RESUMO
In this study it is reported the retrieval of the phonon density of states for solid aluminium from the temperature dependent heat capacity, the inverse heat capacity problem. The singularity in this ill posed problem was removed by the Tikhonov approach with the regularization parameter calculated as the L curve maximum curvature. A sensitivity analysis was also coupled to the numerical inversion. For temperatures ranging from 15 K to 300 K the heat capacity results, calculated from the inverted phonon density of states, yields an average error of about 0.3%, within the experimental errors that ranged from 2% to 3%. The predicted entropy, enthalpy and Gibbs free energy are also within experimental errors.
RESUMO
The present work discusses quantum phase shift sensitivity analysis with respect to the potential energy function. A set of differential equations for the functional derivative of the quantum phase shift with respect to the potential energy function was established and coupled with the variable phase equation. This set of differential equations provides a simple, exact and straightforward way to establish the sensitivity matrix. The present procedure is easier to use than the finite difference approach, in which several direct problems have to be addressed. Furthermore, integration of the established equations can be used to demonstrate how the sensitivity phase shift is accumulated as a function of the interatomic distance. The potential energy function was refined to produce a better quality function. The average error on the phase shift decreased from 9.8% in the original potential function to 0.13% in the recovered potential. The present procedure is an important initial step for further work towards recovering potential energy functions in upper dimensions or to recovering this function from cross sections.
