Reorientation-effect measurement of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo>〈</mml:mo><mml:msubsup><mml:mn>2</mml:mn><mml:mn>1</mml:mn><mml:mo>+</mml:mo></mml:msubsup><mml:mo>∥</mml:mo><mml:mover accent="true"><mml:mrow><mml:mi>E</mml:mi><mml:mn>2</mml:mn></mml:mrow><mml:mo></mml:mo></mml:mover><mml:mo>∥</mml:mo><mml:msubsup><mml:mn>2</mml:mn><mml:mn>1</mml:mn><mml:mo>+</mml:mo></mml:msubsup><mml:mo>〉</mml:mo></mml:mrow></mml:math>matrix element in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mrow/><mml:mn>10</mml:mn></mml:msup></mml:math>Be

The highly-efficient and segmented TIGRESS $\ensuremath{\gamma}$-ray spectrometer at TRIUMF has been used to perform a reorientation-effect Coulomb-excitation study of the 2${}_{1}^{+}$ state at 3.368 MeV in ${}^{10}$Be. This is the first Coulomb-excitation measurement that enables one to obtain information on diagonal matrix elements for such a high-lying first excited state from $\ensuremath{\gamma}$-ray data. With the availability of accurate lifetime data, a value of $\ensuremath{-}0.110\ifmmode\pm\else\textpm\fi{}0.087$ $e$b is determined for the $\ensuremath{\langle}{2}_{1}^{+}\ensuremath{\parallel}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{E2}\ensuremath{\parallel}{2}_{1}^{+}\ensuremath{\rangle}$ diagonal matrix element, which assuming the rotor model, leads to a negative spectroscopic quadrupole moment of ${Q}_{{}_{S}}({2}_{1}^{+})=\ensuremath{-}0.083\ifmmode\pm\else\textpm\fi{}0.066$ $e$b. This result is in agreement with both no-core shell-model calculations performed in this work with the CD-Bonn 2000 two-nucleon potential and large shell-model spaces, and Green's function Monte Carlo predictions with two- plus three-nucleon potentials.