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Background: Shape coexistence in heavy nuclei poses a strong challenge tostate-of-the-art nuclear models, where several competing shape minima are foundclose to the ground state. A classic region for investigating this phenomenonis in the region around $Z=82$ and the neutron mid-shell at $N=104$.  Purpose: Evidence for shape coexistence has been inferred from $\alpha$-decaymeasurements, laser spectroscopy and in-beam measurements. While the latterallow the pattern of excited states and rotational band structures to be mappedout, a detailed understanding of shape coexistence can only come frommeasurements of electromagnetic matrix elements.  Method: Secondary, radioactive ion beams of $^{202}$Rn and $^{204}$Rn werestudied by means of low-energy Coulomb excitation at the REX-ISOLDE facility inCERN.  Results: The electric-quadrupole ($E2$) matrix element connecting the groundstate and first-excited $2^{+}_{1}$ state was extracted for both $^{202}$Rn and$^{204}$Rn, corresponding to ${B(E2;2^{+}_{1} \to 2^{+}_{1})=29^{+8}_{-8}}$W.u. and $43^{+17}_{-12}$ W.u., respectively. Additionally, $E2$ matrixelements connecting the $2^{+}_{1}$ state with the $4^{+}_{1}$ and $2^{+}_{2}$states were determined in $^{202}$Rn. No excited $0^{+}$ states were observedin the current data set, possibly due to a limited population of second-orderprocesses at the currently-available beam energies.  Conclusions: The results are discussed in terms of collectivity and thedeformation of both nuclei studied is deduced to be weak, as expected from thelow-lying level-energy schemes. Comparisons are also made to state-of-the-artbeyond-mean-field model calculations and the magnitude of the transitionalquadrupole moments are well reproduced.

Collectivity in the light radon nuclei measured directly via Coulomb excitation