Abstract
By analyzing 482 pb\$^-1\$ of \$e^+e^-\$ collision data collected at \$\sqrt
s=4.009\$ GeV with the BESIII detector at the BEPCII storage ring, we measure
the absolute branching fractions for the semileptonic decays \$D\_s^+\to\eta
e^+\nu\_e\$ and \$D\_s^+\eta'e^+\nu\_e\$ to be
\$B(D\_s^+\rightarrowe^+\nu\_e)=(2.30\pm0.31\pm0.09)\$\% and
\$B(D\_s^+\rightarrow\eta'e^+ \nu\_e) = (0.93\pm0.30\pm0.05)\$\%,
respectively, and their ratio
\$B(D\_s^+\rightarrow\eta'e^+\nu\_e)
B(D\_s^+\rightarrowe^+\nu\_e)=0.40\pm0.14\pm0.02\$, 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.
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