Calculations for nuclear matter and finite nuclei within and beyond energy-density-functional theories through interactions guided by effective field theory

We propose a novel idea to construct an effective interaction under energy-density-functional (EDF) theories which is adaptive to the enlargement of the model space. Guided by effective field theory principles, iterations of interactions as well as enlargements of the model space through particle-hole excitations are carried out for infinite nuclear matter and selected closed-shell nuclei (${}^4\mathrm{He}, {}^{16}\mathrm{O}, {}^{40}\mathrm{Ca}, {}^{56}\mathrm{Ni}$, and ${}^{100}\mathrm{Sn}$) up to next-to-leading order. Our approach provides a new way for handling the nuclear matter and finite nuclei within the same scheme, with advantages from both EDF and ab initio approaches.

Figure 1

Ground state energies of ${}^4\mathrm{He}$ (a), ${}^{16}\mathrm{O}$ (b), and ${}^{40}\mathrm{Ca}$ (c) as a function of $\hslash \omega$. Results obtained from a $t_0-t_3$ model and full SLy5 and SkP functionals are plotted as black solid, red dotted, and green dashed lines, respectively. The empirical $\hslash \omega$ value for each nucleus is marked as a red vertical dashed line. The horizontal blue lines represent the experimental energies. The SM energy per particle at LO is plotted as a function of the density $\rho$ in the inset.

Figure 2

Once-iterated diagrams for the interaction $V_{\mathrm{iter}}^{\mathrm{LO}}$. ${\mathbf{k}}_1$ (${\mathbf{k}}_2$) denotes the single-particle momentum of the initial (final) state, and $\mathbf{q}$ is the transferred momentum.

Figure 3

Left panels (a)–(c): Ground state energies up to NLO for ${}^4\mathrm{He}, {}^{16}\mathrm{O}$, and ${}^{40}\mathrm{Ca}$ as a function of $\mathrm{\Lambda }$. Right panel (d): Rel. err. $=(E_b-E_{\exp .})/\left|E_{\exp .}\right|$ for the first five closed-shell, $N=Z$ nuclei. The labels NLO (i) and NLO (ii) refer to the two prescriptions described in the main text, where parameters in NLO (ii) are obtained by either fitting to EoS only (fit EoS) or an overall fit including EoS and all five nuclei (fit all). Their corresponding EoSs are plotted in (e).