RETRIEVAL OF SPIN DENSITIES FROM POLARIZED-NEUTRON DIFFRACTION DATA USING MAXIMUM ENTROPY. R. J. Papoular, Laboratoire Leon Brillouin, CEN-Saclay, 91191 Gif-sur-Yvette Cedex, France

In this work, Maximum-Entropy (MaxEnt) is viewed as a powerful and flexible regularizing tool used to solve an ill-posed linear inverse problem: the retrieval of model-free 3-dimensional magnetization densities m(r) from scarce and noisy data sets of measured flipping ratios. Beside the ability of MaxEnt to reduce truncation effects of the standard Fourier synthesis drastically (Papoular et al, 1990, Europhys. Lett, 429-434), it also brings forth three radical improvements:

* The retrieval of a 2D projection is now a 3D reconstruction problem, which makes use of all the experimental data This results from the nonlinearity of the MaxEnt algorithm. In extreme cases, quite decent projections can be obtained even without a single Bragg reflection from the horizontal scattering plane (Papoular et al, 1995, Acta Cryst, A51, 295-300).

* Previous chemical knowledge can be introduced as a 3D non-uniform prior spin density in real space. This is particularly valuable when the neutron data are too scarce and/or noisy. The features not present in the data are then taken from the best available model for the spin density prior to the experiment (Zheludev et al, 1995, Acta Cryst., A51, 450-455).

* The retrieval of spin densities pertaining to acentric structures can now be achieved, once the flipping ratios pertaining to acentric Bragg peaks have been suitably linearized (Papoular et al, 1994, Phys. Rev. Lett., 72, 1486-1489).

Resulting MaxEnt density maps can and should be used to improve on already existing models, e.g. via a refined multipole expansion.

Collaboration with A. Delapalme (LLB), J. Schweizer, E. Ressouche, A. Zheludev (CENG) and F. Tasset (ILL) is gratefully acknowledged.