Evidence for a dynamically refracted primary bow in weakly bound ${}^9\mathrm{Be}$ rainbow scattering from ${}^{16}\mathrm{O}$

We present for the first time evidence for the existence of a dynamically refracted primary bow for ${}^9\mathrm{Be}+{}^{16}\mathrm{O}$ scattering. This is demonstrated through the use of coupled channel calculations with an extended double folding potential derived from the density-dependent effective two-body force and precise microscopic cluster wave functions for ${}^9\mathrm{Be}$. The calculations reproduce the experimental Airy structure in ${}^9\mathrm{Be}+{}^{16}\mathrm{O}$ scattering well. It is found that coupling of a weakly bound ${}^9\mathrm{Be}$ nucleus to excited states plays the role of a booster lens, dynamically enhancing the refraction over the static refraction due to the Luneburg lens mean field potential between the ground states of ${}^9\mathrm{Be}$ and ${}^{16}\mathrm{O}$.

Figure 1

The angular distributions of ${}^9\mathrm{Be}+{}^{16}\mathrm{O}$ scattering at (a) $E\left({}^9\mathrm{Be}\right)=157.7$ MeV and (b) 74.25 MeV $\left[E\right({}^{16}\mathrm{O})=132$ MeV] calculated in a single channel (solid lines) are compared with the experimental data (points) [18, 19, 21]. The calculated cross sections are decomposed into the farside component (dashed lines) and the nearside component (dash-dotted lines).

Figure 2

The angular distributions of ${}^9\mathrm{Be}+{}^{16}\mathrm{O}$ scattering at (a) $E\left({}^9\mathrm{Be}\right)=157.7$ MeV and (b) 74.25 MeV $\left[E\right({}^{16}\mathrm{O})=132$ MeV] calculated using the coupled channel method with coupling to both the $5/2^{-}$ and $7/2^{-}$ states including reorientations (solid lines) are compared with the experimental data (points) [18, 19, 21]. The farside component of the calculated cross sections is indicated by the dashed lines. The single channel calculations where the coupling is switched off are displayed for comparison with dotted lines.

Figure 3

The energy evolution of the Airy minimum $A1$ and $A2$ of the Airy structure in the angular distributions between $E\left({}^9\mathrm{Be}\right)=157.7$ MeV and 74.25 MeV $\left[E\right({}^{16}\mathrm{O})=132$ MeV], calculated using the CC method, are displayed with solid lines. The experimental data [18, 19, 21] are indicated by the points.

Figure 4

Illustrative refractive trajectories (solid lines) in nuclear rainbow scattering. The refracted angle ${\theta }_R$ is a rainbow angle for the primary nuclear rainbow caused by the mean field optical potential (Luneburg lens [3]) of the nucleus (indicated by a circle) without coupling to the excited states. The angular region $\theta \le {\theta }_R$ is the bright side of the primary nuclear rainbow and $\theta >{\theta }_R$ is the dark side. By coupling to the excited states of ${}^9\mathrm{Be}$ the refraction is dynamically enhanced and the rainbow angle is increased to ${\theta }_{Rd}$.

Figure 5

Same as Fig. 2 but for the calculations with the M3Y force. The angular distributions of ${}^9\mathrm{Be}+{}^{16}\mathrm{O}$ scattering at (a) $E\left({}^9\mathrm{Be}\right)=157.7$ MeV and (b) 74.25 MeV $\left[E\right({}^{16}\mathrm{O})=132$ MeV] calculated using the coupled channel method with coupling to both the $5/2^{-}$ and $7/2^{-}$ states including reorientations (solid lines) are compared with the experimental data (points) [18, 19, 21]. The farside and nearside component of cross sections calculated using the CC method are indicated with dashed lines and dashed-dotted lines, respectively. The single channel calculations where the coupling is switched off are displayed for comparison with dotted lines.