  The structure of exotic nuclei provides valuable tests for state-of-the-art
nuclear theory. In particular electromagnetic transition rates are more
sensitive to aspects of nuclear forces and many-body physics than excitation
energies alone. We report the first lifetime measurement of excited states in
$^{21}$O, finding
$\tau_{1/2^+}=420^{+35}_{-32}\text{(stat)}^{+34}_{-12}\text{(sys)}$\,ps. This
result together with the deduced level scheme and branching ratio of several
$\gamma$-ray decays are compared to both phenomenological shell-model and ab
initio calculations based on two- and three-nucleon forces derived from chiral
effective field theory. We find that the electric quadrupole reduced transition
probability of $\rm B(E2;1/2^+ \rightarrow 5/2^+_{g.s.}) = 0.71^{+0.07\
+0.02}_{-0.06\ -0.06}$~e$^2$fm$^4$, derived from the lifetime of the $1/2^+$
state, is smaller than the phenomenological result where standard effective
charges are employed, suggesting the need for modifications of the latter in
neutron-rich oxygen isotopes. We compare this result to both large-space and
valence-space ab initio calculations, and by using multiple input interactions
we explore the sensitivity of this observable to underlying details of nuclear
forces.
