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Manuscript Title: A program to calculate magnetic form factors for transition metal systems.
Authors: L.A. Barnes, G.S. Chandler, B.N. Figgis, D.C. Khan
Program title: MAGFAC
Catalogue identifier: AABR_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 36(1985)373
Programming language: Fortran.
Computer: CYBER CDC720.
RAM: 170K words
Keywords: Solid state physics, Crystal field, Neutron scattering, Form factor magnetic, Spin, Orbital, Spherical, Aspherical, Density magnetization.
Classification: 7.3.

Nature of problem:
MAGFAC calculates magnetic form factors for a transition metal ion under the influence of a crystal field. This can be defined, in the formalism of Trammell, as the expectation value of the operator representing the magnetic interaction of the neutron with the ion at a particular lattice site. The program calculates each Cartesian component of the form factor, as well as its magnitude. The spherical, dipole approximation and free atom form factors are also calculated.

Solution method:
The wavefunction for the ion is expressed as a sum of n-electron or n- hole Slater determinants of single particle wvefunctions. The program determines the non-zero matrix elements of the interaction operator, via the Condon-Shortley rules, for the input wavefinction. The spin and orbital operator contributions are evaluated using standard angular momenta relations. These non-zero matrix elements are expanded in terms of spherical harmonics, Ylm, Condon-Shortley coefficients, C**L(l,m;l', m'), and the radial integrals <jL>and <gL>. The form factors are thus calculated for any reflaection (h,k,l) in the Cartesian system determined by the user.

MAGFAC is restricted to Hartree-Fock level crystal field wavefunctions for transition metal systems with a partially filled 3d shell. The structure of the program enables the case of 4f electrons to be incorporated in a straightforward manner. The present dimensions restrict the input wavefunction to 50 determinants, with 5 electrons or holes maximum for d electrons. The radial function is represented by a basis set of up to 5 Slater Type Orbitals, and up to 350 reflections are allowed.

Running time:
This varies widely from problem to problem. A typical run with 20 three-electron determinants and 340 reflections was accomplished in 16 s on the Cyber CDC720. The test cases here all took <= 0.6 s. Compilation time is ~12 s.