Programs in Physics & Physical Chemistry
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|Manuscript Title: KLEIN: Coulomb functions for real lambda and positive energy to high accuracy.|
|Authors: A.R. Barnett|
|Program title: KLEIN: COULOMB WFN, REAL L,ETA,X|
|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.|
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.
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.
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.
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