From homogeneous matter to finite nuclei: Role of the effective mass

Recent astronomical observations, nuclear-reaction experiments, and microscopic calculations have placed new constraints on the nuclear equation of state (EoS) and revealed that most nuclear-structure models fail to satisfy those constraints upon extrapolation to infinite matter. A reverse procedure for imposing EoS constraints on nuclear structures has been elusive. Here, we present for the first time a method to generate a microscopic energy density functional (EDF) for nuclei from a given immutable EoS. The method takes advantage of a natural ansatz for homogeneous nuclear matter, the Kohn-Sham framework, and the Skyrme formalism. We apply it to the nuclear EoS of Akmal-Pandharipande-Ravenhall and describe successfully closed-(sub)shell nuclei. In the process, we provide predictions for the neutron-skin thickness of nuclei based directly on the given EoS. Crucially, bulk and static nuclear properties are found practically independent of the assumed effective mass value—a unique result in bridging EDF of finite and homogeneous systems in general.

Figure 1

Nuclear symmetry energy. The KIDS-ad2 equation of state employed in this paper is compared with other available models which have been fitted to nuclear data under various protocols.

Figure 2

Energy of pure neutron matter $E_{\mathrm{PNM}}$ divided by the free-gas value $E_{\mathrm{FG}}$ as a function of $|a{k}_N|$, where $a(=-18.9\mathrm{fm})$ is the neutron-neutron scattering length in free space, and $k_N^{}$ is the neutron Fermi momentum. Corresponding density values are indicated on the upper abscissa. The KIDS-ad2 equation of state (full line) is compared with the results of chiral EFT (gray band), a QMC calculation (points), the EFT-inspired model YGLO(Akmal) (black dashed line) and other available models fitted to nuclear data under various protocols.

Figure 3

Results for binding energy per nucleon $E/A$, charge radius $R_c$, and neutron-skin thickness $\mathrm{\Delta }{r}_{np}$. All results for ${}^{16}\mathrm{O},{}^{28}\mathrm{O},{}^{60}\mathrm{Ca},{}^{90}\mathrm{Zr},{}^{132}\mathrm{Sn}$, and ${}^{218}\mathrm{U}$ and all neutron-skin results are predictions. Data of energy per particle and charge radius are taken from the National Nuclear Data Center and Ref. [38], whereas neutron-skin data from Refs. [39, 40, 41].

Figure 4

Energies of occupied proton levels of ${}^{208}\mathrm{Pb}$ from various models compared with empirical removal energies [44]. The KIDS results for $K_0=240\mathrm{MeV},{\mu }_v=0.82$, and varying ${\mu }_s$ are on the left of the experimental levels. The number under each model name is the deviation $D$ of Eq. (9), in percentage points, for the levels shown underneath.

Figure 5

Energy per particle of (a) Ca and (b) Sn isotopes without considering pairing correlations. The KIDS results for $K_0=240\mathrm{MeV},{\mu }_v=0.82$, and varying ${\mu }_s$ are shown along with those from representative Skyrme functionals (SLy4, GSkI) and experimental data.