INVERTING SPECULAR NEUTRON REFLECTIVITY. C. F. Majkrzak and N. F. Berk, Materials Science and Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899-0001, USA

Recent progress has been made in the problem of measuring the phase of neutron reflectivity, thereby opening new possibilities for the analysis of specular reflectometry, including the determination of scattering length densities by direct inversion of data. We describe two approaches which we have recently developed.

In one [1] both the complex reflection coefficient and the measured reflectivity are shown to be expressed by the same three functions of the elements of a 2X2 transfer matrix. These functions are measurable from the reflectivity spectra of three samples, each consisting of the same unknown film and one of three known reference layers. While this method requires three measurements, it entails only algebraic and local extraction of the reflection amplitude, the phase determination at each wavevector depending only on data at that point.

A second method [2] uses a single reflectivity spectrum but is restricted to mirror symmetric films, i.e., films which present the same scattering length density profile from either direction. Often such potentials may be formed by abbutting identical specimens of the film of interest. The phase of reflection for symmetric potentials of known, finite length is determined by the phase of transmission, which is recoverable from the reflectivity using a logarithmic dispersion relation.

Knowledge of the complex reflection coefficient enables direct inversion of neutron reflectometry using the Gel'fand-Levitan-Marchenko integral equation or related methods. Examples will be discussed.

[1] C.F. Majkrzak and N.F. Berk, Phys. Rev. B 52, 10827 (1995).

[2] N.F. Berk and C.F. Majkrzak, J. Phys. Soc. Japan, to be published.