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Mass measurements of fission and projectile fragments, produced via $^{238}$Uand $^{124}$Xe primary beams, have been performed with the multiple-reflectiontime-of-flight mass spectrometer (MR-TOF-MS) of the FRS Ion Catcher with a massresolving powers (FWHM) up to 410,000 and an uncertainty of $6\cdot 10^{-8}$.The nuclides were produced and separated in-flight with the fragment separatorFRS at 300 to 1000 MeV/u and thermalized in a cryogenic stopping cell. Thedata-analysis procedure was developed to determine with highest accuracy themass values and the corresponding uncertainties for the most challengingconditions: down to a few events in a spectrum and overlapping distributions,characterized only by a broader common peak shape. With this procedure, theresolution of low-lying isomers is increased by a factor of up to threecompared to standard data analysis. The ground-state masses of 31 short-livednuclides of 15 different elements with half-lives down to 17.9~ms and countrates as low as 11 events per nuclide were determined. This is the first directmass measurement for seven nuclides. The excitation energies and theisomer-to-ground state ratios of six isomeric states with excitation energiesdown to about 280~keV were measured. For nuclides with known mass values, theaverage relative deviation from the literature values is $(2.9 \pm 6.2) \cdot10^{-8}$. The measured two-neutron separation energies and their slopes nearand at the N=126 and Z=82 shell closures indicate a strong element-dependentbinding energy of the first neutron above the closed proton shell Z=82. Theexperimental results deviate strongly from the theoretical predictions,especially for N=126 and N=127.

High-resolution, accurate MR-TOF-MS for short-lived, exotic nuclei of few events in their ground and low-lying isomeric states