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Manuscript Title: Exact Slater integrals.
Authors: L.B. Golden
Program title: SLATER INTEGRALS
Catalogue identifier: ACYB_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 14(1978)255
Programming language: PL/1.
Computer: IBM 370/168.
Operating system: IBM OS-21.8, HASP - 2.T4E.
RAM: 1K words
Word size: 32
Keywords: Atomic physics, Non-numeric, Hydrogenic, Slater integral, Wave function.
Classification: 2.7.

Nature of problem:
In atomic structure calculations, one has to evaluate the Slater integrals. In the present program, we evaluate exactly the Slater integral when hydrogenic wave functions are used for the bound-state orbitals.

Solution method:
When hydrogenic wave functions are used, the Slater integrals involve integrands which can be written in the form of a product of an expotential, exp(alphax) and a known analytic polynomial function, f(x). By repeated partial integration such an integral can be expressed in terms of a finite series involving the expotential, the polynomial function and its derivatives. PL/1-FORMAC has a built-in subroutine that will analytically find the derivatives of any multinomial. Thus, the finite series and hence the Slater integral can be evaluated analytically.

Restrictions:
FORMAC square roots should be in the form ROOT.(NUMBER). The function, f(x), must be of order 20 or less. The order can be increased by increasing the upper limit on each occurence of the DO function in the program. There must be no numbering or ID data on the data cards.

Unusual features:
This program is non-numeric routine. It evaluates the Slater integral analytically. The results are exact.

Running time:
The running times for the test run are as follows: Compile time - 2 s, CPU time - 5 s, Elapsed time - 12 s.