A review of recent results on the model calculations and evaluations connected with the development of a reference charged particle cross section database for medical radioisotope production is presented. Nuclear reaction models and codes used in those investigations are briefly outlined, with examples of a few calculation results. The method of statistical optimization of experimental data, based on discrete optimization with rational functions (Pade approximation) is described, and the results of evaluations of excitation functions are presented.
Calculations and evaluationsIn evaluation process, with a view to developing recommended nuclear data, three main interconnected areas of activity can be noted: 1. Collection, selection and expert analysis of experimental data. 2. Model calculations with the corresponding codes, analysis of the results and parameters used, and comparison with experimental data. 3. Working out the recommendations, using the selected and corrected information. The first stage is not easy to formalize and reduce to algorithm, because it includes a critical analysis of experimental methods. It should be performed by experimentalists as a rule. At this stage the model calculations can help in the selection of experimental data also. The results of model calculation with well defined parameters can serve as a guide, even when experimental data are not available. At the final stage the selected experimental data and the results of model calculations using various mathematical methods should be analyzed simultaneously.It was recognized at the very first meeting of the IAEA Coordinated Research Project (CRP) on Development of Reference Charged Particle Cross Section Database for Medical Radioisotope Production in 1995 [1] that no evaluation methodology existed and hence modeling would play an important role in predicting cross sections where measurements are either not available or have large discrepancies.*Methods of mathematical physics could be used also in evaluation process.
Methods of statistical optimisation and approximation of experimental data with rational functionsWhen a reasonable amount of independent measurements are available that do not show inexplicable discrepancies between them and when for all points reliable estimations are available, a statistical fit over the selected data points can be performed. For the approximation of experimental data various analytical functions can be used. The polynomial approximation is the simplest, best developed and most popular one. Well-known Spline fit method is based on the approximation by polynomials. However, the physics of the problem often dictates the necessity to use more complicated functions having special analytical features. Rational functions (ratio of two polynomials) represent the more general class of analytical functions as compared with polynomials. In particular, these functions enable to describe in a natural way the nuclear reaction cross sections in the resonance region, which are determined by the positions of poles ...