Hartree-Fock Gamow basis from realistic nuclear forces

Abstract

The development of the radioactive nuclear beams has made it possible to study the exotic nuclei near the drip line. The theoretical description of these nuclei which are far from the valley of stability is still a challenge in nuclear physics. These nuclei exhibit unusual properties such as halo densities and weak bindings. The coupling to the continuum is needed for the theoretical description. The Gamow shell model which extends the traditional shell model to the complex plane, can efficiently include the continuum coupling. This model unifies nuclear structure and reaction properties, and has proven to be a promising tool for the descriptions of weakly bound and unbound nuclei. The starting point of the Gamow shell model is the Berggren completeness where bound, resonant (or Gamow) and scattering states are treated on an equal footing. Employing the Berggren basis, first principle calculations can also be extended to study weak-binding nuclei and nuclear reactions. A big concern is how to obtain the single-particle Berggren basis which is used to construct the Slater determinants in many-body calculations. The single-particle basis in Gamow shell-model calculations are normally constructed from a Woods-Saxon potential with parameters fitted to experimental single-particle energies. However, in a fully microscopic approach, the single-particle basis constructed from the nucleon-nucleon interaction is preferred. In this paper, we present a method to generate the Berggren basis microscopically from realistic nucleon-nucleon forces. The obtained basis is called Hartree-Fock (HF) Gamow basis. We first performed the HF iteration in harmonic oscillator basis, and then the HF potential obtained is analytically continued to the complex- k plane. The continuation is accomplished directly by a basis transformation in which the complex Laguerre polynomials are used. By discretizing the integral of the Schrodinger equation in momentum space, the equation becomes a complex symmetric eigenvalue problem. The HF Gamow basis can be obtained by diagonalizing the complex symmetric matrix. As examples, we apply this method to 4He and 22O with the softened chiral N3LO potential. The single-particle p3/2 resonant state in 4He and d3/2 resonance state in 22O are obtained and the numerical convergence is checked. We also discuss the method to obtain the resonance state from the phase shifts of the real-energy scattering states. With the phase-shift method, the obtained 22O neutron d3/2 resonance state is consistent with the result of the complex-plane calculation. The Gamow basis obtained can be further used in many-body calculations of weakly bound nuclei.