  We carried out wide-field BVI CCD photometric observations of the GCs M3 and
M13 using the BOAO 1.8 m telescope equipped with a 2K CCD. We present CMDs of
M3 and M13. We have found AGB bumps at V = 14.85 for M3 at V = 14.25 for M13.
It is found that AGB stars in M3 are more concentrated near the bump, while
those in M13 are scattered along the AGB sequence. We identified the RGB bump
of M3 at V = 15.50 and that of M13 at V = 14.80. We have estimated the ratios R
and R2 for M3 and M13 and found that of R for M3 is larger than that for M13
while R2's for M3 and M13 are similar when only normal HB stars are used in R
and R2 for M13. However, we found that R's for M3 and M13 are similar while R2
for M3 is larger than that for M13 when all the HB stars are included in R and
R2 for M13. We have compared the observed RGB LFs of M3 and M13 with the
theoretical RGB LF of Bergbusch & VandenBerg at the same radial distances from
the cluster centers as used in R and R2 for M3 and M13. We found "extra stars"
belonging to M13 in the comparison of the observed RGB LF of M13 and the
theoretical RGB LF of Bergbusch & VandenBerg. In the original definition of R
of Buzzoni et al., N(HB) corresponds to the lifetime of HB stars in the RR
Lyrae instability strip at log T_eff = 3.85. So, the smaller R value resulting
for M13 compared with that for M3 in the case where only normal HB stars are
included in R and R2 for M13 may be partially caused by "extra stars", and the
similar R's for M3 and M13 in the case where the all HB stars are included in R
and R2 for M13 may be caused by "extra stars" in the upper RGB of M13. If
"extra stars" in the upper RGB of M13 are caused by an effective "deep mixing"
these facts support the contention that an effective "deep mixing" could lead
to different HB morphologies between M3 and M13 and subsequent sequences.
