Microscopic nuclear form factors for the pygmy dipole resonance

It is shown that the use of a proper form factor in the study of the pygmy dipole resonance (PDR) is of paramount importance in order to determine the correct values for the relevant quantities characterizing these new modes. Form factors calculated within a microscopic model are compared with those provided by different macroscopic collective models. Their differences, shown in the shape and magnitude, are reflected on the calculated cross section and therefore jeopardize the extracted physical quantities.

Figure 1

Schematic representation of the PDR state generated as an oscillation of the core against the neutron skin.

Figure 2

RPA transition densities for the (a) low-lying dipole states and (b) ISGDR for ${}^{68}\mathrm{Ni}$ calculated with the SGII interaction. As indicated in the legend, we plot the proton, neutron, isoscalar, and isovector components.

Figure 3

Comparison among the RPA transition densities and the ones calculated within our MPM [Eq. (7)] for the low-lying dipole states for ${}^{68}\mathrm{Ni}$. As indicated in the legend, we plot the proton and neutron transition densities for both microscopic and macroscopic calculations.

Figure 4

Comparison between the isoscalar microscopic (RPA) transition densities (solid black line) and the one calculated according to Eq. (3) (HD) (red dashed line) for two dipole states of ${}^{68}\mathrm{Ni}$: (a) PDR state, (b) ISGDR state.

Figure 5

Comparison among the microscopic (RPA) transition densities, one calculated according to Eq. (3) (HD), and one by the MPM, Eq. (7), for the PDR state of ${}^{68}\mathrm{Ni}$.

Figure 6

Form factors for the system ${}^{68}\mathrm{Ni}$+${}^{12}\mathrm{C}$ for the PDR state left frame and for the ISGDR right frame. All of them are calculated with the double-folding procedure but starting from different transition densities: microscopic RPA, HD, and MPM [Eq. (7)].

Figure 7

Differential cross sections for the system ${}^{68}\mathrm{Ni}$ + ${}^{12}\mathrm{C}$ at 10 MeV/u for the (a) PDR state and (b) ISGDR state. They have been calculated with the dwuck4 code.