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In this study, the first forbidden beta decay matrix elements have been directly calculated within Saxon-Woods potential. Procedures for calculating the relevant matrix elements and combining them to form the decay rate are described. Calculations have been performed by two different methods. The values of our single particle matrix elements have been compared with the calculated values in the two different tables.doi:10.3390/mca10020179 fatcat:s6z646ncsvhq5kvktryyagqbwe