  Recent experiments have suggested that, at low enough temperature, the
homogeneous nucleation of bubbles occurs in liquid helium near the calculated
spinodal limit. This was done in pure superfluid helium 4 and in pure normal
liquid helium 3. However, in such experiments, where the negative pressure is
produced by focusing an acoustic wave in the bulk liquid, the local amplitude
of the instantaneous pressure or density is not directly measurable. In this
article, we present a series of measurements as a function of the static
pressure in the experimental cell. They allowed us to obtain an upper bound for
the cavitation pressure P_cav (at low temperature, P_cav < -2.4 bar in helium
3, P_cav < -8.0 bar in helium 4). From a more precise study of the acoustic
transducer characteristics, we also obtained a lower bound (at low temperature,
P_cav > -3.0 bar in helium 3, P_cav > - 10.4 bar in helium 4). In this article
we thus present quantitative evidence that cavitation occurs at low temperature
near the calculated spinodal limit (-3.1 bar in helium 3 and -9.5 bar in helium
4). Further information is also obtained on the comparison between the two
helium isotopes. We finally discuss the magnitude of nonlinear effects in the
focusing of a sound wave in liquid helium, where the pressure dependence of the
compressibility is large.
