The laser rf double-resonance technique in a Paul trap has been used t
o make high-precision measurements of the hyperfine structure (hfs) of
the 4f7(S-8(7/2)6s S-9(4) ground state in Eu-151, Eu-153+. We have ob
tained linewidths below 1 kHz for the magnetic-field-dependent rf tran
sitions at frequencies between 1.7 and 10 GHz. After corrections for t
he second-order hfs we obtain values for the magnetic-dipole, electric
-quadrupole, magnetic-octupole, and electric-hexadecapole interaction
constants.