${}^6\mathrm{Li}+{}^{15}\mathrm{N}$ interaction at $E_{\text{c.m.}}=23.1 \mathrm{MeV}$: Validation of the $\alpha +d$ cluster model of ${}^6\mathrm{Li}$

An extensive data set for the ${}^6\mathrm{Li}+{}^{15}\mathrm{N}$ system at an energy $E_{\mathrm{c}.\mathrm{m}.}=23.1$ MeV, consisting of elastic and inelastic scattering to excited states of ${}^{15}\mathrm{N}$ and the $3_1^{+}$, $2_1^{+}$, and $1_1^{+}$ spin-orbit triplet of $L=2$, $T=0$ resonances in ${}^6\mathrm{Li}$, was analyzed with a single calculation including the ${}^6\mathrm{Li}\to \alpha +d$ breakup, excitation of the ${}^{15}\mathrm{N}$ levels, and the ${}^{15}\mathrm{N}({}^6\mathrm{Li},{}^7\mathrm{Li}){}^{14}\mathrm{N}$ one-neutron pickup reaction employing the coupled discretized continuum channel, coupled channel, and coupled reaction channel techniques, respectively. Since the experiment was performed in inverse kinematics, and owing to the specific structure properties of ${}^{15}\mathrm{N}$, it was possible to measure an angular distribution for population of the $1_1^{+}$ resonance of ${}^6\mathrm{Li}$ for the first time, without the need for time-consuming and complicated coincidence measurements through detection of the scattered ${}^{15}\mathrm{N}$. A good description of the cross sections for populating all three ${}^6\mathrm{Li}$ resonances was obtained, confirming the validity of the $\alpha +d$ cluster model of ${}^6\mathrm{Li}$. In the methodology adopted the surface absorption was mostly generated by the included couplings, and while the ${}^6\mathrm{Li}$ breakup had the most important influence on the elastic scattering, coupling to the ${}^{15}\mathrm{N}$ inelastic excitations was also found to have a significant effect, particularly at midrange angles. By contrast, the one-neutron pickup coupling had a negligible effect on the other channels.

Figure 1

Typical ${}^{15}\mathrm{N}$ and ${}^6\mathrm{Li}$ energy spectra from the ${}^6\mathrm{Li}({}^{15}\mathrm{N},{}^{15}\mathrm{N}){}^6\mathrm{Li}$ scattering. The curves denote the fitted symmetric Gaussian forms from which the peak yields were obtained.

Figure 2

Comparison of OM (solid curve, ${\chi }^2=1.2$ per data point) and CC (dotted curve, ${\chi }^2=1.4$ per data point) calculations with the elastic scattering data.

Figure 3

Results of the CC calculation (dotted curves) compared to the data for inelastic scattering to excited states of ${}^{15}\mathrm{N}$. The solid curves denote the results of the final CRC calculation [the results of the CDCC calculations including coupling to the excited states of ${}^{15}\mathrm{N}$ but not including the ${}^{15}\mathrm{N}({}^6\mathrm{Li},{}^7\mathrm{Li}){}^{14}\mathrm{N}$ one-neutron pickup are graphically indistinguishable].

Figure 4

Angular distribution of the elastic scattering differential cross section (ratio to Rutherford cross section). The dotted curve denotes the result of a CDCC calculation taking the ${}^6\mathrm{Li}\to \alpha +d$ breakup into account, the dashed curve shows the effect of adding coupling to the inelastic excitations of ${}^{15}\mathrm{N}$, and the solid curve shows the result of the final CRC calculation further adding coupling to the ${}^{15}\mathrm{N}({}^6\mathrm{Li},{}^7\mathrm{Li}){}^{14}\mathrm{N}$ one-neutron pickup reaction.

Figure 5

Angular distributions of the ${}^6\mathrm{Li}+{}^{15}\mathrm{N}$ inelastic scattering leading to the 2.186-MeV $3^{+}$, 4.31-MeV $2^{+}$, and 5.65-MeV $1^{+}$ resonant states of ${}^6\mathrm{Li}$. The curves have the same meaning as in Fig. 4.