  A detailed torsional oscillator (TO) study on a stable solid 4He sample at 49
bar with To = 0.5K, is reported to T below the dissipation peak at Tp . We find
hysteretic behavior starting below Tc = about 75 mK, in period shift, as well
as in dissipation, with changes of AC excitation amplitude Vac . The derived
difference of non-linear rotational susceptibility DeltaNLRS(T)hys across the
hysteresis loop under a systematic condition is analyzed as a function of Vac
and T . We propose that DeltaN LRS(T)hys is proportional to non- classical
rortational inertia fraction, NCRIF, and is actually the supersolid density
rho_ss of the 3D supersolid state below Tc . rho_ss changes linearly with T
down to about 60 mK and then increases much more steeply, and approaching a
finite value towards T = 0. We find an AC velocity of 40 micrometer/s beyond
which the hysteresis starts at T < Tc and a critical AC velocity, about 1 cm/s,
above which rho_ss is completely destroyed. We discuss also the coherence
length of the supersolid.
