Three clusters of the SMC from ACS/WFC HST archive data: NGC 265, K 29 and NGC 290 and their field population

Aims. We determine the age, metallicity and initial mass function of three clusters, namely NGC 265, K 29, NGC 290, located in the main body of the Small Magellanic Cloud. In addition, we derive the history of star formation in the companion fields. Methods. We make use of ACS/WFC HST archive data. For the clusters, the age and metallicity are derived fitting the integrated luminosity function with single synthetic stellar population by means of the chi(2) minimization. For the companion fields, the history of star formation is derived using the chi(2) minimization together with the downhill-simplex method. Results. For the clusters we find the following ages and metallicities: NGC 265 has log(Age) = 8.5 +/- 0.3 yr and metallicity 0.004 +/- 0.003 (or [Fe/H] = -0.62); K 29 has log( Age) = 8.2 +/- 0.2 yr and metallicity Z = 0.003 0.002 (or [Fe/H] = -0.75); NGC 290 has log( Age) = 7.8 +/- 0.5 yr and metallicity 0.003 +/- 0.002 (or [Fe/H] = -0.75). The superior quality of the data allows the study of the initial mass function down to M similar to 0.7 M-circle dot. The initial mass function turns out to be in agreement with the standard Kroupa model. The comparison of the NGC 265 luminosity function with the theoretical ones from stellar models both taking overshoot from the convective core into account and neglecting it, seems to suggest that a certain amount of convective overshoot is required. However, this conclusion is not a strong one because this cluster has a certain amount of mass segregation which makes it difficult to choose a suitable area for this comparison. The star formation rate of the field population presents periods of enhancements at 300-400 Myr, 3-4 Gyr and finally 6 Gyr. However it is relatively quiescent at ages older than 6 Gyr. This result suggests that at older ages, the tidal interaction between the Magellanic Clouds and the Milky Way was not able to trigger significant star formation events.