We carry out state-selective Rabi and Ramsey magnetic-resonance experiments
on ground-state Cs-133(F=4) atoms. Novel line shapes are obtained, which e
xhibit very sharp features with a width much smaller than the inverse durat
ion of the magnetic-resonance pulse. The sensitivity of ordinary magnetic-r
esonance experiments with total spin F > 1/2 is significantly less than the
Heisenberg limit, which can be exactly realized only with maximally correl
ated spin states. We show that the stale-selective resonances yield sensiti
vity very close to the Heisenberg limit, without any state preparation beyo
nd ordinary optical pumping. [S1050-2917(99)51192-5].