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Manuscript Title: KLEIN: Coulomb functions for real lambda and positive energy to high accuracy.
Authors: A.R. Barnett
Catalogue identifier: ABNJ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 24(1981)141
Programming language: Fortran.
Computer: IBM 370/165.
Operating system: OS/360 GL HX (LEVEL 2.2.1).
RAM: 12K words
Word size: 32
Keywords: General purpose, Klein-gordon, Coulomb for real Angular momentum, Dirac, Schrodinger, Spherical bessel, Continued-fraction, Heavy-ion, Pionic, Kaonic, Exotic atoms, Scattering states, N-dimensional h-atom.
Classification: 4.5.

Nature of problem:
KLEIN computes relativistic Schrodinger (Klein-Gordon) equation solutions, i.e. Coulomb functions for real lambda > - 1, F lambda (eta,x), G lambda (eta,x), F'lambda (eta,x) and G'lambda (eta,x) for real x > 0 and real eta, -10**4 < eta < 10**4. Hence it is also suitable for Bessel and spherical Bessel functions. Accuracies are in the range 10**-14 -10**-16 in oscillating region, and approximately 10**-30 on an extended precision compiler. The program is suitable for generating Klein-Gordon wavefunctions for matching in pion and kaon physics.

Solution method:
An extended version of Steed's method used previously for integer lambda in subroutine RCWFN, is adopted.

The standard version loses accuracy as x>xlamda (the turning point) and eventually when G>~10**6 the subroutine is ineffective; a JWKB approximation and full information is output.

Running time:
The test deck took about 2 s to run on the G1 compiler, and HX compiler; with AUTODBLE and REAL*16 variables the same deck took 76 s (ACCUR = 10**-16) and 109 s (ACCUR = 10**-33). Note that about one half the time demonstrates error conditions.