A singular value decomposition is used to determine how much and what kind of information about a potential surface is obtainable from a given set of measurements. From the functional sensitivities which relate a set of observable cross sections to the potential, an orthogonal set of potential variations is produced which provides a basis set for describing errors in the potential model. Corresponding to each basis function is an image vector representing a linear combination of cross sections which is the observable response to that particular correlated potential variation. The inclusion of realistic models of measurement uncertainties and potential model uncertainties in the analysis makes possible the division of the potential variation space spanned by the potential variation basis into (i) a subspace of measurable model errors and (ii) a complementary subspace of model errors which the proposed measurements will be unable to estimate. The analysis procedure may be used to assess the value of proposed measurements for inversion, and the technique is compatible with an allied inversion method under development. The method is illustrated for the He-H2 rigid rotor system using as observables a candidate set of generalized cross sections which could be obtained from measurements of viscosity and thermal conductivity in the presence and absence of a magnetic field. The set of observables considered here is found to be capable of providing five distinguishable pieces of information, primarily about the repulsive potential wall and its anisotropy. Field effect measurements of the quality now available are thus shown to offer a means for refining existing models of the anisotropy of the rare-gas-diatom interaction.
All Science Journal Classification (ASJC) codes
- General Physics and Astronomy
- Physical and Theoretical Chemistry