Comment on 'Alpha decay of thermally excited nuclei'

In their recent study of α-decay of thermally excited nuclei [1], Perez Velasquez, Caballero, and Kelkar (hereafter PVCK) claim an extraordinary reduction of the α-decay half-life of ²¹²Po by almost 5 orders of magnitude at a temperature of 2 Giga-Kelvin (T₉ = 2 in usual astrophysical notation). Besides the generally marginal dependence of radioactive decay rates on the environment and its temperature, there are two reasons which make this claim striking. (i) A statistical approach for the same nucleus in PVCK leads to a much more moderate temperature dependence of the α-decay half-life. (ii) The α-decay half-lives of individual levels in ²¹²Po (see table 3 of PVCK) are longer than 10⁻¹¹ s in all cases which is less than 5 orders of magnitude faster than the ground state half-life of 2.9 × 10⁻⁷ s. (Note that the 2⁺ level at 1679 keV has a short half-life of 5.4 × 10⁻¹³ s; in a combination of the α-decay branching of 0.3% this leads to a partial α-decay half-life of 1.8 × 10⁻¹⁰ s.) Together with the Boltzmann factor $\exp (-{E}^{* }/{kT})$ which at T₉ = 2 is about one per cent for the first excited state in ²¹²Po at 727 keV and much lower for higher-lying states, it is difficult to envisage that the effective α-decay half-life of ²¹²Po is reduced by almost 5 orders of magnitude at T₉ = 2.

A careful re-analysis of the properties of excited states in ²¹²Po shows that the α-decay properties of several levels are at least questionable. Furthermore, after deadline of the adopted levels in [2], there are updated half-life measurements for several states. This re-analysis exceeds the scope of this comment and will be published in a separate paper [3]. The results of [3] are summarized in figure 1 and briefly discussed in the next paragraph.

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The recommended result in [3] is based on updated level properties in ²¹²Po. In particular, several questionable α-decay branches in [2] were excluded. Furthermore, some recent half-life measurements were included in the recommended result. A lower limit of the half-life of ²¹²Po is obtained in [3] by including all questionable α-decay branchings. This lower limit is very close to a calculation using the level properties in table 3 of PVCK. Contrary, the original calculation of PVCK (also based on the data in table 3 of PVCK) shows by far stronger temperature dependence of the α-decay half-life of ²¹²Po. The reason for this discrepancy remains unclear. Interestingly, two further calculations in PVCK using the statistical so-called Q_eff approach (see equations (14)–(18) in PVCK) lead to a much weaker temperature dependence for t_1/2; unfortunately, no further explanations for the discrepancy between the different approaches are provided in PVCK.

To summarize, the claim by PVCK for a dramatic reduction of the α-decay half-life of ²¹²Po for temperatures above T₉ ≈ 1 is not confirmed by the present re-analysis. Instead, only a moderate reduction of the α-decay half-life with temperature is found (e.g. a factor of ≈3 at T₉ = 2).

Acknowledgments

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