Skyrme functional with tensor terms from ab initio calculations of neutron-proton drops

A new Skyrme functional devised to account well for standard nuclear properties as well as for spin and spin-isospin properties is presented. The main novelty of this work relies on the introduction of tensor terms guided by ab initio relativistic Brueckner-Hartree-Fock calculations of neutron-proton drops. The inclusion of tensor term does not decrease the accuracy in describing bulk properties of nuclei, experimental data of some selected spherical nuclei such as binding energies, charge radii, and spin-orbit splittings can be well fitted. The new functional is applied to the investigation of various collective excitations such as the giant monopole resonance, the isovector giant dipole resonance, the Gamow-Teller resonance, and the spin-dipole resonance. The overall description with the new functional is satisfactory and the tensor terms are shown to be important particularly for the improvement of the spin-dipole resonance results. Predictions for the neutron skin thickness based on the nonenergy weighted sum rule of the spin-dipole resonance are also given.

Figure 1

Neutron matter and symmetric nuclear matter equation of state calculated by new fitted Skyrme functional SAMi-T (blue solid line), in comparison with those of SAMi functional (purple dotted line) [59]. The shaded area are constraints of neutron matter from different ab initio calculations, see text for detail.

Figure 2

Total energy (in units of $\hslash \omega N^{4/3}$) of neutron drops with $N$ from 8–50 in a HO trap ($\hslash \omega =10\mathrm{MeV}$) calculated by SAMi-T, in comparison with results of SAMi and of RBHF theory using the Bonn A interaction [50], Quantum Monte Carlo method using local chiral interaction ${\mathrm{N}}^2\mathrm{LO}$ with two cutoffs $1.0\mathrm{fm}$ and $1.2\mathrm{fm}$ [48], coupled-cluster theory using chiral interaction ${\mathrm{N}}^3\mathrm{LO}$ [47]. The shaded area represents the values spanned by quantum Monte Carlo calculations using AV8'+UIX and AV8'+IL7 [45, 46].

Figure 3

Two-neutron energy difference of neutron drops in a HO trap ($\hslash \omega =10\mathrm{MeV}$) calculated by SAMi-T, in comparison with results of SAMi and of the RBHF theory using the Bonn A interaction [50].

Figure 4

Neutron and proton $1p$ and $1d$ spin-orbit splittings of neutron-proton drops calculated by SAMi-T, in comparison with results of SAMi functional and RBHF theory using the Bonn A interaction. The results of SAMi-T and SAMi have been shifted so that the first points ($N=20$) meet with those of RBHF.

Figure 5

From top to bottom panel, $1p,1d,1f$, and $2p$ spin-orbit splittings of $N$-neutron drops in a HO trap ($\hslash \omega =10\mathrm{MeV}$) calculated by SAMi-T, in comparison with results of SAMi functional and RBHF theory using the Bonn A interaction [50].

Figure 6

Values of $\alpha$ and $\beta$ in Eq. (13) from different Skyrme functionals. See text for details.

Figure 7

Strength function associated with the GMR (left) and IVGDR (right), calculated by using the SAMi-T functional and compared with results of SAMi [59] and with the experimental centroid energies [87, 88]. For theoretical results, we adopt a smoothing with Lorentzian functions having $1\mathrm{MeV}$ width.

Figure 8

GTR strength function for ${}^{48}\mathrm{Ca}$, ${}^{90}\mathrm{Zr}$, and ${}^{208}\mathrm{Pb}$ calculated by SAMi-T with and without tensor, in comparison with experimental data [89, 90, 91, 92, 93] and with the results of the SAMi functional [59]. For theoretical results, we adopt a smoothing with Lorentzian functions having $1\mathrm{MeV}$ width.

Figure 9

SDR strength function in the ${\tau }_{-}$ channel for ${}^{208}\mathrm{Pb}$, calculated by SAMi-T with and without tensor, in comparison with experimental data [93] and the results with SAMi [59]. From top to bottom, the total strength and the $J^{\pi }=0^{-},1^{-}$, and $2^{-}$ components are shown. For theoretical results, we adopt a smoothing with Lorentzian functions having $2\mathrm{MeV}$ width.

Figure 10

SDR strength function of the ${\tau }_{-}$ (top) and ${\tau }_{+}$ (bottom) channel in ${}^{90}\mathrm{Zr}$ calculated by SAMi-T with and without tensor, in comparison with experimental data [100] and SAMi functional [59]. For theoretical results, a Lorentzian smearing parameter equal to $2\mathrm{MeV}$ is used.

Figure 11

Pearson product-moment correlation coefficient matrix predicted by the covariance analysis of SAMi-T functional for various properties of nuclear matter and ${}^{208}\mathrm{Pb}$ (see text for details).

Figure 12

Position where instability occurs in the density $\rho$ and momentum transfer $q$ plane for (a) SAMi-T and (b) SAMi functionals.