Measurements and computational analysis on the natural decay of $^{176}$Lu

International audience; Background: Mainly because of its long half-life and despite its scientific relevance, spectroscopic measurements of 176Lu beta decays are very limited and lack formulation of shape factors. Direct 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 measurement of 176Lu beta-decay spectrum and attempt the observation of its electron capture decays, as well as perform the first precision direct measurement of the 176Lu beta-decay Q-value. Compare the shape of the precisely determined experimental beta-spectrum to theoretical calculations, and compare the end-point energy to that obtained from an independent Q-value measurement.Method: The 176Lu beta-decay spectra and the search for electron capture decays were measured with an experimental set-up that employed lutetium-based scintillator crystals and an NaI(Tl) spectrometer for coincidence counting. The 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 beta-spectrum calculations were performed within the Fermi theory formalism with nuclear structure effects calculated using a shell model approach.Results: Both beta transitions of 176Lu were experimentally observed and corresponding shape factors formulated in their entire energy ranges. Search for electron captures decay branches led to an experimental upper limit of 6.3x10-6 compared to its beta decays. The 176Lu beta-decay and electron capture Q-values were measured using PTMS to be 1193.0(6) keV and 108.9(8) keV, respectively. This enabled precise beta end-point energies of 596.2(6) keV and 195.3(6) keV for the primary and secondary beta-decays, respectively, to be determined. The conserved vector current hypothesis was applied to calculate the relativistic vector matrix elements. The beta-spectrum shape was shown to significantly depend on the Coulomb displacement energy and on the value of the axial vector coupling constant gA, which was extracted according to different assumptions.