# Investigation on Rare Nuclear Processes in Hf Nuclides

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## Abstract

**:**

## Simple Summary

^{174}Hf, some other rare nuclear processes, such as the alpha decay of

^{176}Hf in

^{172}Yb and

^{177}Hf in

^{173}Yb are near the theoretical expectations, giving hope to their first observation in the near future. In addition, a short emphasis on several types of Hf-based crystal scintillators is reported.

## Abstract

## 1. Introduction

## 2. Searching for Double Beta Decay in Hafnium Isotopes

## 3. Searching for Alpha Decays in Hafnium Isotopes

**Table 3.**Main potential $\alpha $ decay of Hf nuclides. Isotopes with natural abundance ($\delta $) greater than zero (i.e., naturally present in nature) and with Q${}_{\alpha}>0$ for transitions between g.s. or between g.s. and lowest bounded level (with spin/parity ${J}^{\pi}$) are listed. Theoretical predictions and experimental measurements (if exist) on the T${}_{1/2}$’s are reported in the latest columns.

Nuclide Transition | ${\mathit{J}}^{\mathit{\pi}}$ | $\mathit{\delta}$ | Q${}_{\mathit{\alpha}}$ | T${}_{1/2}$ (y) | |||
---|---|---|---|---|---|---|---|

Parent→ | (%) | (keV)
| Theoretical | ||||

Daughter Nuclei | [31] | [26] | Experimental | ||||

and Its Level (keV) | [32] | [33] | [34] | ||||

${}^{174}$Hf$\phantom{\rule{3.33333pt}{0ex}}\to {\phantom{\rule{3.33333pt}{0ex}}}^{170}$Yb | ${0}^{+}\to {0}^{+}$, g.s. | 0.156(6) [27] | 2494.5(2.3) | $7.0\left(1.2\right)\times {10}^{16}$ [27] | $3.5\times {10}^{16}$ | $7.4\times {10}^{16}$ | $3.5\times {10}^{16}$ |

${0}^{+}\to {2}^{+}$, 84.2 | ⩾$2.8\times {10}^{16}$ [30] | $1.3\times {10}^{18}$ | $3.0\times {10}^{18}$ | $6.6\times {10}^{17}$ | |||

${}^{176}$Hf$\phantom{\rule{3.33333pt}{0ex}}\to {\phantom{\rule{3.33333pt}{0ex}}}^{172}$Yb | ${0}^{+}\to {0}^{+}$, g.s. | 5.26(70) | 2254.2(1.5) | ⩾$9.3\times {10}^{19}$ [27] | $2.5\times {10}^{20}$ | $6.6\times {10}^{20}$ | $2.0\times {10}^{20}$ |

${0}^{+}\to {2}^{+}$, 78.7 | ⩾$3.0\times {10}^{17}$ [35] | $1.3\times {10}^{22}$ | $3.5\times {10}^{22}$ | $4.9\times {10}^{21}$ | |||

${}^{177}$Hf$\phantom{\rule{3.33333pt}{0ex}}\to {\phantom{\rule{3.33333pt}{0ex}}}^{173}$Yb | $7/{2}^{-}\to 5/{2}^{-}$, g.s. | 18.60(16) | 2245.7(1.4) | ⩾$3.2\times {10}^{20}$ [27] | $4.5\times {10}^{20}$ | $5.2\times {10}^{22}$ | $4.4\times {10}^{22}$ |

$7/{2}^{-}\to 7/{2}^{-}$, 78.6 | ⩾$1.3\times {10}^{18}$ [35] | $9.1\times {10}^{21}$ | $1.2\times {10}^{24}$ | $3.6\times {10}^{23}$ | |||

${}^{178}$Hf$\phantom{\rule{3.33333pt}{0ex}}\to {\phantom{\rule{3.33333pt}{0ex}}}^{174}$Yb | ${0}^{+}\to {0}^{+}$, g.s. | 27.28(28) | 2084.4(1.4) | ⩾$5.8\times {10}^{19}$ [27] | $3.4\times {10}^{23}$ | $1.1\times {10}^{24}$ | $2.2\times {10}^{23}$ |

${0}^{+}\to {2}^{+}$, 76.5 | ⩾$1.3\times {10}^{18}$ [30] | $2.4\times {10}^{25}$ | $8.1\times {10}^{25}$ | $7.1\times {10}^{24}$ | |||

${}^{179}$Hf$\phantom{\rule{3.33333pt}{0ex}}\to {\phantom{\rule{3.33333pt}{0ex}}}^{175}$Yb | $9/{2}^{+}\to 7/{2}^{+}$, g.s. | 13.62(11) | 1807.7(1.4) | ⩾$2.5\times {10}^{20}$ [27] | $4.5\times {10}^{29}$ | $4.0\times {10}^{32}$ | $4.7\times {10}^{31}$ |

$9/{2}^{+}\to 9/{2}^{+}$, 104.5 | ⩾$2.7\times {10}^{18}$ [30] | $2.0\times {10}^{32}$ | $2.5\times {10}^{35}$ | $2.2\times {10}^{34}$ | |||

${}^{180}$Hf$\phantom{\rule{3.33333pt}{0ex}}\to {\phantom{\rule{3.33333pt}{0ex}}}^{176}$Yb | ${0}^{+}\to {0}^{+}$, g.s. | 35.08(33) | 1287.1(1.4) | – | $6.4\times {10}^{45}$ | $5.7\times {10}^{46}$ | $9.2\times {10}^{44}$ |

${0}^{+}\to {2}^{+}$, 82.1 | ⩾$1.0\times {10}^{18}$ [35] | $4.0\times {10}^{49}$ | $4.1\times {10}^{50}$ | $2.1\times {10}^{48}$ |

**Figure 4.**Simplified decay schemes of potential $\alpha $ decay of Hf isotopes considering the first two energy levels of the daughter nuclei. The corresponding gamma transitions and the probability related for a single energy level are also shown. The ${}^{175}$Yb isotope is unstable via ${\beta}^{-}$ decay with T${}_{1/2}=4.185\left(1\right)$ d [36], all the other Yb nuclei are stable.

## 4. Perspectives and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**(

**a**) Energy spectrum acquired with the experiment at HADES [29] in the region of interest for the 2$\nu $2K and 2$\nu $KL of ${}^{174}$Hf (solid histogram, online red). The dots (online blue) is the background data without the Hf sample and normalized to the time of acquisition. Solid line (online black) is the fit of the background model, and the dashed line is the excluded effect. (Taken from Ref. [29] with permission). (

**b**) Energy spectrum acquired with the experiment at LNGS [30], in the region of interest for the $\alpha $ decay of ${}^{174}$Hf (see next section). However, the low energy range of the panel shows the energy region of interest for the case of 2$\nu $2K and 2$\nu $KL of ${}^{174}$Hf decay, where the dominant background is due to the Hf X-rays. The solid line (online red) is the background model for the $\alpha $ decay of ${}^{174}$Hf and the dashed line is the excluded effect. (Taken from Ref. [30] with permission).

**Figure 5.**Mean time ($\langle t\rangle $) versus energy for the data accumulated over 2848 h using a CHC crystal scintillator (see text). The lines corresponding to sigma intervals (at the 99% of events) for the $\langle t\rangle $ values of $\beta /\gamma $ and $\alpha $ particles are painted (on-line: red solid lines and blue dashed lines, respectively). (Inset) Distribution of the $\langle t\rangle $ for the data in the energy range of (0.4–3.0) MeV (taken from Ref. [27] with permission).

**Figure 6.**$\alpha $ energy spectrum picked out using the PSD from the data accumulated with the CHC crystal scintillator over 2848 h. The fit model built from $\alpha $ decays of ${}^{238}$U and ${}^{232}$Th with daughters is highlighted by blue solid line, and some individual fit contributions are also presented. The energy scale is in $\alpha $ energy having considered the Q.F. studied in Ref. [27] (taken from Ref. [27] with permission).

**Figure 7.**Using the PSD, the energy spectrum of $\alpha $ events from the acquired data with a CHC scintillator over 2848 h is shown. For the energy scale, the authors have considered the Q.F. of $\alpha $ particles (see text or Ref. [27] for details). (

**left**) The fit of the data, in the energy region of interest, for the ${}^{174}$Hf $\alpha $ decay. The fit model is built considering the $\alpha $ decays of ${}^{147}$Sm, ${}^{174}$Hf (red line) and taking into account some degraded alpha particles (online solid blue line). The yellow band is the background model. (

**right**) The fit of the data by a modified model similar to the previous one but considering one peak (instead of two) in the energy (2.2–2.6) MeV (taken from Ref. [27] with permission).

**Figure 8.**Diagram T${}_{1/2}$ vs the inverse of the square root of alpha energy in MeV. The black symbols are the results in Refs. [1,27]. The $\alpha $ decay of ${}^{174}$Hf has been observed [27], while only lower limits at 90% C.L. are reported for the other three Hf isotopes naturally present. The blue band is the extrapolation of the predictions for all the Hf isotopes using the Geiger-Nuttall scaling law and the observed data point [27]. The red symbols represent the sensitivity that the measurement can reach using a CHC crystal scintillator with 43.83 kg × day of exposure. As evident, there is a good perspective to observe the $\alpha $ decay of ${}^{176}$Hf and ${}^{176}$Hf (see also Table 3).

Channel of the Decay | Decay Mode | Level of Daughter Nucleus | E${}_{\mathit{\gamma}}$ (keV) | Detection Efficiency (%) | |
---|---|---|---|---|---|

J${}^{\mathit{\pi}}$, Energy (keV) | [29] | [30] | |||

$2L$ | $2\nu $ | ${2}^{+}$, 76.5 | 76.5 | $0.39$ | $3.15$ |

$2K$ | $0\nu $ | g.s. | 977.4 | $4.53$ | $7.59$ |

$KL$ | $0\nu $ | g.s. | 1028.9 | $4.46$ | $7.32$ |

$2L$ | $0\nu $ | g.s. | 1080.4 | $4.39$ | $7.09$ |

$2K$ | $0\nu $ | ${2}^{+}$, 76.5 | 900.9 | $4.67$ | $8.01$ |

$KL$ | $0\nu $ | ${2}^{+}$, 76.5 | 952.4 | $4.59$ | $7.72$ |

$2L$ | $0\nu $ | ${2}^{+}$, 76.5 | 1003.9 | $4.51$ | $7.45$ |

$K{\beta}^{+}$ | $2\nu +0\nu $ | g.s. | 511 | $10.6$ | $11.8$ |

$L{\beta}^{+}$ | $2\nu +0\nu $ | g.s. | 511 | $10.7$ | $11.8$ |

Channel of the Decay | Decay Mode | Level of Daughter Nucleus | Experimental Limit of T${}_{1/2}$ (90% C.L. (y)) | |
---|---|---|---|---|

J${}^{\mathit{\pi}}$, Energy (keV) | [29] | [30] | ||

$2K$ | $2\nu $ | g.s. | ≥$7.1\times {10}^{16}$ | ≥$1.4\times {10}^{16}$ |

$KL$ | $2\nu $ | g.s. | ≥$4.2\times {10}^{16}$ | ≥$1.4\times {10}^{16}$ |

$2K$ | $2\nu $ | ${2}^{+}$, 76.5 | ≥$5.9\times {10}^{16}$ | ≥$7.9\times {10}^{16}$ |

$KL$ | $2\nu $ | ${2}^{+}$, 76.5 | ≥$3.5\times {10}^{16}$ | ≥$7.9\times {10}^{16}$ |

$2L$ | $2\nu $ | ${2}^{+}$, 76.5 | ≥$3.9\times {10}^{16}$ | ≥$7.9\times {10}^{16}$ |

$2K$ | $0\nu $ | g.s. | ≥$5.8\times {10}^{17}$ | ≥$2.7\times {10}^{18}$ |

$KL$ | $0\nu $ | g.s. | ≥$1.9\times {10}^{18}$ | ≥$4.2\times {10}^{17}$ |

$2L$ | $0\nu $ | g.s. | ≥$7.8\times {10}^{17}$ | ≥$3.6\times {10}^{17}$ |

$2K$ | $0\nu $ | ${2}^{+}$, 76.5 | ≥$7.1\times {10}^{17}$ | ≥$2.4\times {10}^{18}$ |

$KL$ | $0\nu $ | ${2}^{+}$, 76.5 | ≥$6.2\times {10}^{17}$ | ≥$3.1\times {10}^{17}$ |

$2L$ | $0\nu $ | ${2}^{+}$, 76.5 | ≥$7.2\times {10}^{17}$ | ≥$9.4\times {10}^{17}$ |

$K{\beta}^{+}$ | $2\nu +0\nu $ | g.s. | ≥$1.4\times {10}^{17}$ | ≥$5.6\times {10}^{16}$ |

$L{\beta}^{+}$ | $2\nu +0\nu $ | g.s. | ≥$1.4\times {10}^{17}$ | ≥$5.6\times {10}^{16}$ |

Scintillator | Percentage of Hf in Weight (%) | Density (g/cm${}^{3}$) | L.Y. (phe/MeV) | Main Decay Time (ns) | Main Emission Peak (nm) |
---|---|---|---|---|---|

BaHfO${}_{3}$(Ce) | 49 | 8.3 | ∼40,000 | ∼25 | ∼400 |

CaHfO${}_{3}$ | 67 | 6.9 | ∼10,000 | ∼33 | ∼439 |

Cs${}_{2}$HfCl${}_{6}$ | 31 | 3.8 | ∼50,000 | ∼10,000 | ∼400 |

HfF${}_{4}$ | 70 | 7.1 | ∼300 | ∼29 | ∼350 |

HfO${}_{2}$ | 85 | 9.7 | ∼30,000 | ∼9500 | ∼480 |

La${}_{2}$Hf${}_{2}$O${}_{7}$(Ti) | 23 | 7.9 | ∼13,000 | ∼10,000 | ∼475 |

SrHfO${}_{3}$(Ce) | 57 | 6.7 | ∼40,000 | ∼42 | ∼410 |

∼36 (89%); | |||||

Tl${}_{2}$HfCl${}_{6}$ | 22 | 5.3 | ∼25,000 | ∼217 (6%); | ∼380 |

∼1500 (11%) |

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**MDPI and ACS Style**

Caracciolo, V.; Belli, P.; Bernabei, R.; Cappella, F.; Cerulli, R.; Incicchitti, A.; Laubenstein, M.; Leoncini, A.; Merlo, V.; Nagorny, S.;
et al. Investigation on Rare Nuclear Processes in Hf Nuclides. *Radiation* **2022**, *2*, 234-247.
https://doi.org/10.3390/radiation2020017

**AMA Style**

Caracciolo V, Belli P, Bernabei R, Cappella F, Cerulli R, Incicchitti A, Laubenstein M, Leoncini A, Merlo V, Nagorny S,
et al. Investigation on Rare Nuclear Processes in Hf Nuclides. *Radiation*. 2022; 2(2):234-247.
https://doi.org/10.3390/radiation2020017

**Chicago/Turabian Style**

Caracciolo, Vincenzo, Pierluigi Belli, Rita Bernabei, Fabio Cappella, Riccardo Cerulli, Antonella Incicchitti, Matthias Laubenstein, Alice Leoncini, Vittorio Merlo, Serge Nagorny,
and et al. 2022. "Investigation on Rare Nuclear Processes in Hf Nuclides" *Radiation* 2, no. 2: 234-247.
https://doi.org/10.3390/radiation2020017