The core of the galactic globular cluster 47 Tucanae was observed by t
he Faint Object Camera on the refurbished Hubble Space Telescope for t
he first time through medium-band F253M and F346M filters centered at
255 and 348 nm. A total of 442 stars down to the detection limit at m3
46 congruent-to 24 in the 7'' x 7'' field were accurately placed on a
m346 versus m253 - m346 magnitude diagram to characterize the stellar
populations in the core. Approximately 100 objects above and to the ri
ght of the main-sequence turnoff are the same as those classified earl
ier with the aberrated HST, but the rest below it are new objects seen
now for the first time thanks to the substantial improvement in sensi
tivity. The new objects form a well-defined main sequence whose lumino
sity function turns over dramatically at m346 congruent-to 19 well bef
ore the completeness limit and well before the end of the slowly incre
asing luminosity function for the outer fields measured from the groun
d by Hesser et al. We interpret this premature drop in the number of s
tars below approximately 0.8 M. in the core as the effect of mass segr
egation due to two-body relaxation. The position of nine objects in th
e range 20 < m346 < 24 and - 1.5 < m253 - m346 < 0 is consistent with
the expected location of a approximately 0.5 M. white dwarf cooling se
quence and luminosity function.