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Manuscript Title: Coulomb wave functions for all real eta and rho. | ||

Authors: A.R. Barnett, D.H. Feng, J.W. Steed, L.J.B. Goldfarb | ||

Program title: RCWFN | ||

Catalogue identifier: ABPC_v1_0Distribution format: gz | ||

Journal reference: Comput. Phys. Commun. 8(1974)377 | ||

Programming language: Fortran. | ||

Computer: CDC 7600, IBM 370/165, IBM 360/195. | ||

Operating system: UMRCC SCOPE V2.0. | ||

RAM: 1K words | ||

Word size: 60 | ||

Keywords: General purpose, Runge-Kutta, Schrodinger equation, Reactions, Scattering, Heavy ion, Wavefunction, Coulomb, Potential, Hypergeometric function, Continued fraction. | ||

Classification: 4.5. | ||

Revision history: | ||

Type | Tit
le | Reference |

adaptation | 0001RCWFF | See below |

correction | A00ACORRECTION TO 0001 26/10/77 | See below |

Nature of problem:The subroutine RCWFN calculates the regular and irregular Coulomb wavefunctions, Fl(eta,rho) and Gl(eta,rho) and their radial derivatives for real, positive energy for all (eta,rho), (-1000 <= eta <= 1000, rho >0) rapidly and with high accuracy. It is well suited for calculations of Coulomb matrix elements for heavy-ion scattering [1] (1 < eta < 200, eta < rho < 1000) and for all programs which require matching to asymptotic Coulomb wavefunctions in both nuclear and atomic physics. | ||

Solution method:An entirely new technique, developed by Steed [2], is used, which differs greatly from standard methods [3]. The method is based on the continued-fraction expansion of the quantities Fl'/Fl and (Gl'+Fl')/(Gl+iFl) and it is applicable for all values of rho >= rhoTP= eta + [eta**2 + l(l+1)]**1/2 without restriction. A somewhat modified method is used for values of rho<rhoTP. The results are given for all l-values between MINL and MAXL inclusive (MAXL >= MINL >= 0) and for any required rho-value. In general results are obtained without integrating the differential equation. The subroutine is fast and compact; the results can be obtained to any desired accuracy in the range 10**-6 - 10**-12. When the $-separator format on the CDC card input is used the entire subroutine occupies 36 cards. | ||

Restrictions:Subroutine RCWFN has been programmed for real values of eta and rho: the value of eta is unrestricted (positive, negative or zero) while the value of rho cannot be zero. There is a loss of accuracy in cases when rho < 0.2rhoTP. | ||

Running time:For the l=o functions the averaging running time (CDC 7600 CP time) is 0.005 s for ACCUR = 10**-7 and STEP = 100.0 (i.e. practical values), and there is no significant increase with l-value. | ||

References: | ||

[1] | A.R. Barnett, D.H. Feng and L.J.B. Goldfarb, Phys. Lett. 48B (1974) 290; and Computer Phys. Commun., to be published. | |

[2] | J.W. Steed, PhD thesis, University of Manchester (1967) unpublished. | |

[3] | C.E. Froberg, Rev. Mod. Phys. 27 (1955) 399; C. Bardin et al., Computer Phys. Commun. 3 (1972) 73. | |

ADAPTATION SUMMARY | ||

Manuscript Title: RCWFF - a modification of the real Coulomb wavefunction program RCWFN. | ||

Authors: A.R. Barnett | ||

Program title: 0001RCWFF | ||

Catalogue identifier: ABPC_v1_0Distribution format: gz | ||

Journal reference: Comput. Phys. Commun. 11(1976)141 | ||

Programming language: Fortran. | ||

Keywords: General purpose, Runge-Kutta, Schrodinger equation, Reactions, Scattering, Heavy ion, Wavefunction, Coulomb, Potential, Hypergeometric function, Continued fraction. | ||

Classification: 4.5. | ||

Nature of problem:The subroutine RCWFF calculates Coulomb wavefunctions and returns (1) Fl(eta,rho); or (2) Fl(eta,rho) and Gl(eta,rho); or (3) Fl(eta,rho), Gl(eta,rho), Fl'(eta,rho) and Gl'(eta,rho), where the primes denote d/dr and rho = kr. When in use as under 3) it is identical with subroutine RCWFN [1] and the range of values, method of solution, restrictions, and timing remain the same. When used as in (1) or (2) the program is somewhat faster, since less calculation and normalisation is required, and it requires no array space for the unwanted quantities. The subroutine has been incorporated into the DWBA program PATIWEN [2,3] which is used to evaluate light-ion and heavy-ion Coulomb nuclear interference in inelastic scattering. For these calculations real Coulomb matrix elements of the form Integral(a-b) Fl(eta,kr)r**(-lambda-1)fl'(eta',k'r)dr are required for the bulk of the calculation and so RCWFF is called as in (1) above. | ||

Running time:The time saving depends on the relative time spent in evaluating the two continued fractions compared with the calculation of the unwanted quantities: when only Fl(eta, rho) is required savings of up to 30% have been found, if the parameters are in the range normal for heavy-ion physics calculations. The testing routine has been modified to call RCWFF three times for the different modes of operation. The results are displayed one after the other in the order of the original test of RCWFN. | ||

References: | ||

[1] | A.R. Barnett, D.H. Feng, J.W. Steed and L.J.B. Goldfarb, Computer Phys. Commun. 8 (1974) 377. | |

[2] | D.H. Feng and A.R. Barnett, Computer Phys. Commun. 10 (1975) 401. | |

[3] | A.R. Barnett, D.H. Feng and L.J.B. Goldfarb, Phys. Rev. C 13 (1976) no. 3. | |

CORRECTION SUMMARY | ||

Manuscript Title: Unpublished correction to RCWFF: a modification of the real Coulomb
wavefunction program RCWFN. | ||

Authors: A.R. Barnett | ||

Program title: A00ACORRECTION TO 0001 26/10/77 | ||

Catalogue identifier: ABPC_v1_0Distribution format: gz | ||

Classification: 4.5. |

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