Airy structure in ${}^{16}\mathrm{O}+{}^{14}\mathrm{C}$ nuclear rainbow scattering

The Airy structure in ${}^{16}\mathrm{O}+{}^{14}\mathrm{C}$ rainbow scattering is studied with an extended double-folding (EDF) model that describes all the diagonal and off-diagonal coupling potentials derived from the microscopic realistic wave functions for ${}^{16}\mathrm{O}$ by using a density-dependent nucleon-nucleon force. The experimental angular distributions at $E_L=132$, 281, and 382.2 MeV are well reproduced by the calculations. By studying the energy evolution of the Airy structure, the Airy minimum around $\theta ={76}^{\circ }$ in the angular distribution at $E_L=132$ MeV is assigned as the second-order Airy minimum $A2$ in contrast to the recent literature which assigns it as the third order $A3$. The Airy minima in the ${90}^{\circ }$ excitation function is investigated in comparison with well-known ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ and ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ systems. Evolution of the Airy structure into the molecular resonances with the ${}^{16}\mathrm{O}+{}^{14}\mathrm{C}$ cluster structure in the low-energy region around $E_{\mathrm{c}.\mathrm{m}.}=30$ MeV is discussed. It is predicted theoretically for the first time for a non-$4N{}^{16}\mathrm{O}+{}^{14}\mathrm{C}$ system that Airy elephants in the ${90}^{\circ }$ excitation function are present.

Figure 1

Comparison of the single-channel DF potential model calculations (blue solid line) with the experimental angular distributions of cross sections (ratio to Rutherford scattering) (points) [12] in elastic ${}^{16}\mathrm{O}+{}^{14}\mathrm{C}$ scattering at (a) $E_L=132$ MeV, (b) 281 MeV, and (c) 382.2 MeV. The dashed (green) and dash-dotted (gray) lines display the calculated farside and nearside components, respectively. The angular distributions calculated by switching off the imaginary potential ($W=0$) are displayed by the dotted (pink) lines.

Figure 2

The energy evolution of the Airy structure in the angular distributions of cross sections (ratio to Rutherford scattering) in ${}^{16}\mathrm{O}+{}^{14}\mathrm{C}$ scattering calculated by using the single-channel DF potential by switching off the imaginary potential is shown by the solid lines. The dashed lines at 116 and 132 MeV are the farside component of the calculated cross sections.

Figure 3

Comparison of the coupled-channel calculations (blue solid line) with experimental angular distributions of cross sections (ratio to Rutherford scattering) (points) [12] in ${}^{16}\mathrm{O}+{}^{14}\mathrm{C}$ scattering at (a) $E_L=132$ MeV, (b) 281 MeV, and (c) 382.2 MeV. The dashed (green) and dash-dotted (gray) lines display the calculated farside and nearside components, respectively. The angular distributions calculated by switching off the imaginary potential ($W=0$) are displayed with dotted (pink) lines. Note that the upper horizon scale is for panels (a) and (b) and the lower horizontal scale is for panel (c).

Figure 4

The observed minima (filled circles) in the ${90}^{\circ }$ excitation functions for the ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ [3, 26, 29, 30], ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ [5, 31, 32], and ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ [9] systems are shown as a function of reduced mass. The predicted Airy minima for the ${}^{16}\mathrm{O}+{}^{14}\mathrm{C}$ system, $A1$ and $A2$, are indicated by open squares. The line is to guide the eye.

Figure 5

The values of the volume integrals per nucleon pair of the real potential, $J_V$, for ${}^{16}\mathrm{O}+{}^{14}\mathrm{C}$ rainbow scattering (red filled circles) are shown in comparison with those for ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ (pink open squares [9], pink filled diamonds [13]), ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ (blue up triangles) [26] and ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ (black down triangles) [10] rainbow scattering. The line is to guide the eye.