Shape coexistence has been extensively studied both experimentally and theoretically ever since the discovery of a large change in mean-square charge radii in the neutron-deficient mercury isotopes . It is this region of the nuclear chart that has received much of the focus of efforts to understand and characterise what now appears to be a fundamental feature of nuclear structure .
Experimentally, a large array of techniques have been employed - in-beam spectroscopy , excited-state lifetime measurements , laser spectroscopy  and Coulomb excitation , for example - to elucidate the shape of coexisting structures in the light-lead region. The latter two have formed the basis of large experimental campaigns at ISOLDE utilising RILIS and Miniball, respectively.
Information on the electromagnetic properties of the low-spin states that form the complex low-energy level scheme leads to a determination of the shape of the nucleus. Critically, a determination of both the magnitude and sign of the deformation parameters is possible via a complete set of EM matrix elements coupling the low-lying states . Coulomb excitation uniquely affords this possibility due to the sensitivity of the excitation cross section to the sign of the matrix elements. In the case of shape coexistence, information on the mixing between the structures can also be obtained.
In this seminar, I will present the details of a series of experiments employing Coulomb-excitation with radioactive ion beams at REX-ISOLDE, CERN. I will show how the unique information on the signs of matrix elements can be combined with complementary information from other experimental techniques, such as lifetime measurements and laser spectroscopy, to build a picture of shape coexistence in nuclei.
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