Abstract
Abstract The complex scaling method (CSM) is one of the most powerful methods of describing the resonances with complex energy eigenstates based on non-Hermitian quantum mechanics. We present the basic application of CSM to the properties of the unbound phenomena of light nuclei. In particular, we focus on many-body resonant and non-resonant continuum states observed in unstable nuclei. We also investigate the continuum level density (CLD) in the scattering problem in terms of the Green’s function with CSM. We discuss the explicit effects of resonant and non-resonant contributions in CLD and transition strength functions.
Highlights
The physics of resonance is closely related to non-Hermitian physics, because resonances are complex energy states
The description by Siegert is based on a stationary-state picture, and the complex energy state can be obtained as a solution of the time-independent Schrödinger equation under the boundary condition for outgoing waves
We have explained the frameworks of the complex scaling method (CSM) to study many-body resonances and continuum states, and presented applications to many-body nuclear systems in the recently developed physics of unstable nuclei
Summary
The physics of resonance is closely related to non-Hermitian physics, because resonances are complex energy states. Eα − iα /2 describe the energy and decay probability of the emitted α particle, respectively He explained that the decay constant, λ = α /, can be evaluated by a tunneling effect of the α particle with the energy Eα for a potential barrier by the repulsive Coulomb force between the α particle and the daughter nucleus. This description of the decay process is based on a time-dependent picture of the wave function. The description by Siegert is based on a stationary-state picture, and the complex energy state can be obtained as a solution of the time-independent Schrödinger equation under the boundary condition for outgoing waves
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