Doubly magic nuclei from lattice QCD forces at $M_{\mathrm{PS}}=469\mathrm{MeV}/c^2$

We perform ab initio self-consistent Green's function calculations of the closed shell nuclei ${}^4\mathrm{He}$, ${}^{16}\mathrm{O}$, and ${}^{40}\mathrm{Ca}$, based on two-nucleon potentials derived from lattice QCD simulations, in the flavor SU(3) limit and at the pseudoscalar meson mass of 469 MeV/$c^2$. The nucleon-nucleon interaction is obtained using the hadrons-to-atomic-nuclei-from-lattice (HAL) QCD method, and its short-distance repulsion is treated by means of ladder resummations outside the model space. Our results show that this approach diagonalizes ultraviolet degrees of freedom correctly. Therefore, ground-state energies can be obtained from infrared extrapolations even for the relatively hard potentials of HAL QCD. Comparing to previous Brueckner Hartree-Fock calculations, the total binding energies are sensibly improved by the full account of many-body correlations. The results suggest an interesting possible behavior in which nuclei are unbound at very large pion masses and islands of stability appear at first around the traditional doubly magic numbers when the pion mass is lowered toward its physical value. The calculated one-nucleon spectral distributions are qualitatively close to those of real nuclei even for the pseudoscalar meson mass considered here.

Figure 1

Diagrammatic content of the ADC(3) approximation. (a) The self-energy splits into a static mean-field part and an energy-dependent contribution according to Eq. (2). (b) The dynamic contributions are obtained as infinite resummations of ladder (pp/hh) and ring (ph) diagrams. The ADC(3) approach includes static corrections to the coupling of nucleons to intermediate excitations [matrix $\mathbf{D}$ in Eq. (2)], an example of which is shown by the top portion of the last Goldstone diagram [44].

Figure 2

Ground-state energy of ${}^4\mathrm{He}$, ${}^{16}\mathrm{O}$, and ${}^{40}\mathrm{Ca}$ as a function of the harmonic oscillator frequency $\hslash \mathrm{\Omega }$ and the model space size $N_{\max }$. Symbols mark the results for the HAL469 potential from full self-consistent calculations in the $T^{\mathrm{BGE}}\left(\omega \right)$ plus ADC(3) approach.

Figure 3

Calculated ground-state energies of ${}^4\mathrm{He}$ and ${}^{40}\mathrm{Ca}$ for the HAL469 potential as a function of the effective box radius $L_2$. Left: Solution for the bare interaction at $N_{\max }=9$ and 11 and varying oscillator frequencies without ladders from the excluded space $Q$. Middle: Full calculation, including all ladder diagrams in $Q$. Different colors and broken lines are a guide to the eye connecting results of the same $N_{\max }$. The data points included in the fit are marked with crosses and are also shown separately in the inset. Right: Same as the middle panel but for ${}^{40}\mathrm{Ca}$. For all panels, the full black line is the result of the IR extrapolation, with the inclusion of the $T^{\mathrm{BGE}}$ ladder, according to Eq. (7).

Figure 4

Single-particle spectral strength distribution of ${}^{16}\mathrm{O}$ obtained from the dressed propagator in the full $T^{\mathrm{BGE}}\left(\omega \right)$ plus ADC(3) approach. Each panel displays partial waves of different angular momenta. The vertical axes give the quasiparticle energies [that is, the poles of Eq. (1)], while the lengths of the horizontal bars give the calculated spectroscopic factors.