Spontaneous double alpha decay: First experimental limit and prospects of investigation
aa r X i v : . [ nu c l - e x ] F e b Spontaneous double alpha decay:First experimental limit and prospects of investigation
V.I. Tretyak Institute for Nuclear Research of NASU, 03028 Kyiv, Ukraine
Abstract
Nuclear decays with simultaneous emission of two alpha particles are energetically possiblefor a number of nuclides. Prospects of searching for such kind of decay for nuclides presentin the natural isotopic composition of elements are discussed here. The first experimentallimit on half-life for 2 α decay is set for Bi as T / > . × y at 90% C.L., using thedata of work [P. de Marcillac et al., Nature 422 (2003) 876]. Theoretical T / estimationsfor the process are also given. Using these values, which are on the level of 10 y ormore, one can conclude that the prospects of experimental observation of 2 α decay arevery pessimistic. Keywords : double alpha decay, low background experiments, theoretical and experimentalhalf-lives.
We know today several kinds of decay of atomic nuclei in which two particles of the same natureare emitted simultaneously.Double beta (2 β ) decay, in which two electrons are emitted together with two antineutrinos,was predicted in 1935 by Goeppert-Mayer [1] and is registered to-date for 14 nuclides [2, 3].Neutrinoless mode of this decay, in which only two electrons are emitted without antineutrinos,was first discussed by Furry in 1939 [4]. It is forbidden in the Standard Model (SM) of particlesbecause it violates the lepton number by two units, but is predicted by many theories whichconsider the SM as a low-energy approximation; it is not observed yet but is actively searchedfor in many worldwide experiments [3, 5].Deexcitation of an excited nuclear state with emission of two gammas, 2 γ decay, was con-sidered by Goeppert-Mayer in 1929 [6] (see also [7]). It was observed in 1963 for nuclei with0 + → + transitions, like O, Ca and Zr, where emission of single γ is forbidden, andallowed are emissions of a conversion electron, or electron-positron pair, or two gammas [8]. In2015, it was also observed for the first time for Ba, where emission of a single γ is allowed,as a competitive mode on the level of 10 − [9].Also, nuclear decays with simultaneous emission of two protons (2 p ) and two neutrons (2 n )are known; see [10] and Refs. therein.However, possibility of nuclear decay with emission of two alpha particles at the sametime (2 α decay) was not analyzed on the same level of attention as the 2 β , 2 γ , 2 p and 2 n radioactivities. To our knowledge, it was discussed only in a brief theoretical article [11] (seealso [12]), and there were no experimental searches for such processes yet. [email protected]. α decay (Section 2), givetheoretical estimations of half-lives for a number of nuclides present in the natural isotopiccomposition of elements (Section 3) and set the first experimental limit for such a process(Section 4). It should be noted that in interactions of nuclei with high-energy particles thedefragmentation of nuclei with emission of few α particles is possible [13] but we are interestedhere in the spontaneous 2 α decay. α decay Analyzing atomic masses from the last atomic mass evaluation [14], one can see that 2 α decayis energetically possible for many nuclei (for 1459 isotopes from 3436 listed in [14]). Energyreleases Q α can reach quite big values (maximal value is 22.7 MeV for Cn) that, supposingan exponential dependence of half-life T / on Q α similar to single alpha decay, increasesprobability of this process. However, many of such nuclides are unstable with short half-livesrespective to their main decay branch; they should be created at accelerators or extracted fromfission products at nuclear reactors. It would be quite difficult to see a rare 2 α process on thebig radioactive α and β backgrounds. Instead, we will concentrate here on techniques whichare typical in searches for rare nuclear decays, like 2 β [2, 3, 5], single α and β [15], dark matter[16, 17], or in neutrino measurements [18].In such an approach, massive (from ∼ . ∼ α decay are listed in Table 1. Table 1: Naturally abundant 80 nuclides candidates for 2 α decay. δ is the natural abundance of the motherisotope [19]. Energy release Q α is calculated with atomic masses [14]. Half-life T / is given for the daughterisotope [20]. If value of Q α is greater than 3 MeV, it is marked in bold (red); in this case big abundance (ifso) and unstable daughter isotope (if so) are also marked in bold (red). In the last column, the theoreticalestimation of T / is given, calculated with receipt from [21] for Be emission. 2 ε is for double electron capture, εβ + is for electron capture with positron emission.Mother δ ,% Q α , keV Daughter Additional possible α and β decay Theor.isotope [19] [14] isotope modes of mother isotope T / , y( T / [20]) Nd 23.798 289.1 ± Ba (stable) α ( Nd → Ce Ba)
Nd 8.293 1439.5 ± Ba (stable) α ( Nd → Ce Ba)
Nd 17.189 2485.9 ± Ba (stable) 2 β − , α ( Nd → Ce → Ba)
Nd 5.756 1011.5 ± Ba (12.7 d) 2 β − , α ( Nd → Ce → Ba)
Sm 15.00 2831.7 ± Ce (137.6 d) α ( Sm → Nd → Ce)
Sm 11.25 ± Ce (stable) α ( Sm → Nd → Ce) 5 . × Sm ± Ce (32.5 d) α ( Sm → Nd → Ce) 4 . × Sm 7.37 2632.2 ± Ce (stable) α ( Sm → Nd → Ce)
Continued on next page able 1 continued Mother δ ,% Q α , keV Daughter Additional possible α and β decay Theor.isotope [19] [14] isotope modes of mother isotope T / , y( T / [20]) Sm 26.74 819.4 ± Ce (284.9 d) α ( Sm → Nd → Ce) Eu ± Pr (13.6 d) α ( Eu → Pm → Pr) 1 . × Eu 52.191 1408.9 ± Pr (6.0 h) α ( Eu → Pm → Pr)
Gd 0.20 ± Nd (2.3e15 y) 2 ε, α ( Gd → Sm → Nd) 1 . × Gd 2.18 2370.1 ± Nd (stable) α ( Gd → Sm → Nd)
Gd 14.80 1227.0 ± Nd (11.0 d) α ( Gd → Sm → Nd)
Gd 20.47 23.3 ± Nd (stable) α ( Gd → Sm → Nd)
Dy 0.056 ± Sm (7.0e15 y) εβ + , α ( Dy → Gd → Sm) 8 . × Dy 0.095 1794.0 ± Sm (stable) 2 ε , α ( Dy → Gd → Sm)
Dy 2.329 240.0 ± Sm (stable) α ( Dy → Gd Sm)
Er 0.139 2521.6 ± Gd (stable) εβ + , α ( Er → Dy → Gd)
Er 1.601 1742.2 ± Gd (stable) 2 ǫ , α ( Er → Dy → Gd)
Er 33.503 913.7 ± Gd (stable) α ( Er → Dy → Gd)
Er 22.869 420.4 ± Gd (18.5 h) α ( Er → Dy Gd)
Er 26.978 100.7 ± Gd (stable) α ( Er → Dy Gd)
Tm 100 1336.5 ± Tb (6.9 d) α ( Tm → Ho → Tb)
Yb 0.123 ± Dy (stable) εβ + , α ( Yb → Er → Dy)
Yb 2.982 2567.7 ± Dy (stable) α ( Yb → Er → Dy)
Yb 14.086 2224.5 ± Dy (stable) α ( Yb → Er → Dy)
Yb 21.686 1862.7 ± Dy (stable) α ( Yb → Er → Dy)
Yb 16.103 1211.6 ± Dy (2.3 h) α ( Yb → Er → Dy)
Yb 32.025 790.4 ± Dy (81.6 h) α ( Yb → Er → Dy)
Yb 12.995 218 ± Dy (8.7 m) 2 β , α ( Yb → Er Dy)
Lu 97.401 2265.2 ± Ho (3.1 h) α ( Lu → Tm → Ho)
Lu 2.599 1829 ± Ho (3.0 m) α ( Lu → Tm → Ho)
Hf 0.16 ± Er (stable) εβ + , α ( Hf → Yb → Er) 4 . × Hf 5.26 ± Er (stable) α ( Hf → Yb → Er) Hf ± Er (9.4 d) α ( Hf → Yb → Er) 1 . × Hf 27.28 2823.6 ± Er (stable) α ( Hf → Yb → Er)
Hf 13.62 2406.2 ± Er (7.5 h) α ( Hf → Yb → Er)
Hf 35.08 1854.4 ± Er (49.3 h) α ( Hf → Yb → Er)
Ta 0.01201 ± Tm (63.6 h) α ( Ta → Lu → Tm) 2 . × Ta 99.98799 2967.9 ± Tm (8.2 h) α ( Ta → Lu → Tm)
W 0.12 ± Yb (stable) 2 ε , α ( W → Hf → Yb) 3 . × W 26.50 ± Yb (stable) α ( W → Hf → Yb) W ± Yb (4.2 d) α ( W → Hf → Yb) 1 . × W 30.64 2936.1 ± Yb (stable) α ( W → Hf → Yb)
W 28.43 2337 ± Yb (74 m) 2 β − , α ( W → Hf → Yb)
Continued on next page able 1 continued Mother δ ,% Q α , keV Daughter Additional possible α and β decay Theor.isotope [19] [14] isotope modes of mother isotope T / , y( T / [20]) Re ± Lu (6.7 d) α ( Re → Ta → Lu) 1 . × Re ± Lu (4.6 h) α ( Re → Ta → Lu) 8 . × Os 0.02 ± Hf (stable) εβ + , α ( Os → W → Hf) 2 . × Os 1.59 ± Hf (stable) α ( Os → W → Hf) 7 . × Os 1.96 ± Hf (stable) α ( Os → W → Hf) 3 . × Os 13.24 ± Hf (stable) α ( Os → W → Hf) Os ± Hf (42.4 d) α ( Os → W → Hf) 9 . × Os 26.26 2491.9 ± Hf (9.0e5 y) α ( Os → W → Hf)
Os 40.78 767 ± Hf (4.1 h) 2 β − , α ( Os → W → Hf) Ir ± Ta (5.1 d) α ( Ir → Re → Ta) 4 . × Ir 62.7 2008 ± Ta (49.4 m) α ( Ir → Re → Ta)
Pt 0.012 ± W (stable) εβ + , α ( Pt → Os → W) 3 . × Pt 0.782 ± W (stable) α ( Pt → Os → W) 6 . × Pt 32.864 2898.6 ± W (stable) α ( Pt → Os → W) Pt 33.775 2263.3 ± W (23.7 h) α ( Pt → Os → W) Pt 25.211 1173.5 ± W (69.4 d) α ( Pt → Os → W) Au 100 1989.5 ± Re (24.3 h) α ( Au → Ir → Re)
Hg 0.15 ± Os (stable) 2 ε , α ( Hg → Pt → Os) 2 . × Hg 10.04 2903.6 ± Os (stable) α ( Hg → Pt → Os)
Hg 16.94 1999.3 ± Os (15.4 d) α ( Hg → Pt → Os)
Hg 23.14 1529.1 ± Os (stable) α ( Hg → Pt → Os)
Hg 13.17 881.9 ± Os (30.5 h) α ( Hg → Pt → Os)
Hg 29.74 240.0 ± Os (6.0 y) α ( Hg → Pt → Os)
Tl 29.44 1081.0 ± Ir (2.5 h) α ( Tl → Au → Ir)
Pb 1.4 2684.8 ± Pt (stable) α ( Pb → Hg → Pt)
Pb 24.1 1268.6 ± Pt (stable) α ( Pb → Hg → Pt)
Pb 22.1 86.8 ± Pt (30.8 m) α ( Pb → Hg Pt)
Pb 52.4 0.7 ± Pt (12.5 h) α ( Pb → Hg Pt) Bi
100 3292.2 ± Au (26 m) α ( Bi → Tl → Au) 3 . × Th ± Rn (107 m) β − , α ( Th → Ra → Rn) 3 . × Pa ∗
100 10192.2 ± Fr (21.8 m) α ( Pa → Ac → Fr) 5 . × U 0.0054 ± Ra (1600 y) α ( U → Th → Ra) 2 . × U ± Ra (42.2 m) α ( U → Th → Ra) 6 . × U ± Ra (93 m) α ( U → Th → Ra) 1 . × ∗ While
Pa is listed in [19] as present in the natural isotopic composition with abundance δ = 100%, in fact, it is unstable nuclide with quite short half-life T / = 32760 y [20]. One can see from the Table that all the 2 α candidates also are potentially unstable in4elation to single α decay. Intermediate ( A − , Z −
2) nuclides always [20] live long enoughnot to imitate 2 α decay in fast chain of two single α decays; and in few cases ( , Nd,
Dy, , Er,
Yb, , Pb) α decay of the intermediate nuclide is energetically forbidden.Different methods can be used to look for the 2 α decay, e.g.:(1) Si detectors (or some others, e.g. nuclear emulsions) can register two α particles emittedfrom an external source and measure their energies; however, samples in this case should bevery thin that restricts the mass that can be investigated;(2) An external source can be placed on e.g. HPGe detector; if the daughter nuclide isunstable, one can register characteristic γ quanta emitted in its decay. In this case, mass of asample could be a few kilograms; however, efficiency of HPGe detectors is on the level of onlyfew percents;(3) Very promising is a “source = detector” approach, when a mother nuclide is embeddedin a detector itself as its main component (like W isotopes in CdWO or Bi in Bi Ge O )or as a dopant (like Tl in NaI(Tl)). This approach gives possibility to use detectors with bigmasses (up to ∼ α process (practically100%). Scintillators can be used; however, in this case one cannot expect high energy resolution(it will be on the level of few tens or hundreds keV). Also, scintillators have different light yieldsfor β and γ particles comparing to those for α particles of the same energy (quenching effect,see e.g. [22]). Thus, 2 α light signal will be quenched and shifted to lower energies, where α and β / γ backgrounds are higher. Instead, scintillating bolometers, devices able to measure lightand heat signals for the same event (see e.g. [23]), are very promising techniques. A signal inthe heat channel is not quenched (thus, one will see 2 α signal at Q α value but not at lowerenergies). In addition, energy resolution in the heat channel is on the level of few keV. T / for α decay Calculations of 2 α decay half-lives for some nuclei in framework of the superasymmetric fissionmodel were performed in [11]. The results are presented in table [11, 12], and also in graphicalform as a logarithm of ratio of probability to emit 2 α to that for single α emission. For nuclidespresented in Table 1, results are absent.To estimate the half-life values for 2 α emission, we use here semi-empirical formulae forcluster decays developed in [21] and applied for emission of Be nucleus. As it is known, Beis highly unstable decaying to two α ’s with T / ≃ − s and Q = 91 . α decay should be higher on 91.8 keV comparing to decay with Be emission,and corresponding T / values should be slightly smaller. However, the difference is not big [11]and is acceptable for our aims of T / estimation. The results for some prospective nuclei aregiven in Table 1. One can see that even for the most promising cases, half-life values are toobig for 2 α decay’s experimental observation. T / limit for 2 α decay of Bi To obtain the first limit on 2 α decay of Bi, we can use data from the experiment [24] inwhich single α decay of Bi was observed for the first time. In particular, a BGO (Bi Ge O )scintillating bolometer with mass of 45.7 g was measured during 100 h in this work. Because ofdifferent light yields for β and γ particles comparing to those for α particles of the same energy,5nergy spectrum of α particles and nuclear recoils is effectively discriminated from much moreintensive β and γ background. Because of small range of α particles in the BGO crystal, theyare absorbed in the crystal with practically 100% efficiency. In the heat channel, we shouldobserve a peak for the single α decay of Bi at Q α = 3137 . ± . α decay at Q α = 3292 . ± . Bi single α decay, while the peak at Q α is absent. In fact, noevents are registered in the energy range 3 . − . α peak (full width at half maximum, FWHM is ≃
15 keV [24]). Thus, we can estimate only T / limit for the Bi 2 α decay with the formula:lim T / = ln 2 · ǫ · N · t/ lim S ,where ǫ is the efficiency to detect the expected 2 α decay ( ǫ = 1), N is the number of Bi nuclei in the 45.7 g Bi Ge O crystal ( N = 8 . × ), t is the time of measurements( t = 100 h), and lim S is the upper limit on the number of events of the effect searched for whichcan be excluded at a given confidence level (C.L.). In accordance with the Feldman-Cousinsrecommendations [25], for 0 registered events (and with 0 supposed background), lim S = 2 . Bi 2 α decay: T / > . × y at 90% C.L.The obtained experimental limit is very far from the theoretical expectations presented inSection 3 (for Bi, T / = 3 . × y).Half-life limit for 2 α decay of Th, nuclide with quite big energy release Q α = 8152 keVand high natural abundance near 100%, could be derived from e.g. measurements [26] of2 kg ThO sample with HPGe detector at the Yangyang underground laboratory (Korea).The daughter nuclide Rn is unstable and β decays further to Fr with Q = 800 keV and T / = 107 min [20]. One can look for characteristic γ quanta emitted in Rn decay.
Nuclear decay (
A, Z ) → ( A − , Z −
4) + 2 α with simultaneous emission of two alpha particlesis energetically allowed for near 40% of known isotopes (1459 from 3436 listed in [14]). Amongthem, 80 nuclides are present in the natural isotopic composition of elements [19]. First exper-imental limit for this kind of radioactivity is given for Bi as T / > . × y at 90% C.L.Theoretical T / estimations are calculated for the most prospective candidates. However, thecalculated T / values are very big, 10 y or more, making prospects for future observation ofsuch processes very pessimistic. Acknowledgements
The work was supported in part by the National Research Foundation of Ukraine Grant No.2020.02/0011. It is my pleasure to thank F.A. Danevich, V.V. Kobychev and O.G. Polischukfor useful discussions. 6 eferences [1] M. Goeppert-Mayer, Double beta-disintegration, Phys. Rev. 48 (1935) 512.[2] R. Saakyan, Two-neutrino double-beta decay, Annu. Rev. Nucl. Part. Sci. 63 (2013) 503.[3] K. Blaum et al., Neutrinoless double-electron capture, Rev. Mod. Phys. 92 (2020) 045007.[4] W.H. Furry, On transition probabilities in double beta-disintegration,Phys. Rev. 56 (1939) 1184.[5] M.J. Dolinski, A.W.P. Poon, W. Rodejohann, Neutrinoless double beta decay: Status andprospects, Annu. Rev. Nucl. Part. Sci. 69 (2019) 219.[6] M. Goeppert, Uber die Wahrscheinlichkeit des Zusammenwirkens zweier Lichtquanten ineinem Elementarakt, Naturwissenschaften 17 (1929) 932.[7] M. Goeppert-Mayer, Uber Elementarakte mit zwei Quantensprungen,Ann. Phys. (Leipz.) 401 (1931) 273.[8] G. Sutter, Etude experimentale de la double emission gamma dans les transitions monopo-laires des noyaux O, Ca et Zr, Ann. Phys. (Paris) 13 (1963) 323.[9] C. Walz et al., Observation of the competitive double-gamma nuclear decay,Nature 526 (2015) 406.[10] M. Pfutzner et al., Radioactive decays at limits of nuclear stability,Rev. Mod. Phys. 84 (2012) 567.[11] D.N. Poenaru, M. Ivascu, Two alpha, three alpha and multiple heavy-ion radioactivities,J. Physique Lett. 46 (1985) 591.[12] D.N. Poenaru, M.S. Ivascu,
Particle Emission from Nuclei , Vol. II:
Alpha, Proton, and Heavy Ion Radioactivities , CRC Press (1989) 271 p.[13] W. von Oertzen, Alpha-cluster condensations in nuclei and experimental approaches fortheir studies. In: C. Beck (ed.).
Clusters in Nuclei., Vol. 1 , Springer (2010) 328 p.[14] M. Wang et al., The Ame2016 atomic mass evaluation. (II). Tables, graphs and references,Chin. Phys. C 41 (2017) 030003.[15] P. Belli et al., Experimental searches for rare alpha and beta decays,Eur. Phys. J. A 55 (2019) 140.[16] R. Bernabei et al., First model independent results from DAMA/LIBRA-phase2,Nucl. Phys. At. Energy 19 (2018) 307.[17] E. Aprile et al., The XENON1T dark matter experiment, Eur. Phys. J. C 77 (2017) 881.[18] G. Alimonti et al., The Borexino detector at the Laboratori Nazionali del Gran Sasso,Nucl. Instrum. Meth. A 600 (2009) 568. 719] J. Meija et al., Isotopic compositions of the elements 2013 (IUPAC Technical Report),Pure Appl. Chem. 88 (2016) 293.[20] R.B. Firestone et al.,
Table of Isotopes , John Wiley & Sons, 8th ed. (update 1998).[21] D.N. Poenaru et al., Systematics of cluster decay modes, Phys. Rev. C 65 (2002) 054308.[22] V.I. Tretyak, Semi-empirical calculation of quenching factors for ions in scintillators,Astropart. Phys. 33 (2010) 40.[23] S. Pirro, P. Mauskopf, Advances in bolometer technology for fundamental physics,Annu. Rev. Nucl. Part. Sci. 67 (2017) 161.[24] P. de Marcillac et al., Experimental detection of α -particles from the radioactive decay ofnatural bismuth, Nature 422 (2003) 876.[25] G.J. Feldman, R.D. Cousins, Unified approach to the classical statistical analysis of smallsignals, Phys. Rev. D 57 (1998) 3873.[26] G.W. Kim et al., Improved intensities for the γ transitions with E γ > Pb ∗∗