  This paper is concerned with the qualitative properties of the positive
ground state solutions to the nonlocal Choquard type equation on a ball $B_R$.
First, we prove the radial symmetry of the positive ground state solutions by
using Talenti's inequality. Next we develop Newton's Theorem and then resort to
the contraction mapping principle to establish the uniqueness of the positive
ground state solutions. Finally, by constructing cut-off functions and applying
energy comparison method, we show the convergence of the positive ground state
solutions as $R\to \infty$. Our results generalize and improve the existing
ones in the literature.
