Calculation of three-body nuclear reactions with angular-momentum and parity-dependent optical potentials

Angular-momentum or parity-dependent nonlocal optical potentials for nucleon-${}^{16}\mathrm{O}$ scattering able to fit differential cross-section data over the whole angular regime are developed and applied to the description of deuteron-${}^{16}\mathrm{O}$ scattering in the framework of three-body Faddeev-type equations for transition operators. Differential cross sections and deuteron analyzing powers for elastic scattering and ${}^{16}\mathrm{O}(d,p){}^{17}\mathrm{O}$ transfer reactions are calculated by using a number of local and nonlocal optical potentials and compared with experimental data. Angular-momentum or parity-dependence of the optical potential turns out to be quite irrelevant in the considered three-body reactions whereas nonlocality is essential for a successful description of the differential cross-section data, especially in transfer reactions.

Figure 1

Differential cross section divided by Rutherford cross section and proton analyzing power for $p+{}^{16}\mathrm{O}$ elastic scattering at $E_p=27.3$ MeV. Parameters of local $L$-dependent OP from Ref. [10] (dotted curves), nonlocal $L$-dependent OP (solid curves), and nonlocal $\pi$-dependent OP (dashed-dotted curves) are fitted to experimental $E_p=27.3$ MeV data. Results for nonlocal $L$-independent OP (dashed curves) without proper fit are shown as well. The data are from Refs. [15, 16].

Figure 2

Differential cross section divided by Rutherford cross section and proton analyzing power for $p+{}^{16}\mathrm{O}$ elastic scattering at $E_p=34.1$ MeV. Curves are as in Fig. 1 with OP parameters fit to experimental $E_p=27.3$ MeV data. The results are not constrained in any way by the shown $E_p=34.1$ MeV data from Refs. [15, 16].

Figure 3

Differential cross section and neutron analyzing power for $n+{}^{16}\mathrm{O}$ elastic scattering at $E_n=24$ MeV. Results obtained with various nonlocal potentials are compared with the experimental data from Refs. [20] $(•)$, [22] $(\square )$, and [21] $(\circ )$. The predictions with $p+{}^{16}\mathrm{O}$ potential parameters from Fig. 1 are denoted by (p).

Figure 4

Differential cross section divided by Rutherford cross section and deuteron analyzing powers for $d+{}^{16}\mathrm{O}$ elastic scattering at $E_d=56$ MeV. Predictions obtained by using local $L$-dependent OP from Ref. [10] (dotted curves), four parametrizations of nonlocal $L$-dependent OP (four solid curves,) three parametrizations of nonlocal $\pi$-dependent OP (three dashed-dotted curves), and nonlocal $L$-independent OP (dashed curves) are compared with the experimental data from Ref. [29].

Figure 5

Differential cross section for ${}^{16}\mathrm{O}(d,p){}^{17}\mathrm{O}$ transfer reactions at $E_d=36$ MeV leading to ${}^{17}\mathrm{O}$ ground ${\frac{5}{2}}^{+}$ (top) and excited ${\frac{1}{2}}^{+}$ (bottom) states. Predictions obtained using local $L$-dependent OP from Ref. [10] (dotted curves), nonlocal $L$-dependent OP (solid curves,) nonlocal $\pi$-dependent OP (dashed-dotted curves), and nonlocal $L$-independent OP (dashed curves) are compared with experimental data from Ref. [30].

Figure 6

Differential cross section for ${}^{16}\mathrm{O}(d,p){}^{17}\mathrm{O}$ transfer to ${}^{17}\mathrm{O}$ ground state ${\frac{5}{2}}^{+}$ at $E_d=63.2$ MeV. Predictions obtained by using the nonlocal $L$-dependent OP (solid curves,) nonlocal $\pi$-dependent OP (dashed-dotted curves), and nonlocal $L$-independent OP (dashed curves) are compared with experimental data from Ref. [30].