  First ever measurements of the ratios of free cyclotron frequencies of heavy
highly charged ions with Z>50 with relative uncertainties close to 1e-11 are
presented. Such accurate measurements have become realistic due to the
construction of the novel cryogenic multi-Penning-trap mass spectrometer
PENTATRAP. Based on the measured frequency ratios, the mass differences of five
pairs of stable xenon isotopes, ranging from 126Xe to 134Xe, have been
determined. Moreover, the first direct measurement of an electron binding
energy in a heavy highly charged ion, namely of the 37th atomic electron in
xenon, with an uncertainty of a few eV is demonstrated. The obtained value
agrees with the calculated one using two independent different implementations
of the multiconfiguration Dirac-Hartree-Fock method. PENTATRAP opens the door
to future measurements of electron binding energies in highly charged heavy
ions for more stringent tests of bound-state quantum electrodynamics in strong
electromagnetic fields and for an investigation of the manifestation of Light
Dark Matter in isotopic chains of certain chemical elements.
