Rare nuclear processes in Hf isotopes

Recently, efforts on the building of Hf-based crystal scintillators have been performed. The so-called “source = detector” approach has been implemented to study rare nuclear processes in Hf isotopes with higher efficiency with respect to the HP-Ge spectrometry. In this work, a review of recent studies concerning rare nuclear processes in Hf isotopes are presented.

• DBD modes without the presence of neutrinos, if observed, can open windows on new physics • to test calculations of different nucleus shapes and decay modes that involve the vector and axial-vector weak effective coupling constants; possible study of the "resonant effect" on the 0ν2ε mode; • mutual information from the simultaneous study of positive and negative DBD can constrain the theoretical parameters with very high confidence • the nuclear matrix elements for the two-neutrino mode and for the neutrinoless mode can be related to each other through relevant parameters: in the free nucleon interaction, the g A value is 1.2701, but, when considering a nuclear decay, there are indications that the phenomenological axial-vector coupling value is reduced at g A < 1, more precisely: g A ≈ 1.269 A -0.18 or g A ≈ 1.269 A -0.12 , depending on the nuclear model adopted to infer the g A value. DBD investigation with various nuclei would shed new light in constraining these and other important model-dependent parameters. • As byproduct: developments of new detectors, e.g., new crystal scintillators containing DBD emitters The isotope 174 Hf is one of the potentially 2ε, εβ + radioactive nuclides with the energy of decay Q 2β =1100.0(23)keV and the isotopic abundance δ=0.156(6)% (they used the old value 0.16(12)%).
In case of the 2K and KL capture in 174 Hf, a cascade of X-rays (and Auger electrons) of Yb atom with individual energies, in particular, in the energy interval (50.8-61.3)keV is expected, while energies of the 2L capture X-ray quanta are ≈(7 −10)keV, that are below the detectors' energy thresholds. We took into account only the most intense X-rays of ytterbium: 51.4 keV (the intensity of the X-ray quanta is 27.2%), 52.4 keV (47.4%), 59.2 keV (5.2%), 59.4 keV (10.0%), and 61.0 keV (3.4%).

Nuclear Physics A 996 (2020) 121703
A search for double beta decays in hafnium using HP-Ge gamma spectrometer Section view of the detector and sample (not to scale) with 1) hafnium foils on the top and wrapping the Ge crystal acting as the target and highvoltage contact, 2) copper end cap of 1mm thickness, 3) copper HP-Ge crystal holder, and 4) HP-Ge semi-coaxial ptype crystal.
A search for double beta decays in hafnium using HP-Ge gamma spectrometer • Various theoretical models are continuously developed or improved, e.g., motivated by searches for stable or long-lived superheavy isotopes and predictions of their halflives.
• The study on the nuclear instability offers information about the nuclear structure, the nuclear levels and the properties of nuclei.
• The phenomenon of α decay can offer information about the fusion-fission reactions since the α decay process involves sub-barrier penetration of α particles through the barrier, caused by the interaction between the α and the nucleus • Among the naturally occurring α-emitting nuclides only those with either A > 208 or A ≈ 145 have α half-lives short enough to be detected Some potential transitions of Hf isotopes and related information. Only naturally occurring isotopes (with natural abundance δ) and with Q > 0 between g.s. transitions or between g.s. and lowest bound level transitions (with spin/parity J π ) are listed. E is the kinetic energy of the alpha particle. N is the number of nuclei in the CHC crystal used in this work. Experimental measurements (when available) and theoretical prediction of the half-live are reported in the last four columns.
T.P. Kohman, Phys. Rev. 121, 1758(1961; Eur. Phys. J. A (2020) 56:5 Nuclear Physics A 1012 (2021) 122212 Section view of the detector and sample (not to scale) with 1) hafnium foils on the top and wrapping the Ge crystal acting as the target and high-voltage contact, 2) copper end cap of 1mm thickness, 3) copper HPGe crystal holder, and 4) HPGe semi-coaxial p-type crystal.
A search for alpha decays in excited states of hafnium isotope using HP-Ge gamma spectrometer T.P. Kohman, Phys. Rev. 121, 1758(1961; Schematic cross-sectional view of the experimental set-up (not in scale). There are shown the CHC crystal scintillator (1) coupled with a 3 inches PMT (2), the HP-Ge detector (3), which is separated by a cylindrical Teflon ring (4). They are completely surrounded by a passive shield made by archaeological Roman lead (5), high purity copper (6), low radioactive lead (7). The whole set-up (with the exception of the cold finger for the HP-Ge detector) is enclosed in a Plexiglas box (8)