This paper shows a brief review on CDCC and the microscopic reaction theory as a fundamental theory of CDCC. The Kerman-McManus-Thaler theory for nucleon-nucleus scattering is extended to nucleus-nucleus scattering. New development of four-body CDCC is presented. An accurate method of treating inclusive reactions is presented as an extension of CDCC and the Glauber model. §1. IntroductionThe construction of microscopic reaction theory is one of the most important subjects in nuclear physics. It is a goal of the nuclear reaction theory. Furthermore, the construction is essential for many applications. Particularly for the scattering of unstable nuclei, there is no reliable phenomenological optical potential, since measurements of the elastic scattering are not easy. An important theoretical tool of analyzing inclusive reactions is the Glauber model. 1) The theoretical foundation of the model is shown in Ref.2). The model is based on the eikonal and the adiabatic approximation. It is well known that the adiabatic approximation makes the removal cross section diverge when the Coulomb interaction is included. The Glauber model has thus been applied mainly for lighter targets in which the Coulomb interaction is negligible; see for example Refs. 3)-9) and Refs. 10), 11) for Coulomb corrections to the Glauber model.Meanwhile, the method of continuum discretized coupled channels (CDCC) 12), 13) is an accurate method of treating exclusive reactions such as the elastic scattering and the elastic breakup reaction in which the target is not excited. The theoretical foundation of CDCC is shown in Refs. 14)-16). Actually, CDCC has succeeded in reproducing data on the scattering of not only stable nuclei but also unstable nuclei; see for example Refs. 17)-28) and references therein. The dynamical eikonal approximation 29) is also an accurate method of treating exclusive reactions at intermediate and high incident energies where the eikonal approximation is reliable. The nucleon removal reaction is composed of the exclusive elastic-breakup component and the inclusive nucleon-stripping component. CDCC and the dynamical eikonal approximation can evaluate the elastic-breakup cross section, but not the stripping cross section.The experimental exploration of halo nuclei is moving from lighter nuclei such as He and C isotopes to relatively heavier nuclei such as Ne isotopes. Very recently, Takechi et al. measured the interaction cross section σ I for the scattering of 28−32 Ne at 240 MeV/nucleon and found that σ I is quite large particularly for 31 Ne. 30) A halo structure of 31 Ne was reported with the experiment on the one-neutron removal reaction. 31) This is the heaviest halo nucleus in the present stage suggested experi-

The deformation of Ne isotopes in the island-of-inversion region is determined by the doublefolding model with the Melbourne g-matrix and the density calculated by the antisymmetrized molecular dynamics (AMD). The double-folding model reproduces, with no adjustable parameter, the measured reaction cross sections for the scattering of 28−32 Ne from 12 C at 240MeV/nucleon. The quadrupole deformation thus determined is around 0.4 in the island-of-inversion region and 31 Ne is a halo nuclei with large deformation. We propose the Woods-Saxon model with a suitably chosen parameterization set and the deformation given by the AMD calculation as a convenient way of simulating the density calculated directly by the AMD. The deformed Woods-Saxon model provides the density with the proper asymptotic form. The pairing effect is investigated, and the importance of the angular momentum projection for obtaining the large deformation in the island-of-inversion region is pointed out.

We perform the first quantitative analysis of the reaction cross sections of 28−32 Ne by 12 C at 240 MeV/nucleon, using the double-folding model (DFM) with the Melbourne g-matrix and the deformed projectile density calculated by the antisymmetrized molecular dynamics (AMD). To describe the tail of the last neutron of 31 Ne, we adopt the resonating group method (RGM) combined with AMD. The theoretical prediction excellently reproduce the measured cross sections of 28−32 Ne with no adjustable parameters. The ground state properties of 31 Ne, i.e., strong deformation and a halo structure with spin-parity 3/2 − , are clarified.

Isotope-dependence of measured reaction cross sections in scattering of 28−32 Ne isotopes from 12 C target at 240 MeV/nucleon is analyzed by the double-folding model with the Melbourne g-matrix. The density of projectile is calculated by the mean-field model with the deformed Wood-Saxon potential. The deformation is evaluated by the antisymmetrized molecular dynamics. The deformation of projectile enhances calculated reaction cross sections to the measured values.

We analyze recently measured total reaction cross sections for [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] Mg isotopes incident on 12 C targets at 240 MeV/nucleon by using the folding model and antisymmetrized molecular dynamics (AMD). The folding model well reproduces the measured reaction cross sections, when the projectile densities are evaluated by the deformed Woods-Saxon (def-WS) model with AMD deformation. Matter radii of [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] Mg are then deduced from the measured reaction cross sections by fine tuning the parameters of the def-WS model. The deduced matter radii are largely enhanced by nuclear deformation. Fully microscopic AMD calculations with no free parameter well reproduce the deduced matter radii for [24][25][26][27][28][29][30][31][32][33][34][35][36] Mg, but still considerably underestimate them for 37,38 Mg. The large matter radii suggest that 37,38 Mg are candidates for deformed halo nucleus. AMD also reproduces other existing measured ground-state properties (spin parity, total binding energy, and one-neutron separation energy) of Mg isotopes. Neutron-number (N ) dependence of deformation parameter is predicted by AMD. Large deformation is seen from 31 Mg with N = 19 to a drip-line nucleus 40 Mg with N = 28, indicating that both the N = 20 and 28 magicities disappear. N dependence of neutron skin thickness is also predicted by AMD.

We present an accurate method of treating the one-neutron removal reaction at intermediate incident energies induced by both nuclear and Coulomb interactions. In the method, the nuclear and Coulomb breakup processes are consistently treated by the method of continuum discretized coupled channels without making the adiabatic approximation to the Coulomb interaction, so that the removal cross section calculated never diverges. This method is applied to recently measured one-neutron removal cross section for 31 Ne+ 12 C scattering at 230 MeV/nucleon and 31 Ne+ 208 Pb scattering at 234 MeV/nucleon. The spectroscopic factor and the asymptotic normalization coefficient of the last neutron in 31 Ne are evaluated. typeset using PTPT E X.cls Ver.0.9

The nonlocality of the microscopic nucleon-nucleus optical potential is commonly localized by the Brieva-Rook approximation. The validity of the localization is tested for the proton+ 90 Zr scattering at the incident energies from 65 MeV to 800 MeV. The localization is valid in the wide incident-energy range.

Glauber theory for nucleus-nucleus scattering at high incident energies is reformulated so as to also be applicable to the scattering at intermediate energies. We test the validity of the eikonal and adiabatic approximations used in the formulation, and discuss the relationship between the present theory and the conventional Glauber calculations using either the empirical nucleon-nucleon profile function or the modified one including the in-medium effect. * )