Barcelona-Catania-Paris-Madrid functional with a realistic effective mass

The Barcelona-Catania-Paris-Madrid functional recently proposed to describe nuclear structure properties of finite nuclei is generalized as to include a realistic effective mass. The resulting functional is as good as the previous one in describing binding energies, radii, deformation properties, etc. In addition, the description of giant quadrupole resonance energies is greatly improved.

Figure 1

Proton (p, full line) and neutron (n, dotted line) effective masses corresponding to the linear fit of Eq. (13) are plotted as a function of the density for different values of the isospin asymmetry parameter $\beta$.

Figure 2

Binding energy difference $\mathrm{\Delta }B=B_{\mathrm{th}}-B_{\exp }$ (MeV) as a function of the shifted [by $N_0\left(Z\right)]$ neutron number $N-N_0\left(Z\right)$. The values of $Z$ and the neutron number shift $N_0\left(Z\right)$ are given in each panel. In all the panels the ordinate $\mathrm{\Delta }B$ axis ranges from $-6.5$ MeV to 5.5 MeV with long ticks at $-6$, $-4$, etc., MeV. The $N-N_0\left(Z\right)$ axis spans a range of 40 units with long ticks every ten units and short ones every two units. For instance, for the nucleus of ${}^{132}\mathrm{Ce}$ ($Z=58$, $N=74$) the value of $N_0$ is 66 and therefore $N-N_0=8$. In every panel, a horizontal line corresponding to $\mathrm{\Delta }B=0$ has been plotted to guide the eye. Additional perpendicular lines signaling the position of magic neutron numbers have also been included. Black curves correspond to theoretical binding energies computed with the HFB method whereas the red curves additionally include the rotational energy correction ${\epsilon }_{\mathrm{rot}}$ discussed in the text. The HFB calculations have been carried out with the basis 3 set.

Figure 3

The experiment-theory deviation $r_{\mathrm{ch}}-r_{\exp }$ for the 315 even-even nuclei with known experimental data [34] is plotted as a function of mass number $A$.

Figure 4

Potential energy surface for fission, including the rotational energy correction, computed as a function of the quadrupole moment (in units of $b=100{\mathrm{fm}}^2$) for the Gogny D1S, BCPM, and ${\mathrm{BCPM}}^{*}$ functionals.

Figure 5

Excitation energies of the monopole and quadrupole giant resonances as a function of mass number $A$ obtained with the scaling approximation. The estimation $58A^{-1/3}$ for the quadrupole and $86A^{-1/3}$ for the monopole [25] are drawn to guide the eye. The dotted curve $67A^{-1/3}$ corresponds to the best fit of the quadrupole excitation energy.