Proton-nucleus elastic scattering: Comparison between phenomenological and microscopic optical potentials

Background: Elastic scattering is a very important process to understand nuclear interactions in finite nuclei. Despite decades of efforts, the goal of reaching a coherent description of this physical process in terms of microscopic forces is still far from being completed.

Purpose: In previous papers we derived a nonrelativistic theoretical optical potential from nucleon-nucleon chiral potentials at fourth (${\mathrm{N}}^3\mathrm{LO}$) and fifth order (${\mathrm{N}}^4\mathrm{LO}$). We checked convergence patterns and established theoretical error bands. With this work we study the performances of our optical potential in comparison with those of a successful nonrelativistic phenomenological optical potential in the description of elastic proton scattering data on several isotopic chains at energies around and above 200 MeV.

Methods: We use the same framework and the same approximations as adopted in our previous papers, where the nonrelativistic optical potential is derived at the first-order term within the spectator expansion of the multiple scattering theory and adopting the impulse approximation and the optimum factorization approximation.

Results: The cross sections and analyzing powers for elastic proton scattering off calcium, nickel, tin, and lead isotopes are presented for several incident proton energies, exploring the range $156\le E\le 333$ MeV, where experimental data are available. In addition, we provide theoretical predictions for ${}^{56}\mathrm{Ni}$ at 400 MeV, which is of interest for the future experiments at EXL.

Conclusions: Our results indicate that microscopic optical potentials derived from nucleon-nucleon chiral potentials at ${\mathrm{N}}^4\mathrm{LO}$ can provide reliable predictions for the cross section and the analyzing power both of stable and exotic nuclei, even at energies where the reliability of the chiral expansion starts to be questionable.

Figure 1

Ratio of the differential cross section to the Rutherford cross section as a function of the center-of-mass scattering angle $\theta$ for elastic proton scattering off ${}^{16}\mathrm{O}$. Calculations are performed at $E=200$ MeV (laboratory energy) with the microscopic OPs derived from the EKM [17, 19] (EKM, red band) and EMN [20, 21] (EMN, green band) $NN$ chiral potentials at ${\mathrm{N}}^4\mathrm{LO}$ and with the phenomenological global OP of Ref. [42] (KD, violet line). The interpretation of the bands is explained in the text. Experimental data are from Refs. [45, 46].

Figure 2

The same as in Fig. 1 for ${}^{40,42,44,48}\mathrm{Ca}$ isotopes at 200 MeV. Experimental data are from Refs. [45, 46].

Figure 3

The same as in Fig. 1 for Ni isotopes: ${}^{58}\mathrm{Ni}$ at $E=192$ and 295 MeV, ${}^{60}\mathrm{Ni}$ at $E=178$ MeV, and ${}^{62}\mathrm{Ni}$ at $E=156$ MeV. Experimental data are from Refs. [45, 46].

Figure 4

The same as in Fig. 1 for Sn isotopes: ${}^{120}\mathrm{Sn}$ at $E=200$ MeV and ${}^{116,118,120,122,124}\mathrm{Sn}$ at $E=295$ MeV. Experimental data are from Refs. [45, 46].

Figure 5

The same as in Fig. 1 for Pb isotopes: ${}^{208}\mathrm{Pb}$ at $E=200$ MeV and ${}^{204,206,208}\mathrm{Pb}$ at $E=295$ MeV. Experimental data are from Refs. [45, 46].

Figure 6

The same as in Fig. 1 for ${}^{16}\mathrm{O}$ and ${}^{40,42,44,48}\mathrm{Ca}$ at $E=318$ MeV and ${}^{58}\mathrm{Ni}$ at $E=333$ MeV. Experimental data are from Refs. [45, 46].

Figure 7

(upper panel) Ratio of the differential cross section to the Rutherford cross section as a function of the center-of-mass scattering angle $\theta$ for ${}^{56}\mathrm{Ni}(p,p){}^{56}\mathrm{Ni}$ elastic scattering at $E=400$ MeV/u. (lower panel) Differential cross section as a function of the Mandelstam variable $t$ in the laboratory frame for ${}^{56}\mathrm{Ni}(p,p){}^{56}\mathrm{Ni}$ elastic scattering at $E=400$ MeV/u. Calculations are performed with the microscopic OPs derived from the EKM [17, 19] (EKM, red band) and EMN [20, 21] (EMN, green band) $NN$ chiral potentials at ${\mathrm{N}}^4\mathrm{LO}$ and with the phenomenological global OP of Ref. [42] (KD, violet line). The interpretation of the bands is explained in the text and differs from that of Fig. 1.

Figure 8

The same as in Fig. 2 but for the analyzing power $A_y$. Experimental data are from Refs. [45, 46].

Figure 9

The same as in Fig. 4 but for the analyzing power $A_y$. Experimental data are from Refs. [45, 46].

Figure 10

Analyzing power $A_y$ as a function of the angle $\theta$ for elastic proton scattering on ${}^{16}\mathrm{O}$, and ${}^{208}\mathrm{Pb}$ at $E=200$ MeV, ${}^{58}\mathrm{Ni}$ at $E=192$ MeV, and ${}^{60}\mathrm{Ni}$ at $E=178$ MeV. Experimental data are from Refs. [45, 46].