  The electromagnetic structure of $^{140}$Sm was studied in a low-energy
Coulomb excitation experiment with a radioactive ion beam from the REX-ISOLDE
facility at CERN. The $2^+$ and $4^+$ states of the ground-state band and a
second $2^+$ state were populated by multi-step excitation. The analysis of the
differential Coulomb excitation cross sections yielded reduced transition
probabilities between all observed states and the spectroscopic quadrupole
moment for the $2_1^+$ state. The experimental results are compared to
large-scale shell model calculations and beyond-mean-field calculations based
on the Gogny D1S interaction with a five-dimensional collective Hamiltonian
formalism. Simpler geometric and algebraic models are also employed to
interpret the experimental data. The results indicate that $^{140}$Sm shows
considerable $\gamma$ softness, but in contrast to earlier speculation no signs
of shape coexistence at low excitation energy. This work sheds more light on
the onset of deformation and collectivity in this mass region.
