We have used the WFPC2 on board HST to investigate the stellar population in a field located 4'.6 E of the center of the globular cluster 47 Tuc (NGC 104), close to the half-mass radius, through wide band imaging at 606 and 812 nm. A total of similar to 3000 stars are accurately classified by two-color photometry to form a color-magnitude diagram extending down to a limiting magnitude m(814) similar or equal to m(I) similar or equal to 24. A rich cluster main sequence is detected spanning the range from m(814) similar or equal to 18 through m(814) similar or equal to 23, where it spreads considerably due to the increasing photometric uncertainty and galaxy contamination. A secondary sequence of objects is also detected, parallel to the main sequence, as expected for a population of binary stars. The measured binary fraction in the range 19 < m(814) < 21 is greater than or similar to 5%. The main sequence luminosity function obtained from the observed CMD increases with decreasing luminosity following a power-law trend with index alpha similar or equal to 0.15 in the range 5 < M(814) < 9, but then drops sharply down to the measurement limit. Photometric completeness is similar to 67% in the faintest magnitude bin at I similar or equal to 24 due to crowding. On the basis of the available mass-luminosity relation for this metallicity, the resultant mass function shows a power-law increase in numbers for decreasing masses in the range 0.8-0.3 M(.) with a slope alpha not similar to 1.5, but then flattens out in the 0.3-0.15 M(.) range. The comparison of the mass function of 47 Tuc with that of NGC 6397 (Paper I) and of M 15 (PaperII), previously investigated with the same instrumentation, suggests that the stellar population near the half-mass radius of these clusters should not be very sensitive to either internal or externally-driven dynamical processes. The difference between their mass functions could then be attributed to metallicity, reflecting an intrinsic difference in their initial mass functions, unless mass-segregation is stronger in 47 Tuc than in the other two clusters. This latter circumstance could be due, for instance, to the large number of binaries discovered in 47 Tuc. In all cases, however, the mass function is found to flatten below 0.3 M(.) and the flattening is most likely an intrinsic property of the initial mass function itself, implying that very low mass stars are not produced in any dynamically significant amount by globular clusters, irrespective of their metal content or cluster history. This result is consistent with recent determinations of the initial mass function both in the disk and in the halo, suggesting the existence of some limitation in the mechanism of low-mass star formation.
