Qualitatively, for a plum pudding model atom (where the positive charge of each atom is even diffused throughout the volume of the atom) I think that the deflection of incident alpha particles would be caused by the electrons and not the positive charge at all. Is this correct?
Quantitatively, for a detector at a specific angle with respect to the incident beam, the number of particles per unit area striking the detector is given by the Rutherford formula (source linked here):
where $N_i$ is the number of incident alpha particles, $n$ is the number of atoms per unit volume in target, $L$ is the thickness of the target, $Z$ is the atomic number of the target, $k$ is Coulomb's constant, $e$ is the electron charge, $r$ is the target-detector distance, $KE$ is the kinetic energy of the alpha particles, and $\theta$ is the scattering angle.
For a plum pudding atom, would this formula still hold as is or would it need to be modified?