Coupled Hartree-Fock calculations in various basis sets yield values i
n the range 6.7 to 6.8 for the Sternheimer antishielding factor (1 - g
amma(infinity)) of the nitrogen nucleus in the ammonium ion. These are
in substantial agreement with the value of 9 that is obtained from a
model of measured relaxation times in solid ammonium chloride when all
owance is made for effects of the crystalline environment on the chlor
ide ion Sternheimer antishielding factor. Other experimental estimates
of the nitrogen Sternheimer factor are discussed. The new value is us
ed to derive cation field gradients from measured quadrupole coupling
constants in solid NH4ReO4 and NH4IO4.