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We formulate a scattering radius, which will be demonstrated to be a good measure of the spatial size of a general exclusive reaction. The scattering radius is presented in a framework of the partial-wave expansion method in a general two-body scattering problem. A microscopic coupled-channel calculation is performed for proton scattering by 12 C in the range of the proton's incident energy, E p = 29.95-200 MeV, and the scattering radii are evaluated for elastic scattering and inelastic scattering, going to the Hoyle 0 + 2 state with a well-developed 3α structure. A prominent enhancement of the scattering radius is clearly confirmed in the 3α final channel in comparison to the elastic channel. The scattering radius is also calculated for excitation to the giant monopole resonance (GMR) in a microscopic coupled-channel framework. The scattering radius for the 3α excitation is much more enhanced than the scattering radius for the GMR excitation. The proton's incident-energy dependence of the scattering radius is also investigated, and the energy systematics strongly suggest that the scattering radius can characterize the spatial size of a reaction area, which is determined by the matter radius of a nucleus excited to a final state.

The rotational bands of α + 15 O(1/2 − ) in 19 Ne are calculated by employing a simple potential model. The α − 15 O interaction potential is constructed from the calculation of the 20 Ne = α + 16 O structure and the α + 15 N elastic scattering. The resonant levels and their decay width are identified by imposing the absorbing boundary condition. The present calculations predict the sequence of the discrete and overlapping resonances in the negative-and positive-parity states of 19 Ne, respectively. The excitation function of the α + 15 O elastic scattering is also calculated, and the appropriate condition to observe the resonances is discussed.

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