$B_c^{\pm}$-$^{12}$C states and detailed study of momentum space method for $\Upsilon$- and $\eta_b$-nucleus bound states

We perform a detailed study of the $\Upsilon$-, $\eta_b$-, and $B_c$-nucleus systems in momentum space to calculate the bound-state energies and the corresponding coordinate-space radial wave functions. The attractive strong potentials for the meson-nucleus systems are calculated from the Lorentz scalar mass modifications of these mesons in nuclear matter in the local density approximation in the nucleus. The downward shift of the meson masses may be regarded as a signature of partial restoration of chiral symmetry in a nuclear medium applied in the present study in an empirical sense, because the origin of the negative mass shift in this study is not directly related to the chiral symmetry mechanism. Furthermore, as an initial and realistic study, the $B_c^{\pm}$-$^{12}$C bound states are studied for the first time, with the effects of self-consistently calculated Coulomb potentials in $^{12}$C (when the $B_c^{\pm}$ mesons are absent).