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We report the first measurements of absolute branching fractions for the$W$-exchange-only processes $\Lambda^+_c\to\Xi^0K^+$ and$\Lambda^+_c\to\Xi(1530)^0K^+$ with the double-tag technique, by analyzing an$e^{+}e^{-}$ collision data sample, that corresponds to an integratedluminosity of 567 pb$^{-1}$ collected at a center-of-mass energy of 4.6 GeV bythe BESIII detector. The branching fractions are measured to be$\mathcal{B}(\Lambda^+_c\to\Xi^0K^+)=(5.90\pm0.86\pm0.39)\times10^{-3}$ and$\mathcal{B}(\Lambda^+_c\to\Xi(1530)^0K^+)=(5.02\pm0.99\pm0.31)\times10^{-3}$,where the first uncertainties are statistical and the second systematic. Ourresults are more precise than the previous relative measurements.

Measurements of Absolute Branching Fractions for $\Lambda^+_c\to\Xi^0K^+$ and $\Xi(1530)^0K^+$