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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• Tensor-optimized shell model with bare nucleon-nucleon interaction for 4He
• Tensor correlation in 4He and its Effect on the doublet splitting in 5He
• Bound state techniques to solve the multiparticle scattering problem
• Level Density in the Complex Scaling Method
• Exploring the anomaly in the interaction cross section and matter radius of 23O
• Trapped one-dimensional ideal Fermi gas with a single impurity
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• Combination of complex momentum representation and Green's function methods in relativistic mean-field theory
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