The complex scaling method (CSM) is a useful similarity transformation of the Schrodinger equation, in which bound-state spectra are not changed but continuum spectra are separated into resonant and non-resonant continuum ones. Because the asymptotic
wave functions of the separated resonant states are regularized by the CSM, many-body resonances can be obtained by solving an eigenvalue problem with the $L^2$ basis functions. Applying this method to a system consisting of a core and valence nucleons, we investigate many-body resonant states in weakly bound nuclei very far from the stability lines. Non-resonant continuum states are also obtained with the discretized eigenvalues on the rotated branch cuts. Using these complex eigenvalues and eigenstates in CSM, we construct the extended completeness relations and Greens functions to calculate strength functions and breakup cross sections. Various kinds of theoretical calculations and comparisons with experimental data are presented.
We investigate the three-body Coulomb breakup of a two-neutron halo nucleus $^{11}$Li. We use the coupled-channel $^9$Li + $n$ + $n$ three-body model, which includes the coupling between last neutron states and the various $2p$-$2h$ configurations in
$^9$Li due to the tensor and pairing correlations. The three-body scattering states of $^{11}$Li are described by using the combined methods of the complex scaling and the Lippmann-Schwinger equation. The calculated breakup cross section successfully reproduces the experiments. The large mixing of the s-state in the halo ground state of $^{11}$Li is shown to play an important role in explanation of shape and strength of the breakup cross section. In addition, we predict the invariant mass spectra for binary subsystems of $^{11}$Li. It is found that the two kinds of virtual s-states of $^9$Li-$n$ and $n$-$n$ systems in the final three-body states of $^{11}$Li largely contribute to make low-lying peaks in the invariant mass spectra. On the other hand, in the present analysis, it is suggested that the contributions of the p-wave resonances of $^{10}$Li is hardly confirmed in the spectra.
The breakup cross section (BUX) of 22C by 12C at 250 MeV/nucleon is evaluated by the continuum-discretized coupled-channels method incorporating the cluster-orbital shell model (COSM) wave functions. Contributions of the low-lying 0+_2 and 2+_1 reson
ances predicted by COSM to the BUX are investigated. The 2+_1 resonance gives a narrow peak in the BUX, as in usual resonant reactions, whereas the 0+_2 resonant cross section has a peculiar shape due to the coupling to the nonresonant continuum, i.e., the Fano effect. By changing the scattering angle of 22C after the breakup, a variety of shapes of the 0+_2 resonant cross sections is obtained. Mechanism of the appearance of the sizable Fano effect in the breakup of 22C is discussed.
We study the resonance spectroscopy of the proton-rich nucleus 7B in the 4He+p+p+p cluster model. Many-body resonances are treated on the correct boundary condition as the Gamow states using the complex scaling method. We predict five resonances of 7
B and evaluate the spectroscopic factors of the 6Be-p components. The importance of the 6Be(2+)-p component is shown in several states of 7B, which is a common feature of 7He, a mirror nucleus of 7B. For only the ground state of 7B, the mixing of 6Be(2+) state is larger than that of 6He(2+) in 7He, which indicates the breaking of the mirror symmetry. This is caused by the small energy difference between 7B and the excited 6Be(2+) state, whose origin is the Coulomb repulsion.
We propose a new method to describe three-body breakups of nuclei, in which the Lippmann-Schwinger equation is solved combining with the complex scaling method. The complex-scaled solutions of the Lippmann-Schwinger equation (CSLS) enables us to trea
t boundary conditions of many-body open channels correctly and to describe a many-body breakup amplitude from the ground state. The Coulomb breakup cross section from the 6He ground state into 4He+n+n three-body decaying states as a function of the total excitation energy is calculated by using CSLS, and the result well reproduces the experimental data. Furthermore, the two-dimensional energy distribution of the E1 transition strength is obtained and an importance of the 5He(3/2-) resonance is confirmed. It is shown that CSLS is a promising method to investigate correlations of subsystems in three-body breakup reactions of the weakly-bound nuclei.
We make a systematic study of Li isotopes (A=9,10,11) in the tensor optimized shell model for 9Li and treat the additional valence neutrons in the cluster model approach by taking into account the Pauli-blocking effect caused by the tensor and pairin
g correlations. We describe the tensor correlations in 9Li fully in the tensor-optimized shell model, where the variation of the size parameters of the single particle orbits is essential for getting strong tensor correlations. We have shown in our previous study that in $^{10,11}$Li the tensor and pairing correlations in 9Li are Pauli-blocked by additional valence neutrons, which make the p-shell configurations pushed up in energy. As a result, the $s^2$ valence neutron component increases to reveal the halo structure of 11Li and the inversion phenomenon of the single particle spectrum in 10Li arises. Following the previous study, we demonstrate the reliability of our framework by performing a detailed systematic analysis of the structures of $^{9,10,11}$Li, such as the charge radius, the spatial correlation of halo neutrons of 11Li and the electromagnetic properties of Li isotopes. The detailed effects of the Pauli-blocking on the spectroscopic properties of $^{10,11}$Li are also discussed. It is found that the blocking acts strongly for the 11Li ground state rather than for 10Li and for the dipole excited states of 11Li, which is mainly caused by the interplay between the tensor correlation in 9Li and the halo neutrons. The results obtained in these analyses clearly show that the inert core assumption of 9Li is not realistic to explain the anomalous structures observed in $^{10,11}$Li. For the dipole excitation spectrum of 11Li, the effect of the final state interactions is discussed in terms of the dipole strength function.
