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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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Abstract. Cluster structures in 19 Ne are studied by the microscopic and macroscopic cluster models. In the microscopic calculation, the coupled-channels problem of ( 3 He+ 16 O) + (α+ 15 O) is solved, and the adiabatic energy surfaces, which are the series of the energy eigenvalues as a function of the He-O distance, are investigated. In the adiabatic energy curves, the several local minima are generated in the spatial region of the small core distance, where the neutron hole inside of the He or O nucleus is strongly coupled to the residual nuclei. The energy spectra, which are constructed from the strong coupling states, nicely reproduce the the low-lying energy levels in the 19 Ne nucleus. In the macroscopic approach, the α + 15 O potential is evaluated from the elastic scattering of the α + 15 N system, and the resonant levels of the α + 15 O system are calculated under the absorbing boundary condition. The potential model predicts the existence of the resonances above the α threshold, which has a weak-coupling scheme of the α particle and one hole inside of the 16 O nucleus. The extended microscopic calculations of ( 3 He+ 16 O) + (α+ 15 O) + ( 5 He+ 14 O) are performed in order to see the coupling effect of the 5p-2h configuration, which corresponds to the shell model limit of the 5 He + 14 O cluster configuration. The extended calculation suggests that the 5 He + 14 O configuration plays an important role on the formation of the 3/2 + resonance at 0.5 MeV with respect to the α threshold. IntroductionThe α cluster structures have been extensively studied for the so-called 4N nuclei with N = Z, such as 8 Be = 2α, 12 C = 3α, 16 On the contrary, cluster structures in the 4N systems with a hole in a cluster core, are also interesting research subjects [7][8][9][10][11]. For example, there is a recent study of 11 B = α + α + t, corresponding to a proton hole system of 12 C = 3α [7]. Pioneering work of the hole system is the study of the 19 F nucleus [8][9][10][11]. The 19 F nucleus is the one proton deficient system of 20 Ne, and the rotational bands a

Nuclear radius of three α rotational state in 12 C with a life time of 10 −21 second, which has been expected to have much more extended radius than the ground 12 C nucleus, is speculated from systematic analysis of the differential cross section of the α + 12 C inelastic scattering. Present analysis predicts about 0.6 ∼ 1.0 fm enhancement in the matter radius of the three α rotational state in comparison to the normal radius of the ground state. The spatial extension of the three α rotational state is comparable to the extended radius observed in the neutron halo phenomena.Constraint on the recent ab-initio calculation for the 3α states in 12 C is also discussed.

Cluster structures in 19 Ne are studied by the microscopic cluster model, the generalized twocenter cluster model (GTCM). In the GTCMcalculation, the coupled-channels problem of (3 He+ 16 O) + (α+ 15 O) is solved, and the adiabatic energy surfaces, which are the series of the energy eigenvalues as a function of the He-O distance, are investigated. In the adiabatic energy curves, the several local minima are generated in the spatial region of the small core distance, where the neutron hole inside of the He or O nucleus is strongly coupled to the residual nuclei. The energy spectra, which are constructed from the strong coupling states, nicely reproduce the the low-lying energy levels in the 19 Ne nucleus. lThe extended microscopic calculations of (3 He+ 16 O) + (α+ 15 O) + (5 He+ 14 O) are performed in order to see the coupling effect of the 5p-2h configuration, which corresponds to the shell model limit of the 5 He + 14 O cluster configuration. The extended calculation suggests that the 5 He + 14 O configuration plays an important role on the formation of the 3/2 + resonance at 0.5 MeV with respect to the α threshold.