Pauli rearrangement potential for a scattering state with the nucleon-nucleon interaction in chiral effective field theory

The Pauli rearrangement potential given by the second-order diagram is evaluated for a nucleon optical model potential (OMP) with $G$ matrices of the nucleon-nucleon interaction in chiral effective field theory. The results obtained in nuclear matter are applied for ${}^{40}\mathrm{Ca}$ in a local-density approximation. The repulsive effect is of the order of 5–10 MeV at the normal density. The density dependence indicates that the real part of the microscopic OMP becomes shallower in a central region, but is barely affected in a surface area. This improves the overall resemblance of the microscopic OMP to the empirical one.

Figure 1

(a) Pauli rearrangement diagram in the second order. (b) Illustration of the Pauli blocking in a ground-state ladder correlation.

Figure 2

Example of the Pauli blocking process of the $2\pi$ exchange 3BF: (a) Fujita-Miyazawa type and (b) ChEFT contact term.

Figure 3

Momentum dependence of the Pauli rearrangement potential in symmetric nuclear matter with various Fermi momenta from 0.8 to 1.$5{\mathrm{fm}}^{-1}$. ChEFT interactions [13] including 3NF effects are employed with three different cutoff scales: 450, 550, and 600 MeV, respectively.

Figure 4

Relation between the energy $E$ and the momentum $p$ in symmetric nuclear matter specified by Eq. (3).

Figure 5

Energy dependence of the Pauli rearrangement potential in symmetric nuclear matter with various Fermi momenta from 0.8 to 1.$5{\mathrm{fm}}^{-1}$. ChEFT interactions [13] including 3NF effects are employed with three different cutoff scales: 450, 550, and 600 MeV, respectively.

Figure 6

Momentum dependence of the Pauli rearrangement potential in symmetric nuclear matter calculated with AV18 [21], NSC97 [22], and CD-Bonn [23] NN potentials.

Figure 7

Radial dependence of the real part of the optical model potential for the nucleon incident energy $E_N=65$ MeV evaluated by a simple local-density approximation prescription for ${}^{40}\mathrm{Ca}$. The lowest-order potential $U_{\mathrm{LO}}^{\mathrm{real}}$, Pauli rearrangement potential $U_{\mathrm{rear}.}$, and the sum of them are plotted for three cases of the cutoff scale of the ChEFT interactions. The thin solid curve labeled “folding” represents a localized folding potential [25] obtained with the density-dependent effective two-body interaction parametrized on the basis of $G$ matrices in nuclear matter [8]. The thin solid curve labeled “K-D W-S” is a Woods-Saxon potential by Koning and Delaroche [26].

Figure 8

Same as Fig. 7, but for $E_N=100$ MeV.

Figure 9

The OMP in which the 3NF contribution is separated is shown for ${}^{40}\mathrm{Ca}$ at $E_N=65$ MeV with the cutoff scale of $\mathrm{\Lambda }=550$ MeV.