Physics of many-body resonances with complex scaling and applications to light unstable nuclei

Abstract

We review the exotic phenomena in light unstable nuclei with a focus on many-body resonances, which can decay into more than two constituents, and are frequently observed in unstable nuclei above the three-body threshold energy. The complex scaling transformation of the Schrödinger equation is a powerful method for describing many-body resonances, because it separates the continuum spectra into resonant and non-resonant continuum ones. Since the asymptotic wave functions of the resonances are regularized in the complex scaling, many-body resonances are described using the \(L^2\) basis functions in the eigenvalue problem. The properties of many-body resonances can then be discussed in the same way as those of the bound states. We apply the complex scaling to the system consisting of a stable nucleus and valence nucleons and investigate many-body resonances in neutron-rich and proton-rich light nuclei. Using the eigenstates obtained with the complex scaling, we construct the extended completeness relation and the Green’s function. They are used to calculate the level densities and the general transition strengths into many-body unbound states. We also discuss the interpretation of the complex expectation values associated with resonances, which remains an open problem. We propose a possible scheme for it in terms of the complex-scaled Green’s function.