Bc±-¹²C states and detailed study of momentum space method for Υ- and ηb-nucleus bound states

We perform a detailed study of the Υ-, ηb- and Bc-nucleus systems in momentum space to calculate the bound-state energies and the corresponding coordinate space radial wave functions. A comparison is made among different methods to obtain the partial wave decomposition of meson-nucleus potentials in momentum space, namely, (i) the spherical Bessel transform of the numerically obtained original potential in coordinate space, (ii) the partial wave decomposition of the Fourier transform of the Woods-Saxon approximated form for the original potential, and (iii) the spherical Bessel transform of the Woods-Saxon approximation of the numerically obtained original potential. The strong nuclear bound-state energies for the Υ-⁴He, Υ-¹²C, ηb-⁴He, ηb-¹²C, Bc-⁴He (no Coulomb), and Bc-¹²C (no Coulomb) systems and the corresponding wave functions in coordinate space are compared for the three methods. Furthermore, as an initial and realistic study, the Bc±-¹²C bound states are studied for the first time, with the effects of self-consistently calculated Coulomb potentials in ¹²C (when the Bc± mesons are absent).