We propose a fully quantum-mechanical method of treating four-body nuclear breakup processes in scattering of a projectile consisting of three constituents, by extending the continuum-discretized coupled-channels method. The three-body continuum states of the projectile are discretized by diagonalizing the internal Hamiltonian of the projectile with the Gaussian basis functions. For 6 He+ 12 C scattering at 18 and 229.8 MeV, the validity of the method is tested by convergence of the elastic and breakup cross sections with respect to increasing the number of the basis functions. Effects of the four-body breakup and the Borromean structure of 6 He on the elastic and total reaction cross sections are discussed. PACS numbers: 21.45.+v, 21.60.Gx, 24.10.Eq, The study on neutron-halo nuclei has become one of the central subjects in the unstable nuclear physics since the discovery of such nuclei [1]. In scattering of a two-neutron-halo nucleus such as 6 He and 11 Li, the projectile easily breaks up into its three constituents (n+n+core), indicating that the scattering should be described as a four-body (n+n+core+target) reaction. Then an accurate theory for treating such a fourbody breakup is highly desirable.So far the eikonal and adiabatic calculations were proposed and applied to 6 He and 11 Li scattering around 50 MeV/nucleon [2,3,4,5]. Since these calculations are based on semi-classical approaches, they work well at higher incident energies. In fact, the elastic cross section of 6 He+ 12 C scattering at 229.8 MeV has recently been measured [6] and successfully analyzed by the eikonal calculation with the sixnucleon wave function of 6 He [7]. However, these approaches seem not to be applicable for low-energy scattering such as 12 C( 6 He, 6 He) 12 C at 3 MeV/nucleon [8] measured very recently.In this rapid communication, we present a fully quantummechanical method of treating four-body nuclear breakup. The method is constructed by extending the continuumdiscretized coupled-channels method (CDCC) [9] that treats three-body breakup processes in scattering of the two-body projectile. In CDCC, the total scattering wave function is expanded in terms of bound and continuum states of the projectile. The continuum states are classified by the linear (k) and angular momenta, and they are truncated by setting an upper limit to each quantum number. The k-continuum is then divided into small bins and the continuum states in each bin are averaged into a single state. This procedure of discretization is called the average (Av) method. The S-matrix elements calculated with CDCC converge as the modelspace is extended [9]. The converged CDCC solution is the unperturbed solution of the distorted Faddeev equations, and corrections to the solu- * Electronic address: taku2scp@mbox.nc.kyushu-u.ac.jp tion are negligible within the region of space in which the reaction takes place [10].Also for four-body breakup processes in scattering of the three-body projectile, CDCC has to prepare three-body bound and discretized-continuum states of t...

A new method of pseudostate discretization is proposed for the method of continuum discretized coupled channels to deal with three-body breakup processes. In the method, discrete S-matrix elements to the pseudo (discretized) continuum states are transformed into smooth ones to the exact continuum states of the projectile. As for the basis functions for describing pseudostate wave functions, we take real-and complex-range Gaussian functions, which form in good approximation a complete set in a finite configuration space being important for breakup processes. This "approximate-completeness" property is essential to make transformed S-matrix elements accurate. Moreover, the use of these Gaussian bases is expected to be very useful to describe four-body breakup processes. Accuracy of the method is tested quantitatively for two realistic examples: elastic and projectile-breakup processes in d+ 58 Ni scattering at 80 MeV and those in 6 Li+ 40 Ca at 156 MeV.

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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.

Reaction cross sections (sigma(R)) for 19C, 20C and the drip-line nucleus 22C on a liquid hydrogen target have been measured at around 40A MeV by a transmission method. A large enhancement of sigma(R) for 22C compared to those for neighboring C isotopes was observed. Using a finite-range Glauber calculation under an optical-limit approximation the rms matter radius of 22C was deduced to be 5.4+/-0.9 fm. It does not follow the systematic behavior of radii in carbon isotopes with N < or = 14, suggesting a neutron halo. It was found by an analysis based on a few-body Glauber calculation that the two-valence neutrons in 22C preferentially occupy the 1s(1/2) orbital.