A study of the accuracy of the penning trap mass spectrometer ISOLTRAP and standard-model tests with superallowed $\beta$-decays

ISOLTRAP is a Penning trap mass spectrometer installed at the on-line isotope separator ISOLDE/CERN. It is dedicated to the measurement of the atomic masses of short-lived radioactive nuclides. Relative statistical uncertainties of individual mass measurements are typically of the order of 10$^{−8}$. Using ions of carbon clusters whose mass ratios are exactly known, the various contributions to the total uncertainty of a mass measurement were studied. It was found by these measurements that the limit of the relative uncertainty of a mass measurement is 8$\times$10$^{−9}$, more than an order of magnitude better than previously expected. Using the new measurement and evaluation procedure adopted as a result of this study, the Q-value of the superallowed $\beta$-decay of $^{74}$Rb was determined via a mass measurement of the mother and the daughter nuclide. With a half-life of under 65 ms, $^{74}$Rb is the shortest-lived nuclide ever investigated in a Penning trap. This experimental result allowed a contribution to the verification of the conserved-vector-current hypothesis of the weak interaction, a postulate of the Standard-Model. It also served as a check of calculated parameters that are required for more stringent tests in the future.