The complete pattern of Rydberg binding energies of the 18 n = 9 levels of nickel with L = 6, 7, and 8 was measured using microwave plus resonant-excitation Stark-ionization spectroscopy. The measured pattern is consistent with the form predicted with the effective potential model, showing significant structure proportional to scalar products of tensor operators of order 0-4. The variation of the structure with L separates the various contributing terms and provides determinations of several properties of the Ni + core ion. These include the quadrupole moment, Q = −0.469 78(9) a.u., the hexadecapole moment, = 0.36(5) a.u., the scalar and tensor dipole polarizabilities, α D,0 = 7.949(2) a.u., α D,2 = 0.905(12) a.u., the scalar quadrupole polarizability, α Q,0 = 55(8) a.u., the g value, g J = 1.257 (14), and the vector hyperpolarizability, β D,1 = 0.454 (24) a.u. + A 3 ( X [3] (J c ) · T [3] (r) ) + A 4 X [4] (J c ) · C [4] (r)