We present the star formation history and chemical evolution of the Sextans dSph dwarf galaxy as a function of galactocentric distance. We derive these from the $VI$ photometry of stars in the $42 times 28$ field using the SMART model developed by Yuk & Lee (2007, ApJ, 668, 876) and adopting a closed-box model for chemical evolution. For the adopted age of Sextans 15 Gyr, we find that $>$84% of the stars formed prior to 11 Gyr ago, significant star formation extends from 15 to 11 Gyr ago ($sim$ 65% of the stars formed 13 to 15 Gyr ago while $sim$ 25% formed 11 to 13 Gyr ago), detectable star formation continued to at least 8 Gyr ago, the star formation history is more extended in the central regions than the outskirts, and the difference in star formation rates between the central and outer regions is most marked 11 to 13 Gyr ago. Whether blue straggler stars are interpreted as intermediate age main sequence stars affects conclusions regarding the star formation history for times 4 to 8 Gyr ago, but this is at most only a trace population. We find that the metallicity of the stars increased rapidly up to [Fe/H]=--1.6 in the central region and to [Fe/H]=--1.8 in the outer region within the first Gyr, and has varied slowly since then. The abundance ratios of several elements derived in this study are in good agreement with the observational data based on the high resolution spectroscopy in the literature. We conclude that the primary driver for the radial gradient of the stellar population in this galaxy is the star formation history, which self-consistently drives the chemical enrichment history.
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