Complex scaling: Physics of unbound light nuclei and perspective

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.

Structure of continuum states and srength function in the complex scaling method

We present our recent results of the mirror nuclei 5He and 5Li obtained by analyzing structure of continuum states in the complex scaled α + N two-body model. Decomposed scattering cross section and continuum level density of α + N system are discussed.

Borromean Feshbach resonance in $^{11}$Li studied via $^{11}$Li($p$,$p'$)

A dipole resonance of $^{11}$Li is found by a $^9$Li + $n$ + $n$ three-body model analysis with the complex-scaling method. The resonance can be interpreted as a bound state in the $^{10}$Li + $n$ system, i.e., a Feshbach resonance in the $^9$Li + $n$ + $n$ system. As a characteristic feature of the Feshbach resonance of $^{11}$Li, the $^{10}$Li + $n$ threshold is open above the $^{9}$Li + $n$ + $n$ one, which reflects a distinctive property of the Borromean system. A microscopic four-body reaction calculation for the $^{11}$Li($p$,$p'$) reaction at 6 MeV/nucleon is performed by taking into account the resonant and nonresonant continuum states of the three-body system. The calculation of angular distributions of the elastic and inelastic scattering as well as the energy spectrum reproduced a recent experimental result. Furthermore, the $E1$ strength distribution from a Coulomb dissociation experiment was also reproduced in this framework. This means that the existence of the Borromean Feshbach resonance may consistently answer a long-standing open question of an excited state of $^{11}$Li.

Probing Resonances and Pseudospin Symmetry of the Eckart Potential by the Complex Scaling Method within the Relativistic Framework

The complex scaling method is applied to probe the resonances of a Dirac particle in the Eckart potential, along with the corresponding energies and widths obtained. Then, the dependence of the resonant energies and widths on the parameters of the potential is checked. The results indicate that the energy and width of the pseudospin doublets preserve a good pseudospin symmetry. Furthermore, the quality of pseudospin symmetry is correlated with the parameters of the Eckart potential.