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Manuscript Title: A program to calculate Green's functions.
Authors: S.P. Rountree, T. Burnett, R.J.W. Henry, C.A. Weatherford
Program title: GRN1
Catalogue identifier: ACWN_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 11(1976)27
Programming language: Fortran.
Computer: CDC 6400.
Operating system: SCOPE.
RAM: 42K words
Word size: 60
Keywords: General purpose, Green's functions, Ricatti-bessel, Modified ricatti-bessel, Differential equation, Whittaker functions, Scattering.
Classification: 4.3.

Revision history:
Type Tit le Reference
adaptation 0001 GRN2 See below

Nature of problem:
Regular and irregular solutions to a one-dimensional differential equation are obtained for the cases where the potential includes a Coulomb term and/or a centrifugal barrier, and for positive or negative energies. These Green's function solutions are necessary, for example, in the solution of a scattering problem by non-iterative integral equation method.

Solution method:
A power series expansion for small values of the radial distance is used for both the regular and irregular solutions. When the amplitude of the solutions are approximately the same, the power series is replaced by a Numerov integration method, by which the solutions are generated outwards to large values of the radial distance. For the case of negative energy, the irregular solution is obtained at large radial values by an asymptotic expansion and is generated inwards by a Numerov method.

Restrictions:
The order of the Green's functions is restricted to l<= 24. The arrays used in the storage of the power series coefficients must be increased for l> 24. The program can be used for all positive and negative energies except for energies which can be written in the form E = -n**-2 where n is a positive integer. Numerical inaccuracies will result if the program is used in single precision on a 32 bit/word computer.

ADAPTATION SUMMARY
Manuscript Title: Adaptation of a program to calculate Green's function.
Authors: R.J.W. Henry, S.P. Rountree, E.R. Smith
Program title: 0001 GRN2
Catalogue identifier: ACWN_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 23(1981)233
Programming language: Fortran.
Classification: 4.3.

Nature of problem:
The subroutine GRN2 calculates Green's function solutions to a one- dimensional differential equation and returns Fl(rho) and Gl(rho), where rho = kr. It differs with program GRN1 in that the subroutines have been recoded to extend the range of values to large residual charge z of the target and to effect time savings. The program has been modified to start at any given radial value R1STOP and it will produce Fl(rho) and Gl(rho) at any interval size specified and in blocks of NPTS steps, up to a maximum radial value of R2STOP. Four subroutines POWERD, POWERH, POWERE and POWERF have been added to evaluate, respectively, an asymptotic expansion for cases (1)-(4), i.e. , Z=0, E>0; Z=0, E<0; Z>0, E>0; and Z>0, E<0.

Restrictions:
The order of the Green's function is restricted to l<=50. The arrays used in storage of the power series coefficients must be increased for l>50. The program has been tested for eta<=0 only, i.e., for neutral or attractive Coulomb potentials. The program can be used for all positive and negative energies except for energies which can be written in the form E= -z**2 n**-2, where n is a positive integer. While the program can be called at any rho, it has been tested primarily for initial values which are at either small rho where a power series expansion is valid, or in the asymptotic region where an asymptotically divergent series is used. Input data The input data is described on comment cards in the main program. The second card of the input data differs from that used for program GRN1. The second card for program GRN2 is as follows: 2. ITEST, L, NPTS, R1STOP, R2STOP, ENERGY, CHARGE ITEST, L, ENERGY and CHARGE are as described in GRN1, NPTS number of steps required at one time, R1STOP initial radial value, R2STOP final radial value. Example: If there are 121 steps from R1STOP to R2STOP and NPTS=50, then the program will give the first 50 values of Fl(rho) and Gl(rho), then the next 50 values, and finally the remaining 21 values. Flow diagram A flow diagram for GRN2 is given. The values used for the discrimination TST1 is 15 + 4|eta|/3 + l/10. The value used for discrimination TST2 is 7-l + 1 + 7|eta|.