Nucleon-nucleus optical potential in the particle-hole approach

Feshbach's projection formalism in the particle-hole model space leads to a microscopic description of scattering in terms of the many-body self-energy. To investigate the feasibility of this approach, an optical potential for ${}^{16}\mathrm{O}$ is constructed starting from two previous calculations of the self-energy for this nucleus. The results reproduce the background phase shifts for positive parity waves and the resonances beyond the mean field. The latter can be computed microscopically for energies of astrophysical interest using Green's function theory.

Figure 1

(Color online) Feynman diagrams representation of the self energy. The first diagram on the right-hand side represents the Hartree-Fock–like contribution to the mean field. The remaining ones describe core polarization effects in the particle (2p1h) and hole (2h1p) part of the spectrum.

Figure 2

(Color online) Example of a diagrammatic contribution included in the Faddeev expansion for $R^{(2p1h)}$ (see Fig. 1). A quasiparticle is coupled to the response function ${\Pi }^{(\mathrm{ph})}$ that describes the target nucleus. It can also participate in pairing processes, which are accounted for by the two-body propagator $g^{\mathrm{II},(\mathrm{pp})}$.

Figure 3

(Color online) Phase shifts obtained from the self-consistent self-energy of Ref. 14 [Eq. (1a)] before (dotted lines) and after (dashed lines) correcting the depth of ${\Sigma }^{\mathrm{MF},\mathrm{Fadd}}$ to reproduce the quasiparticle (and quasihole) energies. The full lines are obtained also when the momentum components outside the model space $\mathcal{P}$ are included, Eq. (3a). The $s_{1/2},d_{3/2}$, and $p_{3/2}$ partial waves are shown. For $p_{3/2}$, the dot-dashed line was obtained by fitting $N_{p_{3/2}}^I$ to reproduce the background phase shifts rater than the quasihole energy. The values of the corrections $N_{\mathit{lj}}^I$ are reported in Table . The experimental results are from Refs. 31 (crosses) and [32] (circles).

Figure 4

(Color online) Phase shifts for positive parity waves obtained from the self-energies I (dashed lines) and II (full lines). The experimental results are from Refs. 31 (crosses) and [32] (circles).

Figure 5

(Color online) Phase shifts for negative parity waves obtained from the the self-energies I (dashed lines) and II (full lines). The experimental results are from Refs. 31 (crosses) and [32] (circles).

Figure 6

(Color online) Radial part of the overlap wave functions between ${}^{16}\mathrm{O}$ and the bound $d_{5/2}$ and $s_{1/2}$ states of ${}^{17}\mathrm{F}$.