  Double or extended main-sequence turn-offs (DMSTOs) and dual red clump (RC)
were observed in intermediate-age clusters, such as in NGC 1846 and 419. the
DMSTOs are interpreted as that the cluster has two distinct stellar popula-
tions with differences in age of about 200-300 Myr but with the same
metallicity. The dual RC is interpreted as a result of a prolonged star
formation. Using a stellar population-synthesis method, we calculated the
evolutions of binary-star stellar population (BSP). We found that binary
interactions and merging can reproduce the dual RC in the color-magnitude
diagrams of an intermediate-age cluster, whereas in actuality only a single
population exists. Moreover, the binary interactions can lead to an extended
MSTO rather than DMSTOs. However, the rest of main sequence, subgiant branch
and first giant branch are hardly spread by the binary interactions. Part of
the observed dual RC and extended MSTO may be the results of binary
interactions and merger.
