Effects of chiral three-nucleon forces on ${}^4$He-nucleus scattering in a wide range of incident energies

Abstract

It is a current important subject to clarify properties of chiral three-nucleon forces (3NFs) not only in nuclear matter but also in scattering between finite-size nuclei. Particularly for the elastic scattering, this study has just started and the properties are not understood in a wide range of incident energies ($E_{\mathrm{in}}$). We investigate basic properties of chiral 3NFs in nuclear matter with positive energies by using the Brueckner-Hartree-Fock method with chiral two-nucleon forces of N${}^3$LO and 3NFs of NNLO, and analyze effects of chiral 3NFs on ${}^4$He elastic scattering from targets ${}^{208}$Pb, ${}^{58}$Ni and ${}^{40}$Ca over a wide range of $30\lesssim E_{\mathrm{in}}/A_{\mathrm{P}}\lesssim 200$ MeV by using the $g$-matrix folding model, where $A_{\mathrm{P}}$ is the mass number of projectile. In symmetric nuclear matter with positive energies, chiral 3NFs make the single-particle potential less attractive and more absorptive. The effects mainly come from the Fujita-Miyazawa 2$\pi$-exchange 3NF and slightly become larger as $E_{\mathrm{in}}$ increases. These effects persist in the optical potentials of ${}^4$He scattering. As for the differential cross sections of ${}^4$He scattering, chiral-3NF effects are large in $E_{\mathrm{in}}/A_{\mathrm{P}}\gtrsim 60$ MeV and improve the agreement of the theoretical results with the measured ones. Particularly in $E_{\mathrm{in}}/A_{\mathrm{P}}\gtrsim 100$ MeV, the folding model reproduces measured differential cross sections pretty well. Cutoff ($\Lambda$) dependence is investigated for both nuclear matter and ${}^4$He scattering by considering two cases of $\Lambda =450$ and $550$ MeV. The uncertainty coming from the dependence is smaller than chiral-3NF effects even at $E_{\mathrm{in}}/A_{\mathrm{P}}=175$ MeV.

Comments: 14 pages, 15 figures