Direct measurement of ${B(D}^0\to \phi X^0)$ and ${B(D}^{+}\to \phi X^{+})$

The first measurement of ${B(D}^0\to \phi X^0)$ and an upper limit for ${B(D}^{+}\to \phi X^{+})$ are determined from 22.3 ${\mathrm{pb}}^{-1}$ of $e^{+}{e}^{-}$ annihilation data at a c.m. energy of 4.03 GeV. The data were recorded by the Beijing Spectrometer (BES) at BEPC. A recoil charge method is applied to charm threshold data to determine the charge of the D meson in the recoil from $9054\pm 309\pm 416$ reconstructed $D^0,$ $D^{+}$ mesons. The branching fractions ${B(D}^0\to \phi X^0{)=(1.71\mathrm{}}_{-0.71}^{+0.76\mathrm{}}\pm 0.17)\%,$ and ${B(D}^{+}\to \phi X^{+})<\mathrm{}1.8\%$ are determined from 10 events with a reconstructed D and a recoiling $\phi .$ In addition, a 90% C.L. upper limit of ${B(D}^{+}\to \phi e^{+}{X}^0)<\mathrm{}1.6\%$ is determined from a search for semileptonic decays of the $D^{+}.$