Refractive effects and Airy structure in inelastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ rainbow scattering

Inelastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ rainbow scattering to the $2^{+}$ (4.44 MeV) state of ${}^{12}\mathrm{C}$ was measured at the incident energies, $E_L$ = 170, 181, 200, 260, and 281 MeV. A systematic analysis of the experimental angular distributions was performed using the coupled-channels method with an extended double folding potential derived from realistic wave functions for ${}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}$ calculated with a microscopic $\alpha$ cluster model and a finite-range density-dependent nucleon-nucleon force. The coupled-channels analysis of the measured inelastic-scattering data shows consistently some Airy-like structure in the inelastic-scattering cross sections for the first $2^{+}$ state of ${}^{12}\mathrm{C}$, which is somewhat obscured and still not clearly visible in the measured data. The Airy minimum was identified from the analysis and the systematic energy evolution of the Airy structure was studied. The Airy minimum in inelastic scattering is found to be shifted backward compared with that in elastic scattering.

Figure 1

Angular distributions in ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ (a) elastic and (b) inelastic scattering to the $2^{+}$ state of ${}^{12}\mathrm{C}$ calculated using the coupled-channels method including coupling to the $2^{+}$ and $3^{-}$ states of ${}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}$ with the imaginary potentials in Table 1 (solid lines) compared with the experimental data (points). The green dashed lines in elastic scattering display the calculated far-side components. The blue dotted lines at 200 MeV are calculated with a channel dependent imaginary potential for the $2^{+}$ and $3^{-}$ states of ${}^{12}\mathrm{C}$ (see text). The elastic-scattering data are from Refs. [8, 10].

Figure 2

Angular distributions in ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ (a) elastic and (b) inelastic scattering to the $2^{+}$ state of ${}^{12}\mathrm{C}$ at $E_L$=281 MeV calculated using the coupled-channels method with the imaginary potentials in Table 1 compared with those calculated by switching off the imaginary potential and the experimental data (points). The solid and dashed lines represent the coupled-channels calculations with coupling to the $2^{+}$ and $3^{-}$ states of ${}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}$ and those with coupling to the $2^{+}$ state of ${}^{12}\mathrm{C}$ only, respectively. The dotted lines represent the single-channel calculation.

Figure 3

Angular distributions in inelastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ scattering to the $2{}^{+}$ state of ${}^{12}\mathrm{C}$ (dotted line) and elastic scattering (solid line) at 200 and 330 MeV calculated using the coupled-channels method including coupling to the $2^{+}$ and $3^{-}$ states of ${}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}$ compared with the experimental inelastic (squares) and elastic (points) data [37]. For 330 MeV the potential parameters in Table 1 of Ref. [29] are used.

Figure 4

The positions of the Airy minimum observed in inelastic scattering to the $2^{+}$ state of ${}^{12}\mathrm{C}$ (filled square) and elastic scattering (filled circle) of ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ displayed as a function of the inverse c.m. energies. The lines are drawn by fitting the data.

Figure 5

Angular distributions in ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ elastic (solid line) and inelastic scattering to the $2^{+}$ state of ${}^{12}\mathrm{C}$ (dashed line) at $E_L$=350, 400, 450, 500, and 608 MeV calculated using the coupled-channels method including coupling to the $2^{+}$ and $3^{-}$ states of ${}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}$. The experimental data (points) at 608 MeV are taken from Ref. [17].