Summary: We study and develop the stationary scattering theory for a class of one-body Stark Hamiltonians with short-range potentials, including the Coulomb potential, continuing our study in [T. Adachi et al., “Stationary scattering theory for 1-body Stark operators”, J. Differ. Equations 268, No. 9, 5179–5206 (2020; Zbl 1435.35268)]. The classical scattering orbits are parabolas parametrized by asymptotic orthogonal momenta, and the kernel of the (quantum) scattering matrix at a fixed energy is defined in these momenta. We show that the scattering matrix is a classical type pseudodifferential operator and compute the leading order singularities at the diagonal of its kernel. Our approach can be viewed as an adaption of the method of H. Isozaki and H. Kitada [Sci. Pap. Coll. Arts Sci., Univ. Tokyo 35, 81–107 (1986; Zbl 0615.35065)] used for studying the scattering matrix for one-body Schrödinger operators without an external potential. It is more flexible and more informative than the more standard method used previously by Kvitsinsky-Kostrykin [“Potential scattering in a homogeneous external electrostatic field”, Theor. Math. Phys. 75, No. 3, 619–629 (1988; doi:10.1007/BF01036263); translation from Teor. Mat. Fiz. 75, No. 3, 416–430 (1988)] for computing the leading order singularities of the kernel of the scattering matrix in the case of a constant external field (the Stark case). Our approach relies on Sommerfeld’s uniqueness result in Besov spaces, microlocal analysis as well as on classical phase space constructions.