An ab-initio Gamow shell model approach with a core

Abstract

Gamow shell model (GSM) is usually performed within the Woods-Saxon (WS) basis in which the WS parameters need to be determined by fitting experimental single-particle energies including their resonance widths. In the multi-shell case, such a fit is difficult due to the lack of experimental data of cross-shell single-particle energies and widths. In this paper, we develop an abinitio GSM by introducing the Gamow Hartree-Fock (GHF) basis that is obtained using the same interaction as the one used in the construction of the shell-model Hamiltonian. GSM makes use of the complex-momentum Berggren representation, then including resonance and continuum components. Hence, GSM gives a good description of weakly bound and unbound nuclei. Starting from chiral effective field theory and employing many-body perturbation theory (MBPT) (called nondegenerateQ-box folded-diagram renormalization) in the GHF basis, a multi-shell Hamiltonian (sd-pf shells in this work) can be constructed. The single-particle energies and their resonance widths can also been obtained using MBPT. We investigated 23−28 O and 23−31 F isotopes, for which multi-shell calculations are necessary. Calculations show that continuum effects and the inclusion of the pf shell are important elements to understand the structure of nuclei close to and beyond driplines.

A Guided Tour of ab initio Nuclear Many-Body Theory

“…sections 2.3.8 and 3.2.4), as well as the GSM Coupled Channel (GSM-CC) approach, which was developed to describe reactions between light projectiles and targets that are treated in the GSM with a core [221,328,329]. Thus far, applications of the GSM-CC have been based on phenomenological valence-space interactions, but new efforts are underway to directly construct suitable Hamiltonians based on EFT principles [220,330], or derive the effective interactions from chiral forces with the techniques discussed in section 2.3 (see [214,215]). Of course, the GSM-CC ideas could also be applied to the No-Core GSM [153,155,218], although the computational complexity would limit such an approach to light nuclei.…”

<italic>Ab initio</italic> calculations of nuclear systems

“…The resonant states are indicated by shading, and their widths (in MeV) are given by the numbers above or below the levels indicated by dashes. The longest shading indicates the 25 O scattering states of the 3/2 + channel. CD-Bonn interaction softened by V low-k is used in this calculation.…”

Recent Progress in Gamow Shell Model Calculations of Drip Line Nuclei

“…Internucleon correlations in GSM are induced by configuration mixing, similarly to conventional SM. GSM has been seen to successfully reproduce many situations of physical interest [5,38]; for example, the resonances of oxygen drip line nuclei [38,41,42] and the neutron halo structure of 31 F [18].…”

“…We applied it to the case of the neutron-rich oxygen isotopes up to the neutron drip line. After that, many extensions of the realistic GSM were developed, such as performing the realistic GSM in the Gamow Hartree-Fock basis (GHF) [41].…”

“…In the present review, the framework of the two types of GSM (realistic GSM and phenomenological GSM) is first introduced in Section 2. Then, we review our recent applications of GSM, including the calculations of neutron-rich oxygen and fluorine isotopes [38,39,41,42,46], neutron-rich calcium isotopes [47], and proton decays in 16 Ne and 18 Mg [48]. Finally, a short summary of the review and the future challenges of the next GSM calculations are given.…”