Continuum-discretized coupled-channels method for four-body nuclear breakup in 6^6He+12^{12}C scattering

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.Comment: 5 pages, 6 figures, uses REVTeX 4, submitted to Phys. Rev.

Multi-cluster dynamics in Λ13C^{13}_\Lambda{\rm C} and analogy to clustering in 12C^{12}{\rm C}

We investigate structure of $^{13}_\Lambda{\rm C}$ and discuss the difference and similarity between the structures of $^{12}{\rm C}$ and $^{13}_\Lambda{\rm C}$ by answering the questions if the linear-chain and gaslike cluster states, which are proposed to appear in $^{12}{\rm C}$, survives, or new structure states appear or not. We introduce a microscopic cluster model called, Hyper-Tohsaki-Horiuchi-Schuck-R\"opke (H-THSR) wave function, which is an extended version of the THSR wave function so as to describe $\Lambda$ hypernuclei. We obtained two bound states and two resonance (quasi-bound) states for $J^\pi=0^+$ in $^{13}_\Lambda{\rm C}$, corresponding to the four $0^+$ states in $^{12}{\rm C}$. However, the inversion of level ordering between the spectra of $^{12}{\rm C}$ and $^{13}_\Lambda{\rm C}$, i.e. that the $0_3^+$ and $0_4^+$ states in $^{13}_\Lambda{\rm C}$ correspond to the $0_4^+$ and $0_3^+$ states in $^{12}{\rm C}$, respectively, is shown to occur. The additional $\Lambda$ particle reduces sizes of the $0_2^+$ and $0_3^+$ states in $^{13}_\Lambda{\rm C}$ very much, but the shrinkage of the $0_4^+$ state is only a half of the other states. In conclusion, the Hoyle state becomes quite a compact object with ${^{9}_\Lambda{\rm Be}}+\alpha$ configuration in $^{13}_\Lambda{\rm C}$ and is no more gaslike state composed of the $3\alpha$ clusters. Instead, the $0_4^+$ state in $^{13}_\Lambda{\rm C}$, coming from the $^{12}{\rm C}(0_3^+)$ state, appears as a gaslike state composed of $\alpha+\alpha+^{5}_\Lambda{\rm He}$ configuration, i.e. the Hoyle analog state. A linear-chain state in a $\Lambda$ hypernucleus is for the first time predicted to exist as the $0_3^+$ state in $^{13}_\Lambda{\rm C}$ with more shrunk arrangement of the $3\alpha$ clusters along $z$-axis than the $3\alpha$ linear-chain configuration realized in the $^{12}{\rm C}(0_4^+)$ state.Comment: 9 pages, 6 figures, figures rearranged, accepted for publication in PL

Light Ξ\Xi hypernuclei in four-body cluster models

Detailed structure calculations in $^{\: 12}_{\Xi^-}$Be, $^{\: 5}_{\Xi^-}$H, $^{\: 9}_{\Xi^-}$Li, $^{\: 7}_{\Xi^-}$H and $^{\:10}_{\Xi^-}$Li are performed within the framework of the microscopic two-, three- and four-body cluster models using the Gaussian Expansion Method.Comment: 14 pages, 19 figures. To be published in Phys. Rev.

New treatment of breakup continuum in the method of continuum discretized coupled channels

A new method of pseudo-state discretization is proposed for the method of continuum discretized coupled channels (CDCC) to deal with three-body breakup processes. We propose real- and complex-range Gaussian bases for the pseudo-state wave functions, and show that they form in good approximation a complete set in the configuration space which is important for breakup processes. Continuous S-matrix elements are derived with the approximate completeness from discrete ones calculated by CDCC. Accuracy of the method is tested quantitatively for two realistic examples, d+$^{58}$Ni scattering at 80 MeV and $^{6}$Li+$^{40}$Ca scattering at 156 MeV with the satisfactory results. Possibility of application of the method to four-body breakup processes is also discussed.Comment: 10 pages, 14 Postscript figures, uses REVTeX 4, submitted to Phys. Rev.

Four-body structure of Λ7^7_{\Lambda}Li and ΛN\Lambda N spin-dependent interaction

Two spin-doublet states of %$3/2^+$-$1/2^+$ and $7/2^+$-$5/2^+$ in $^7_{\Lambda}$Li are studied on the basis of the $\alpha +\Lambda +n+p$ four-body model. We employ the two-body interactions which reproduce the observed properties of any subsystems composed of $\alpha N$, $\alpha \Lambda$ and $\alpha NN$, and $\alpha \Lambda N$. Furthermore, the $\Lambda N$ interaction is adjusted so as to reproduce the $0^+$-$1^+$ splitting of in $^4_{\Lambda}$H. The calculated energy splittings of $3/2^+$-$1/2^+$ and $7/2^+$-$5/2^+$ states in $^7_{\Lambda}$Li are 0.69 MeV and 0.46 MeV, which are in good agreement with the resent observed data. The spin-dependent components of the $\Lambda N$ interaction are discussed.Comment: 6 pages, 2 figures, published to be in Phys. Rev.

Continuum-discretized coupled-channels method for four-body breakup reactions

Development of the method of CDCC (Continuum-Discretized Coupled-Channels) from the level of three-body CDCC to that of four-body CDCC is reviewed. Introduction of the pseudo-state method based on the Gaussian expansion method for discretizing the continuum states of two-body and three-body projectiles plays an essential role in the development. Furthermore, introduction of the complex-range Gaussian basis functions is important to improve the CDCC for nuclear breakup so as to accomplish that for Coulomb and nuclear breakup. A successful application of the four-body CDCC to $^6$He+$^{12}$C scattering at 18 and 229.8 MeV is reported.Comment: Latex file of revtex4 class, 14 pages, 10 figures. A talk given at the Workshop on Reaction Mechanisms for Rare Isotope Beams, Michigan State University, March 9-12, 2005 (to appear in an AIP Conference Proceedings