Global well-posedness and blow-up for the hartree equation

For 2 < γ < min {4,n}, we consider the focusing Hartree equation (0.1)iut+Δu+(|x|-γ*|u|2)u=0,x∈Rn.Let M[u] and E[u] denote the mass and energy, respectively, of a solution u, and Q be the ground state of − Δ Q + Q = (|x|−γ *|Q|2)Q. Guo and Wang [Z. Angew. Math. Phy.,2014] established a dichotomy for scattering versus blow-up for the Cauchy problem of (0.1) if M[u]1-scE[u]sc