  The 6s-np_j (n=6-9) electric-dipole matrix elements and 6s-nd_j (n=5-7)
electric-quadrupole matrix elements in Ba+ are calculated using the
relativistic all-order method. The resulting values are used to evaluate ground
state dipole and quadrupole polarizabilities. In addition, the electric-dipole
6p_j-5d_j' matrix elements and magnetic-dipole 5d_{5/2}-5d_{3/2} matrix element
are calculated using the same method in order to determine the lifetimes of the
6p_{1/2}, 6p_{3/2}, 5d_{3/2}, and 5d_{5/2} levels. The accuracy of the 6s-5d_j
matrix elements is investigated in detail in order to estimate the
uncertainties in the quadrupole polarizability and 5d_j lifetime values. The
lifetimes of the 5d states in Ba+ are extremely long making precise experiments
very difficult. Our final results for dipole and quadrupole ground state
polarizabilities are alpha_{E1} = 124.15 a^3_0 and alpha_{E2} = 4182(34) a^5_0,
respectively. The resulting lifetime values are tau(6p_{1/2})=7.83 ns,
tau(6p_{3/2})=6.27 ns, tau(5d_{3/2})=81.5(1.2) s, and tau(5d_{5/2})=30.3(4) s.
The extensive comparison with other theoretical and experimental values is
carried out for both lifetimes and polarizabilities.
