0.36.

            A PROGRAM FOR CALCULATING ASYMPTOTICS OF HYPERSPHERICAL
                  POTENTIAL CURVES AND ADIABATIC POTENTIALS

    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: 
    1. the maximum value of the total orbital momentum considered; 
    2. 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]. 

    Journal reference: Computer Physics Communications 125 (2000) 259
    For details see: http://cpc.cs.qub.ac.uk/summaries/ADLL_v1_0.html

    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.