We report the final results of the Phase II SIMPLE measurements, comprising two run stages of 15 superheated droplet detectors each, with the second stage including an improved neutron shielding. The analyses include a refined signal analysis, and revised nucleation efficiency based on a reanalysis of previously reported monochromatic neutron irradiations. The combined results yield a contour minimum of $\sigma${}p=5.7\ifmmode\times\else\texttimes\fi{}10-3\,\,pb at 35\,\,GeV/c2 in the spin-dependent sector of weakly interacting massive particle (WIMP) proton interactions, the most restrictive to date for MW$\le${}60\,\,GeV/c2 from a direct search experiment and overlapping, for the first time, with results previously obtained only indirectly. In the spin-independent sector, a minimum of 4.7\ifmmode\times\else\texttimes\fi{}10-6\,\,pb at 35\,\,GeV/c2 is achieved, with the exclusion contour challenging a significant part of the light mass WIMP region of current interest.

Phase II of SIMPLE (Superheated Instrument for Massive ParticLe Experiments) searched for astroparticle dark matter using superheated liquid ${\mathrm{C}}_{2}{\mathrm{ClF}}_{5}$ droplet detectors. Each droplet generally requires an energy deposition with linear energy transfer (LET) $$\gtrsim${}150\text{ }\text{ }\mathrm{keV}/$\mu${}\mathrm{m}$ for a liquid-to-gas phase transition, providing an intrinsic rejection against minimum ionizing particles of order ${10}^{$-${}10}$, and reducing the backgrounds to primarily $$\alpha${}$ and neutron-induced recoil events. The droplet phase transition generates a millimetric-sized gas bubble that is recorded by acoustic means. We describe the SIMPLE detectors, their acoustic instrumentation, and the characterizations, signal analysis and data selection, which yield a particle-induced, ``true nucleation'' event detection efficiency of better than 97% at a 95% C.L. The recoil-$$\alpha${}$ event discrimination, determined using detectors first irradiated with neutrons and then doped with alpha emitters, provides a recoil identification of better than 99%; it differs from those of COUPP and PICASSO primarily as a result of their different liquids with lower critical LETs. The science measurements, comprising two shielded arrays of fifteen detectors each and a total exposure of 27.77 kgd, are detailed. Removal of the 1.94 kgd Stage 1 installation period data, which had previously been mistakenly included in the data, reduces the science exposure from 20.18 to 18.24 kgd and provides new contour minima of ${$\sigma${}}_{p}=4.3\ifmmode\times\else\texttimes\fi{}{10}^{$-${}3}\text{ }\text{ }\mathrm{pb}$ at $35\text{ }\text{ }\mathrm{GeV}/{\mathrm{c}}^{2}$ in the spin-dependent sector of astroparticle dark matter\char21{}proton interactions and ${$\sigma${}}_{N}=3.6\ifmmode\times\else\texttimes\fi{}{10}^{$-${}6}\text{ }\text{ }\mathrm{pb}$ at $35\text{ }\text{ }\mathrm{GeV}/{\mathrm{c}}^{2}$ in the spin-independent sector. These results are examined with respect to the fluorine spin and halo parameters used in the previous data analysis.