Measurements of the absolute branching fractions for D-s(+) -> eta e(+)nu(e) and D-s(+) -> eta ' e(+)nu(e)

By analyzing 482 pb(-1) of e(+) e(-) collision data collected at root s = 4.009 GeV with the BESIII detector at the BEPCII collider, we measure the absolute branching fractionsfor the semileptonic decaysD-s(+) -> eta e(+)nu( e) and D-s(+) -> eta ' e(+)nu( e) to be B(D-s(+) -> eta e(+)nu( e)) = (2.30 +/- 0.31 +/- 0.08)% and B(D-s(+) -> eta ' e(+)nu( e)) = (0.93 +/- 0.30 +/- 0.05)%, respectively, and their ratio B(D-s(+) -> eta ' e(+)nu( e)) / B(D-s(+) -> eta ' e(+)nu( e)) = 0.40 +/- 0.14 +/- 0.02, where the first uncertainties are statistical and the second ones are systematic. The results are in good agreement with previous measurements within uncertainties; they can be used to determine the eta-eta' mixing angle and improve upon the D-s(+) semileptonic branching ratio precision.