THE DETERMINATION OF NUCLEAR-CHARGE DISTRIBUTIONS USING A BAYESIAN MAXIMUM-ENTROPY METHOD

We treat the inference of nuclear charge densities from measurements o f elastic electron scattering cross sections. In order to get the most reliable information from expensively acquired, incomplete and noisy measurements, we use Bayesian probability theory. Very little prior in formation about the charge densities is assumed. We derive a prior pro bability distribution which is a generalization of a form used widely in image restoration based on the entropy of a physical density. From the posterior distribution of possible densities, we select the most p robable one, and show how error bars can be evaluated. These have very reasonable properties, such as increasing without bound as hypotheses about finer scale structures are included in the hypothesis space. Th e methods are demonstrated by using data on the nuclei He-4 and C-12.