%0 Journal Article %T Collectivity in the light radon nuclei measured directly via Coulomb excitation %A L. P. Gaffney %A A. P. Robinson %A D. G. Jenkins %A A. N. Andreyev %A M. Bender %A A. Blazhev %A N. Bree %A B. Bruyneel %A P. A. Butler %A T. E. Cocolios %A T. Davinson %A A. N. Deacon %A H. De Witte %A D. DiJulio %A J. Diriken %A A. Ekstr£¿m %A Ch. Fransen %A S. J. Freeman %A K. Geibel %A T. Grahn %A B. Hadinia %A M. Hass %A P. -H. Heenen %A H. Hess %A M. Huyse %A U. Jakobsson %A N. Kesteloot %A J. Konki %A Th. Kr£¿ll %A V. Kumar %A O. Ivanov %A S. Martin-Haugh %A D. M¨¹cher %A R. Orlandi %A J. Pakarinen %A A. Petts %A P. Peura %A P. Rahkila %A P. Reiter %A M. Scheck %A M. Seidlitz %A K. Singh %A J. F. Smith %A J. Van de Walle %A P. Van Duppen %A D. Voulot %A R. Wadsworth %A N. Warr %A F. Wenander %A K. Wimmer %A K. Wrzosek-Lipska %A M. Zieli¨½ska %J Physics %D 2015 %I arXiv %R 10.1103/PhysRevC.91.064313 %X Background: Shape coexistence in heavy nuclei poses a strong challenge to state-of-the-art nuclear models, where several competing shape minima are found close to the ground state. A classic region for investigating this phenomenon is in the region around $Z=82$ and the neutron mid-shell at $N=104$. Purpose: Evidence for shape coexistence has been inferred from $\alpha$-decay measurements, laser spectroscopy and in-beam measurements. While the latter allow the pattern of excited states and rotational band structures to be mapped out, a detailed understanding of shape coexistence can only come from measurements of electromagnetic matrix elements. Method: Secondary, radioactive ion beams of $^{202}$Rn and $^{204}$Rn were studied by means of low-energy Coulomb excitation at the REX-ISOLDE facility in CERN. Results: The electric-quadrupole ($E2$) matrix element connecting the ground state 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, $E2$ matrix elements connecting the $2^{+}_{1}$ state with the $4^{+}_{1}$ and $2^{+}_{2}$ states were determined in $^{202}$Rn. No excited $0^{+}$ states were observed in the current data set, possibly due to a limited population of second-order processes at the currently-available beam energies. Conclusions: The results are discussed in terms of collectivity and the deformation of both nuclei studied is deduced to be weak, as expected from the low-lying level-energy schemes. Comparisons are also made to state-of-the-art beyond-mean-field model calculations and the magnitude of the transitional quadrupole moments are well reproduced. %U http://arxiv.org/abs/1503.03245v1