Particle-Unstable Nuclei in the Hartree-Fock Theory

Abstract

Ground state energies and decay widths of particle unstable nuclei are calculated within the Hartree-Fock approximation by performing a complex scaling of the many-body Hamiltonian. Through this transformation, the wave functions of the resonant states become square integrable.

Resonant states of deformed nuclei in the complex scaling method

“…Based on the relativistic extension of the ACCC method, the structure of resonant levels was investigated and good pseudospin symmetry was disclosed in realistic nuclei [21,22]. Although it involves the solution of a complex eigenvalue problem which causes some difficulties in practice, the CSM has been widely and successfully used to study resonances in atomic and molecular systems [11,23] and atomic nuclei [24][25][26][27]. Its generalization to the relativistic problem was first outlined by Weder [28].…”

Probing resonances in the Dirac equation with quadrupole-deformed potentials with the complex momentum representation method

“…Moreover, the complex scaled equation can be solved by using the boundstate methods, in which the bound states and resonant states are processed equally. These advantages enable the application of CSM to different theoretical frameworks, including the combinations with the few-body models [14], shell models [15,16], and Hartree-Fock theories [17,18]. More applications can be found in Refs.…”

Real stabilization method for nuclear single-particle resonances

“…In this method, a complex coordinate scaling is introduced to rotate the continuum into the complex energy plane and the wave functions of resonant states, but not scattering states, are transformed into square-integrable functions [10]. Although it involves the solution of a complex eigenvalue problem which causes some difficulties in practice, the CSM has been widely and successfully used to study resonances in atomic and molecular systems [11,12,13] and atomic nuclei [9,10,14,15,16]. The analytical continuation in the coupling constant (ACCC) approach is based on an intuitive idea that a resonant state can be lowered to be bound when the potential becomes more attractive or equivalently the coupling constant stronger, thus a resonant state being related to a series of bound states via an analytical continuation in the coupling constant [17,18,19].…”