Precise electromagnetic tests of ab-initio calculations of light nuclei: States in ¹⁰Be

In order to test {\it ab-initio} calculations of light nuclei, we have remeasured lifetimes in $^{10}$Be using the Doppler Shift Attenuation Method (DSAM) following the $^{7}$Li($^7$Li,$\alpha$)$^{10}$Be reaction at 8 and 10 MeV. The new experiments significantly reduce systematic uncertainties in the DSAM technique. The J$^{\pi}$ = $2^+_1$ state at 3.37 MeV has $\tau$ = 205${\pm}$(5)$_{stat}\pm$(7)$_{sys}$ fs corresponding to a $B$($E2\downarrow$) of 9.2(3) $e^2$fm$^4$ in broad agreement with many calculations. The J$^{\pi}$ = $2^+_2$ state at 5.96 MeV was found to have a $B$($E2\downarrow$) of 0.11(2) $e^2$fm$^4$ and provides a more discriminating test of nuclear models. New Green's Function Monte Carlo (GFMC) calculations for these states and transitions with a number of Hamiltonians are also reported and compared to experiment.