We report the creation of a library of computational routines to assist in the analysis of stochastic models of hyperfine interactions. We call this library the stochastic hyperfine interactions modeling library (SHIML). It provides routines written in the C programming language that (1) read a text description of a model for fluctuating hyperfine fields, (2) set up the Blume matrix, upon which the evolution operator of the system depends, and (3) find the eigenvalues and eigenvectors of the Blume matrix so that theoretical spectra of experimental techniques that measure hyperfine interactions can be calculated. The optimized vector and matrix operations of the BLAS and LAPACK libraries are utilized; however, there was a need to develop supplementary code to find an orthonormal set of (left and right) eigenvectors of complex, non-Hermitian matrices. Examples will be presented to illustrate the use of SHIML to generate perturbed angular correlation spectra for the special case of polycrystalline samples when anisotropy terms of higher order than A22 can be neglected.
This work is funded in part by NSF grant DMR 06-06006 (Metals Program) and computational resources were provided in part by KY EPSCoR grant RSF 012-03.
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