A Ge(Li) detector and the reaction ${\mathrm{Si}}^{30}(d, p){\mathrm{Si}}^{31}$ with $E_d=2-4\mathrm{}$ MeV are used in the coincidence version of the Doppler-shift attenuation method to obtain the following information concerning the mean lives of some low-lying states in ${\mathrm{Si}}^{31}$: $\tau \left(0.75\mathrm{} \mathrm{MeV}\right)=\left({{7.2}_{-1.8\mathrm{}}}^{+2.6\mathrm{}}\right)\times {10}^{-13\mathrm{}}$ sec, $\tau \left(1.69\mathrm{} \mathrm{MeV}\right)=(7.4\mathrm{}\pm 2.3)\times {10}^{-13\mathrm{}}$ sec, $\tau \left(2.32\mathrm{} \mathrm{MeV}\right)<\mathrm{}3\mathrm{}\times {10}^{-13\mathrm{}}$ sec, $\tau \left(3.14\mathrm{} \mathrm{MeV}\right)=\left({{5.0}_{-2.6\mathrm{}}}^{+2.2\mathrm{}}\right)\times {10}^{-13\mathrm{}}$ sec, $\tau \left(3.53\mathrm{} \mathrm{MeV}\right)<\mathrm{}3.7\mathrm{}\times {10}^{-14\mathrm{}}$ sec. From these results, the reduced matrix elements for electromagnetic transitions among some of these states are obtained. A comparison is made between these reduced matrix elements and those predicted by the extreme single-particle model, the Nilsson rotational model, and the shell model with configuration mixing in the $2s_{\frac{1}{2}}$ and $1d_{\frac{3}{2}}$ shells. Our results indicate a value of $\left|\eta \right|={{2.8}_{-0.4\mathrm{}}}^{+0.5\mathrm{}}$ for the Nilsson deformation parameter for ${\mathrm{Si}}^{31}$. A value of 752±1 keV was obtained for the excitation energy of the 0.75-MeV state.

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