Study of the nuclear matter distribution and isoscalar transition rates of 48Ca, 50Ti and 52Cr by scattering of 104 MeV alpha-particles

The differential cross-sections for elastic and inelastic scattering of 104 MeV α-particles on 50Ti and 52Cr have been measured for scattering angles in the range 20 <= THETAsub(CM) <= 950. Additionally using previously measured data for 48Ca, the cross-sections of the N = 28 isotopic sequence 48Ca-50Ti-52Cr were analyzed on the basis of the generalized optical model. Study of the angular distribution of the elastic scattering, using modified phenomenological and microscopic methods, leads to well defined and consistent values for moments of the potentials and of the matter distributions. In particular, the Fourier-Bessel method leads to a nearly model-independent determination of the differences in isotonic radii and also to a realistic determination of error bars. For the analysis of the inelastic scattering a new method is introduced, which strongly reduces the model dependence which arises when simple analytic expressions are used for the form factors (the form of the coupling potentials). For this purpose the Fourier-Bessel method has been extended to the analysis of inelastic scattering using the collective vibrational model. Using the identities between the integral moments of a folded potential and of the underlying nuclear matter distribution, isoscalar transition rates have been derived. The extracted values are confirmed by an explicit folding model analysis. Furthermore, the folding model calculations show that the density dependence of the effective interaction between α-particle and target nucleons must be taken into account also in the analysis of inelastic scattering. (orig.)