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.

20 pages, 18 figures

References in corpus (28)

• Exotic modes of excitation in atomic nuclei far from stability
• Shell Model in the Complex Energy Plane
• Recent development of complex scaling method for many-body resonances and continua in light nuclei
• Roles of the tensor and pairing correlations on the halo formation in 11Li
• Prediction for a four-neutron resonance
• Investigations of three, four, and five-particle exit channels of levels in light nuclei created using a 9C beam
• Ab-initio no-core Gamow shell model calculations of multi-neutron systems
• Can realistic nuclear interactions tolerate a resonant tetraneutron ?
• Resonances of 7He in the complex scaling method
• New description of four-body breakup reaction
• Di-neutron clustering and deuteron-like tensor correlation in nuclear structure focusing on 11Li
• $S$-wave fully charmed tetraquark resonant states
• Non-resonant Density of States Enhancement at Low Energies for Three or Four Neutrons
• Coulomb breakup reactions of ${}^{11}$Li in the coupled-channel ${}^9$Li~+~$n$~+~$n$ three-body model
• Five-body resonances of 8He using the complex scaling method
• Low energy structures in nuclear reactions with 4n in the final state
• Decomposition of scattering phase shifts and reaction cross sections using the complex scaling method
• Five-body resonances in ${}^8$He and ${}^8$C using the complex scaling method
• Possible interpretation of the complex expectation values associated with resonances
• Resonances and scattering in microscopic cluster models with the complex-scaled generator coordinate method
• Mirror symmetry breaking in He isotopes and their mirror nuclei
• Structure of neutron-rich He $\Lambda$ hypernuclei using the cluster orbital shell model
• Modeling the electric dipole strength of neutron-rich ${}^8$He: Prediction of multineutron collective excitations
• Soft dipole resonance in neutron-rich ${}^8$He
• Analytic Map of Three-Channel S Matrix -Generalized Uniformization and Mittag-Leffler Expansion-
• Soft dipole resonance in ${}^8$C and its isospin symmetry with ${}^8$He
• Analysis of bound and resonant states of doubly heavy tetraquarks with spin $J\le 2$
• Complex scaling calculation of phase shifts for positron collisions with positive ions