Recent development of complex scaling method for many-body resonances and continua in light nuclei

Abstract

The complex scaling method (CSM) is a useful similarity transformation of the Schrödinger 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 Green's functions to calculate strength functions and breakup cross sections. Various kinds of theoretical calculations and comparisons with experimental data are presented.

71 pages, 59 figures

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• Resonant states of neutron-rich $\Lambda$ hypernucleus ${}_{\Lambda }^7$He
• Application of a coupled-channel Complex Scaling Method with Feshbach projection to the $K^{-}pp$ system
• High-momentum antisymmetrized molecular dynamics compared with tensor-optimized shell model for strong tensor correlation
• Five-body resonances in ${}^8$He and ${}^8$C using the complex scaling method
• Possible interpretation of the complex expectation values associated with resonances
• Role of quadrupole deformation and continuum effects in the "island of inversion'' nuclei ${}^{28,29,31}$F
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• Modeling the electric dipole strength of neutron-rich ${}^8$He: Prediction of multineutron collective excitations
• Soft dipole resonance in neutron-rich ${}^8$He
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• Cooper pairs in the Borromean nuclei ${}^6$He and ${}^{11}$Li using continuum single particle level density
• Soft dipole resonance in ${}^8$C and its isospin symmetry with ${}^8$He
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• Two-neutron halo structure and anti-halo effect in 31F