Measurements and computational analysis of the natural decay of Lu176

Abstract

Background: Mainly because of its long half-life and despite its scientific relevance, spectroscopic measurements of $^{176}\mathrm{Lu}$ forbidden $\ensuremath{\beta}$ decays are very limited and lack formulation of shape factors. A direct precise measurement of its Q value is also presently unreported. In addition, the description of forbidden decays provides interesting challenges for nuclear theory. The comparison of precise experimental results with theoretical calculations for these decays can help to test underlying models and can aid the interpretation of data from other experiments.Purpose: Perform the first precision measurements of $^{176}\mathrm{Lu}\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$-decay spectra and attempt the observation of its electron capture decays, as well as perform the first precision direct measurement of the $^{176}\mathrm{Lu}\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$-decay Q value. Compare the shape of the precisely determined experimental $\ensuremath{\beta}$ spectra to theoretical calculations, and compare the end point energy to that obtained from an independent Q value measurement.Method: The $^{176}\mathrm{Lu}\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$-decay spectra measurements and the search for electron capture decays were performed with an experimental setup that employed lutetium-containing scintillator crystals and a NaI(Tl) spectrometer for coincidence counting. The $\ensuremath{\beta}$ decay Q value was determined via high-precision Penning trap mass spectrometry (PTMS) with the LEBIT facility at the National Superconducting Cyclotron Laboratory. The $\ensuremath{\beta}$-spectrum calculations were performed within the Fermi theory formalism with nuclear structure effects calculated using a shell model approach.Results: Both $\ensuremath{\beta}$ transitions of $^{176}\mathrm{Lu}$ were experimentally observed and corresponding shape factors formulated in their entire energy ranges. The search for electron capture decay branches led to an experimental upper limit of $6.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ relative to its $\ensuremath{\beta}$ decays. The $^{176}\mathrm{Lu}\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$-decay and electron capture Q values were measured using PTMS to be 1193.0(6) and 108.9(8) keV, respectively. This enabled precise $\ensuremath{\beta}$ end point energies of 596.2(6) and 195.3(6) keV to be determined for the primary and secondary $\ensuremath{\beta}$ decays, respectively. The conserved vector current hypothesis was applied to calculate the relativistic vector matrix elements. The $\ensuremath{\beta}$-spectrum shape was shown to significantly depend on the Coulomb displacement energy and on the value of the axial vector coupling constant ${g}_{A}$, which was extracted according to different assumptions.Conclusion: The implemented self-scintillation method has provided unmatched observations of $^{176}\mathrm{Lu}$, independently validated by the first direct measurements of its $\ensuremath{\beta}$-decay Q value by Penning trap mass spectrometry. Theoretical study of the main $\ensuremath{\beta}$ transition led to the extraction of very different effective ${g}_{A}$ and ${log}_{10}\phantom{\rule{0.16em}{0ex}}f$ values, showing that a high-precision description of this transition would require a realistic nuclear structure with nucleus deformation.