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Manuscript Title: LSFBTR: a subroutine for calculating spherical Bessel transforms.
Authors: J.D. Talman
Program title: LSFBTR
Catalogue identifier: AANZ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 30(1983)93
Programming language: Fortran.
Computer: CYBER 170-835.
Operating system: NOS 2.
RAM: 11K words
Word size: 60
Keywords: General purpose, Hankel transforms, Spherical Bessel functions, Momentum space wave Functions.
Classification: 4.7.

Nature of problem:
Transforming an angular momentum wave function from coordinate to momentum representation requires the calculation of Hankel transforms for spherical Bessel functions. This subroutine calculates such integrals when the function to be transformed is given numerically at r values that are distributed uniformly in the variable ln(r). The resulting values of the transform are given at k values distributed uniformly in the variable ln(k).

Solution method:
The transform can be carried out as two successive Fourier transforms that are calculated numerically using the trapezoidal rule. For meshes with a large number of points these can be calculated very efficiently using the fast Fourier transform method.

The method is most effective for functions which have only a few nodes and have continuous derivatives on (0, infinity). For other functions a very large number of mesh points may be required.

Unusual features:
Remarkably accurate results are obtained for very large values of the transform variable.

Running time:
The program required 0.146 s to calculate the transform at 256 mesh points in the l=0 case on the CYBER 170-835. In the l=5 case the same calculation required 0.172 s. The first time the program is called for a particular mesh, about 0.3 s is required for initialization.