ELECTRON-SCATTERING RESPONSE FUNCTIONS FROM THEIR STIELTJES TRANSFORMS

The possibility to obtain the electro-nuclear response functions from the knowledge of their Stieltjes transforms is investigated. The deute ron longitudinal response is taken as a test case. The Stieltjes trans form is calculated using closure. This leads to a dynamical equation s imilar to a bound-state Schrodinger equation, which can possibly be so lved for few-body systems. Various methods of reconstructing the respo nse are considered. Very good results are always obtained in the low-e nergy region and for the elastic form factor. For a satisfactory descr iption of the response function over a large energy range, the Stieltj es transform must be known with a rather high precision. Only in speci fic cases one may obtain surprisingly good results with less accurate Stieltjes transforms.