Ab initio Gamow in-medium similarity renormalization group with resonance and continuum

We have developed a novel ab initio Gamow in-medium similarity renormalization group (Gamow IMSRG) in the complex-energy Berggren framework. The advanced Gamow IMSRG is capable of describing the resonance and nonresonant continuum properties of weakly bound and unbound nuclear many-body systems. As test grounds, carbon and oxygen isotopes have been calculated with chiral two- and three-nucleon forces from the effective field theory. Resonant states observed in the neutron-dripline ${}^{24}\mathrm{O}$ are well reproduced. The halo structure of the known heaviest Borromean nucleus ${}^{22}\mathrm{C}$ is clearly seen by calculating the density distribution in which the continuum $s$ channel plays a crucial role. Furthermore, we predict low-lying resonant excited states in ${}^{22}\mathrm{C}$. The Gamow IMSRG provides tractable ab initio calculations of weakly bound and unbound open quantum systems.

Figure 1

${}^{24}\mathrm{O}$ spectrum calculated with ${\mathrm{NNLO}}_{\mathrm{opt}}\left(\mathrm{NN}\right)$ and ${\mathrm{NNLO}}_{\mathrm{sat}}\left(\mathrm{NN}+\mathrm{NNN}\right)$. The left two columns give the real-energy EOM-IMSRG calculations (indicated by $\mathrm{R}$-IMSRG) without and with the CoM treatment $\beta H_{\mathrm{CoM}}$. We take the multiplier $\beta =5$. The right three columns show the Gamow EOM-IMSRG calculations (indicated by $\mathrm{G}$-IMSRG) and data [52, 53]. Resonant states are indicated by shading, and their widths (in MeV) are given by the numbers nearby. The gray shading means the continuum above the particle emission threshold. $H_{\mathrm{int}}$ indicates the intrinsic Hamiltonian (1).

Figure 2

Calculated ${}^{22}\mathrm{C}$ ground-state densities displayed on the logarithm scale. $\mathrm{R}$-IMSRG indicates the real-energy IMSRG calculation, whereas $\mathrm{G}$-IMSRG is the Gamow IMSRG calculation. The inset details the densities in the central region of the nucleus with the standard scale.

Figure 3

Excited states in ${}^{22}\mathrm{C}$ predicted by Gamow EOM-IMSRG with ${\mathrm{NNLO}}_{\mathrm{opt}}\left(\mathrm{NN}\right)$ and ${\mathrm{NNLO}}_{\mathrm{sat}}\left(\mathrm{NN}+\mathrm{NNN}\right)$, compared with the complex CC calculation [59]. The channel(s) given at the top of the panel indicates that the partial waves are treated in the resonance and continuum Berggren representation. Other labels are similar to Fig. 1.