We present new analysis of 11 intermediate-age (1-2 Gyr) star clusters in the Large Magellanic Cloud based on Hubble Space Telescope imaging data. Seven of the clusters feature main sequence turnoff (MSTO) regions that are wider than can be accounted for by a simple stellar population, whereas their red giant branches indicate a single value of [Fe/H]. The star clusters cover a range in present-day mass from about 1E4 to 2E5 solar masses. We compare radial distributions of stars in the upper and lower parts of the MSTO region, and calculate cluster masses and escape velocities from the present time back to a cluster age of 10 Myr. Our main result is that for all clusters in our sample with estimated escape velocities > 15 km/s at an age of 10 Myr, the stars in the brightest half of the MSTO region are significantly more centrally concentrated than the stars in the faintest half AND more massive red giant branch and asymptotic giant branch stars. This is not the case for clusters with escape velocities < 10 km/s at an age of 10 Myr. We argue that the wide MSTO region of such clusters is mainly caused by to a 200 - 500 Myr range in the ages of cluster stars due to extended star formation within the cluster from material shed by first-generation stars featuring slow stellar winds. Dilution of this enriched material by accretion of ambient interstellar matter is deemed plausible if the spread of [Fe/H] in this ambient gas was very small when the second-generation stars were formed in the cluster.
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