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

TL;DR

This paper reviews recent advances in the complex scaling method (CSM) for studying many-body resonances and continua in light nuclei, enabling detailed analysis of weakly bound nuclear states and their reactions.

Contribution

It introduces recent developments in applying CSM to complex nuclear systems, including the construction of completeness relations and Green's functions for reaction calculations.

Findings

Successful identification of many-body resonant states in weakly bound nuclei.

Effective separation of resonant and non-resonant continuum states using CSM.

Good agreement with experimental data in theoretical calculations.

Abstract

The complex scaling method (CSM) is a useful similarity transformation of the Schr\"odinger 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.