Optical potential from first principles

We develop a method to construct a microscopic optical potential from chiral interactions for nucleon-nucleus scattering. The optical potential is constructed by combining the Green's function approach with the coupled-cluster method. To deal with the poles of the Green's function along the real energy axis we employ a Berggren basis in the complex energy plane combined with the Lanczos method. Using this approach, we perform a proof-of-principle calculation of the optical potential for the elastic neutron scattering on ${}^{16}\mathrm{O}$. For the computation of the ground state of ${}^{16}\mathrm{O}$, we use the coupled-cluster method in the singles-and-doubles approximation, while for the $A\pm 1$ nuclei we use particle-attached/removed equation-of-motion method truncated at two-particle–one-hole and one-particle–two-hole excitations, respectively. We verify the convergence of the optical potential and scattering phase shifts with respect to the model-space size and the number of discretized complex continuum states. We also investigate the absorptive component of the optical potential (which reflects the opening of inelastic channels) by computing its imaginary volume integral and find an almost negligible absorptive component at low energies. To shed light on this result, we computed excited states of ${}^{16}\mathrm{O}$ using the equation-of-motion coupled-cluster method with singles-and-doubles excitations and we found no low-lying excited states below 10 MeV. Furthermore, most excited states have a dominant two-particle–two-hole component, making higher-order particle-hole excitations necessary to achieve a precise description of these core-excited states. We conclude that the reduced absorption at low energies can be attributed to the lack of correlations coming from the low-order cluster truncation in the employed coupled-cluster method.

Figure 1

Real part of the radial (diagonal) optical potential in the neutron $s$ wave at $E=10\mathrm{MeV}$ as a function of $N_{\mathrm{lanc}}$, the number of Lanczos iterations. Calculations were performed with $N_{\max }=10$ and 50 discretized Berggren shells for the neutron $s_{1/2}$ partial wave.

Figure 2

Real part of the radial (diagonal) optical potential in the neutron $s$ wave at $E=1$ and $E=10\mathrm{MeV}$ using two different contours $L_1^{+},L_2^{+}$ for the single-particle neutron $s_{1/2}$ shells, in a model space with $N_{\max }=10$.

Figure 3

$k$-plane contours $L_1^{+},L_2^{+}$ used in the calculation of the $s$-wave optical potential in Fig. 2.

Figure 4

Imaginary part of the neutron $s$-wave Green's function $G_{s1/2}(r,E)$ at $r=2.4$ fm (see text for details). The dashed lines correspond to calculations with a real HF basis whereas the full lines were obtained using a complex contour. Calculations were performed with $N_{\max }=10$ and 50 discretized shells in the $s_{1/2}$ partial wave.

Figure 5

Real part of the diagonal optical potential in the neutron $s$ wave at $E=10\mathrm{MeV}$. Results are shown for at $N_{\max }=8–14$ and 50 discretized shells in the $s_{1/2}$ partial wave

Figure 6

Real part of $V_{\mathrm{int}}\left(r\right)$ in the neutron $s$ wave at $E=10$ MeV. Results are shown for at $N_{\max }=8–14$. For illustration purpose, we also show the results obtained with the phenomenological potential from Ref. [17].

Figure 7

Contour plot of the real part of the neutron $s$-wave potential $V(r,r^{\prime },E)$ for $N_{\max }=14$ and 50 discretized $s$-wave shells at $E=10\mathrm{MeV}$.

Figure 8

Neutron $s$-wave optical potential at $E=10$ MeV plotted as $V(R+r_{\mathrm{rel}}/2,R-r_{\mathrm{rel}}/2)$ at fixed $R=1/2$ fm. Here $N_{max}=14$ and 50 discretized $s$-wave shells are included in the single-particle basis.

Figure 9

Contour plot of the real part of the neutron $d_{3/2}$-wave potential for $N_{\max }=14$ at $E=10\mathrm{MeV}$.

Figure 10

Imaginary part of the radial (diagonal) optical potential in the neutron $s$ wave at $E=10\mathrm{MeV}$. Calculations were performed at $N_{\max }=10$ with 50 $s_{1/2}$ discretized shells. Results are shown for several values of $\eta$.

Figure 11

Neutron $s$-wave imaginary volume integral $J_W\left(E\right)$ for several values of $\eta$. Calculations were performed at $N_{\max }=14$ with 50 discretized $s_{1/2}$ shells.

Figure 12

Elastic-scattering phase shifts in the neutron $s$ and $d$ waves as a function of $N_{\max }$. In all cases 50 discretized Berggren shells are included.