LIBCOUL90

Calculate real-valued Coulomb and Bessel functions for real-valued arguments. The original COUL90(), available at the Fresco website, has been repackaged here as an fpm package. See the original author's article [1] for more detail. This is largely not my work. No intentional changes to the algorithm have been made. Test suite not yet implemented, but the tester program from the Fresco website is available.

Building with fpm

In the package directory, just run

$ fpm build --profile release

The archive file libcoul90.a and .mod files will be placed in the generated build subdirectory. These files are necessary to compile another program that uses this library.

Using this version of COUL90()

To use this project within your fpm project, add the following to your fpm.toml file:

[dependencies]
libcoul90 = { git="https://github.com/banana-bred/libcoul90" }

or

[dependencies]
libcoul90 = {'namespace'='COULXX'}

The module libcoul90 contains the following public procedures :

• coulf(lambda,eta,x) : return the regular Coulomb function $F_\lambda(\eta,x)$
• coulg(lambda,eta,x) : return the irregular Coulomb function $G_\lambda(\eta,x)$
• sphbessj(lambda,x) : return the spherical Bessel function of the first kind $j_\lambda(x)$
• sphbessy(lambda,x) : return the spherical Bessel function of the second kind $y_\lambda(x)$
• cylbessj(lambda,x) : return the (cylindrical) Bessel function of the first kind $J_\lambda(x)$
• cylbessy(lambda,x) : return the (cylindrical) Bessel function of the second kind $Y_\lambda(x)$
• coul90_wrapper(xlmin, nl, eta, x, f, fp, g, gp, kfn) : a wrapper used to call COUL90(), used by the above-mentioned procedures
• COUL90(X,ETA_IN,XLMIN,LRANGE,FC,GC,FCP,GCP,KFN,IFAIL) : the original code described in [1], with some minor modernizations.
• ricbes(x, lmax, psi, chi, psid, chid, ifail) : a subroutine that returns the Riccati-Bessel functions $zj\lambda(z)$ and $zy\lambda(z)$, and their derivatives in the arrays psi, chi, psid, and chid for orders $0$ -- $\lambda_\text{max}$
• sbesjy(x, lmax, j, y, jp, yp, ifail) : a subroutine that returns the spherical Bessel functions functions $j\lambda(z)$ and $y\lambda(z)$, and their derivatives in the arrays psi, chi, psid, and chid for orders $0$ -- $\lambda_\text{max}$

Above, LMAX is the same as $\lambda\text{max}$ and nl is the number of $\lambda$ values. The variables x and eta are real(real64), while the variable lambda can be an integer or real(real64). The kind real64 (64 bits / 8 bytes) is defined in the intrinsic module `isofortran_env. All public procedures other thanCOUL90()are superfluous — they're provided for convenience or as a simple example of callingCOUL90()`.

The following example program

program test

  use libcoul90, only: coulf
  use iso_fortran_env, only: rp => real64, stdout => output_unit

  integer :: l = 0
  real(rp) :: eta = -0.5_rp
  real(rp) :: x = 20.0_rp

  write(stdout, '("F_", I0, "(", F0.2, ",", F0.2, ") = ", e0.15)') l, eta, x, coulf(l, eta, x)

end program test

should print the following:

F_0(-.50,20.00) = -0.102372301807428

Testing with fpm

The tester program can be run with the following command

$ fpm test

This will read the file test/COULTEST.in and produce a file test/COULTEST.out, whose output can be compared to the reference file test/COULTEST.REF.

Reference(s)

[1] A. R. Barnett The calculation of spherical Bessel and Coulomb functions, Computational Atomic Physics: Electron and Positron Collisions with Atoms and Ions. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. 181-202. URL: https://link.springer.com/chapter/10.1007/978-3-642-61010-3_9