Strong<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>E</mml:mi><mml:mn>1</mml:mn><mml:mn/></mml:math>transitions in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Be</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>9</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Be</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>11</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>13</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>

The Doppler shift attenuation method has been used to make two measurements of the mean life of the $^{11}\mathrm{Be}$ 320-keV level. The results are 150\ifmmode\pm\else\textpm\fi{}30 fs from the $^{9}\mathrm{Be}(t, \mathrm{p}\ensuremath{\gamma})^{11}\mathrm{Be}$ reaction and 168\ifmmode\pm\else\textpm\fi{}17 fs from the $^{3}\mathrm{H}(^{9}\mathrm{Be}, \mathrm{p}\ensuremath{\gamma})^{11}\mathrm{Be}$ reaction. The adopted value of 166\ifmmode\pm\else\textpm\fi{}15 fs, from the present and previous measurements, corresponds to an extremely strong $E1$ transition of 0.36\ifmmode\pm\else\textpm\fi{}0.03 W.u. The adopted energy of the ground state transition from this and previous measurements is 320.04\ifmmode\pm\else\textpm\fi{}0.10 keV. It is shown that the magnitude of this $E1$ transition can be understood on the basis of shell-model calculations only if realistic single-particle wave functions are used. A similar theoretical treatment is given for strong $E1$ transitions in $^{9}\mathrm{Be}$ and $^{13}\mathrm{C}$.NUCLEAR REACTIONS $^{9}\mathrm{Be}(t, \mathrm{p}\ensuremath{\gamma})^{11}\mathrm{Be}$, $E(\mathrm{t})=1.5\ensuremath{-}3.3$ MeV, $^{3}\mathrm{H}(^{9}\mathrm{Be}, \mathrm{p}\ensuremath{\gamma})^{11}\mathrm{Be}$, $E(^{9}\mathrm{Be})=10\ensuremath{-}16$ MeV; measured DSA; deduced $\ensuremath{\tau}(^{11}\mathrm{Be}, 320\ensuremath{-}\mathrm{k}\mathrm{e}\mathrm{V})$; calculated $B(E1)$, $B(M2)$ from thoery and compared to experiment for $^{9}\mathrm{Be}$, $^{11}\mathrm{Be}$, $^{13}\mathrm{C}$.