Resonance and Continuum Contributions for the Scattering Phase Shift

Abstract

Most of knowledge in nuclear and atomic physics has been obtained through scattering experiments, some of which concern resonance structures and scattering phase shifts of the atomic and nuclear systems. Many interesting phenomena can be seen in terms of the resonance structures. We study a formalism of the scattering theory based on the complex scaling method with an L 2 -basis set such as real-range or complex-range Gaussian basis. In this study, the extended completeness relation (1) in the complex scaling method, which has been proposed by Berggren (2) and Romo (3) is applied to calculations of the Green's function. Using this method, we propose a new approach to calculate the scattering phase shifts in the light nuclear systems where the decomposition of scattering phase shifts into resonances and continuum states can be performed. The decomposition of the scattering phase shifts is very useful to understand the associated resonances and continuum states and to clarify the contributions of each state. In this paper, we show the scattering phase shifts not only for resonance states but also for the continuum states of -n and - systems are computed applying the complex scaling to the -n and - orthogonality condition cluster models (4). In addition, several resonance properties of the J  = 0 + wave are investigated for the simple schematic