Quasielastic electron scattering with the KIDS nuclear energy density functional

Isoscalar and isovector effective masses of the nucleon in nuclear medium are explored in the quasielastic electron scattering off nuclei with KIDS (Korea-IBS-Daegu-SKKU) density functional model. Effective masses are varied in the range $(0.7–1.0)M$, where $M$ is the mass of the nucleon in free space. Parameters in the KIDS functional are adjusted to nuclear matter equation of state, energy and radius of selected nuclei, and effective mass of nucleons. The Hartree-Fock equation is solved to obtain the wave functions of the nucleon in target nuclei, and they are plugged in the calculation of electron-nucleus scattering cross sections at the energies of incident electrons 300 MeV–2.5 GeV. The theoretical prediction agrees well with measurement. Dependence on the effective mass is evident: the cross section tends to increase with small isoscalar effective masses. However, the effect of isovector effective mass is negligible. Spectroscopic factors are estimated for the protons in the outermost shells of ${}^{16}\mathrm{O}$, ${}^{40}\mathrm{Ca}$, and ${}^{208}\mathrm{Pb}$. Results are consistent with the values in the literature.

Figure 1

Density profile of charge (left) and neutron (right) for ${}^{16}\mathrm{O}$.

Figure 2

Density profile of charge (left) and neutron (right) for ${}^{40}\mathrm{Ca}$.

Figure 3

Density profile of charge (left) and neutron (right) for ${}^{208}\mathrm{Pb}$.

Figure 4

${}^{40}\mathrm{Ca}$ cross section with parallel kinematics. The experimental data taken from NIKHEF [20].

Figure 5

${}^{208}\mathrm{Pb}$ cross section with parallel kinematics. The experimental data were measured from NIKHEF [21].

Figure 6

${}^{16}\mathrm{O}$ cross section with perpendicular kinematics. The experimental data in the upper panels were measured from Saclay [22] and in the lower panels from JLab [23].

Figure 7

${}^{40}\mathrm{Ca}$ cross section with perpendicular kinematics. The experimental data were measured from NIKHEF [20].

Figure 8

The fourth response functions from ${}^{16}\mathrm{O}$ with the kinematics the same as at JLab.

Figure 9

The left-right asymmetry from ${}^{16}\mathrm{O}$ with the kinematics the same as at JLab.