Elastic transfer and parity dependence of the nucleus-nucleus optical potential

Background: A recent coupled reaction channel (CRC) study shows that the enhanced oscillation of the elastic $^{16}$O+$^{12}$C cross section at backward angles is due mainly to the elastic $\alpha$ transfer or the core exchange. Such a process gives rise to a parity-dependent term in the total elastic $S$-matrix, an indication of the parity dependence of the $^{16}$O+$^{12}$C optical potential (OP). Purpose: To explicitly determine the core exchange potential (CEP) induced by the symmetric exchange of the two $^{12}$C cores in the elastic $^{16}$O+$^{12}$C scattering at $E_{\rm lab}= 132$ and 300 MeV, and explore its parity dependence. Method: $S$-matrix generated by CRC description of the elastic $^{16}$O+$^{12}$C scattering is used as the input for the inversion calculation to obtain the effective local OP that contains both the Wigner and Majorana terms. Results: The high-precision inversion results show a strong contribution by the complex Majorana term in the total OP of the $^{16}$O+$^{12}$C system, and thus provide for the first time a direct estimation of the parity-dependent CEP. Conclusions: The elastic $\alpha$ transfer or exchange of the two $^{12}$C cores in the $^{16}$O+$^{12}$C system gives rise to a complex parity dependence of the total OP. This should be a general feature of the OP for the light heavy-ion systems that contain two identical cores.