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 deuteron longitudinal response is taken as a test case. The Stieltjes transform is calculated using closure. This leads to a dynamical equation similar to a bound-state Schrodinger equation, which can possibly be solved for few-body systems. Various methods of reconstructing the response are considered. Very good results are always obtained in the low-energy region and for the elastic form factor. For a satisfactory description of the response function over a large energy range, the Stieltjes transform must be known with a rather high precision. Only in specific cases one may obtain surprisingly good results with less accurate Stieltjes transforms.