Average and recommended half-life values for two-neutrino double beta decay: upgrade-2019

TL;DR

This paper consolidates and updates the half-life values for various isotopes undergoing two-neutrino double beta decay and electron capture, providing recommended values based on experimental and geochemical data.

Contribution

It offers a comprehensive analysis and recommended half-life values for multiple isotopes, updating previous data with a standardized procedure.

Findings

Recommended half-life values for numerous isotopes established.

Analysis of geochemical data led to new half-life estimates for some isotopes.

Provides a reliable reference for future research in double beta decay.

Abstract

All existing positive results on two neutrino double beta decay and two neutrino double electron capture in different nuclei were analyzed. Using the procedure recommended by the Particle Data Group, weighted average values for half-lives of $^{48}$Ca, $^{76}$Ge, $^{82}$Se, $^{96}$Zr, $^{100}$Mo, $^{100}$Mo - $^{100}$Ru ($0^+_1$), $^{116}$Cd, $^{130}$Te, $^{136}$Xe, $^{150}$Nd, $^{150}$Nd - $^{150}$Sm ($0^+_1$), $^{238}$U, $^{78}$Kr and $^{124}$Xe were obtained. Existing geochemical data were analyzed and recommended values for half-lives of $^{128}$Te and $^{130}$Ba are proposed. I recommend the use of these results as the most currently reliable values for half-lives.

Tables

Table 1. Table 1: Present, positive 2 ​ ν ​ β ​ β 2 𝜈 𝛽 𝛽 2\nu\beta\beta decay results. Here, N is the number of useful events, S/B is the signal-to-background ratio. a) For E 2 ​ e > 1.2 subscript 𝐸 2 𝑒 1.2 E_{2e}>1.2 MeV. b) After correction (see [ 6 ] ). c) For E 2 ​ e > 1.5 subscript 𝐸 2 𝑒 1.5 E_{2e}>1.5 MeV. d) For SSD mechanism. e) In both peaks. f) This value was obtained using average T 1 / 2 subscript 𝑇 1 2 T_{1/2} for 130 Te and very well-known ratio T 1 / 2 subscript 𝑇 1 2 T_{1/2} ( 130 Te)/ T 1 / 2 subscript 𝑇 1 2 T_{1/2} ( 128 Te) = ( 3.52 ± 0.11 ) ⋅ 10 − 4 ⋅ plus-or-minus 3.52 0.11 superscript 10 4 (3.52\pm 0.11)\cdot 10^{-4} [ 46 ] .

Nucleus	N	$T_{1/2}$, y	S/B	Ref., year
48Ca	$\sim 100$	$\left[{4.3}_{-1.1}^{+2.4}\left(stat\right)\pm 1.4\left(syst\right)\right]\cdot {10}^{19}$	1/5	[8], 1996
	5	${4.2}_{-1.3}^{+3.3}\cdot {10}^{19}$	5/0	[9], 2000
	153	$[{6.4}_{-0.6}^{+0.7}{\left(stat\right)}_{-0.9}^{+1.2}\left(syst\right)\cdot {10}^{19}$	3.9	[10], 2016
		Average value: ${5.3}_{-0.8}^{+1.2}\cdot {\mathrm{𝟏𝟎}}^{\mathrm{𝟏𝟗}}$
76Ge	$\sim 4000$	$\left(0.9\pm 0.1\right)\cdot {10}^{21}$	$\sim 1/8$	[11], 1990
	758	${1.1}_{-0.3}^{+0.6}\cdot {10}^{21}$	$\sim 1/6$	[12], 1991
	$\sim$ 330	${0.92}_{-0.04}^{+0.07}\cdot {10}^{21}$	$\sim 1.2$	[13], 1991
	132	${1.27}_{-0.16}^{+0.21}\cdot {10}^{21}$	$\sim 1.4$	[14], 1994
	$\sim 3000$	$\left(1.45\pm 0.15\right)\cdot {10}^{21}$	$\sim 1.5$	[15], 1999
	$\sim 80000$	$\left[1.74\pm 0.01{\left(stat\right)}_{-0.16}^{+0.18}\left(syst\right)\right]\cdot {10}^{21}$	$\sim 1.5$	[16], 2003
	$\sim$ 30000	$\left(1.925\pm 0.094\right)\cdot {10}^{21}$	$\sim 3$	[17], 2015
		Average value: $\left(1.88\pm 0.08\right)\cdot {\mathrm{𝟏𝟎}}^{\mathrm{𝟐𝟏}}$
82Se	89.6	${1.08}_{-0.06}^{+0.26}\cdot {10}^{20}$	$\sim 8$	[18], 1992
	149.1	$\left[0.83\pm 0.10\left(stat\right)\pm 0.07\left(syst\right)\right]\cdot {10}^{20}$	2.3	[19], 1998
	3472	$\left[0.939\pm 0.017\left(stat\right)\pm 0.058\left(syst\right)\right]\cdot {10}^{20}$	4	[20], 2018
		Average value: $\left(0.93\pm 0.05\right)\cdot {\mathrm{𝟏𝟎}}^{\mathrm{𝟐𝟎}}$
96Zr	26.7	$\left[{2.1}_{-0.4}^{+0.8}\left(stat\right)\pm 0.2\left(syst\right)\right]\cdot {10}^{19}$	$1.9{}^{a)}$	[21], 1999
	453	$\left[2.35\pm 0.14\left(stat\right)\pm 0.16\left(syst\right)\right]\cdot {10}^{19}$	1	[22], 2010
		Average value: $\left(2.3\pm 0.2\right)\cdot {\mathrm{𝟏𝟎}}^{\mathrm{𝟏𝟗}}$
100Mo	$\sim 500$	${11.5}_{-2.0}^{+3.0}\cdot {10}^{18}$	1/7	[23], 1991
	67	${11.6}_{-0.8}^{+3.4}\cdot {10}^{18}$	7	[24], 1991
	1433	$\left[7.3\pm 0.35\left(stat\right)\pm 0.8\left(syst\right)\right]\cdot {10}^{18b)}$	3	[25], 1995
	175	${7.6}_{-1.4}^{+2.2}\cdot {10}^{18}$	1/2	[26], 1997
	377	$\left[{6.82}_{-0.53}^{+0.38}\left(stat\right)\pm 0.68\left(syst\right)\right]\cdot {10}^{18}$	10	[27], 1997
	800	$\left[7.2\pm 1.1\left(stat\right)\pm 1.8\left(syst\right)\right]\cdot {10}^{18}$	1/9	[28], 2001
	$\sim$ 350	$\left[7.15\pm 0.37\left(stat\right)\pm 0.66\left(syst\right)\right]\cdot {10}^{18}$	5 c)	[29], 2014
	9000	$\left[6.90\pm 0.15\left(stat\right)\pm 0.37\left(syst\right)\right]\cdot {10}^{18d)}$	10	[30], 2017
	500000	$\left[6.81\pm 0.01{\left(stat\right)}_{-0.40}^{+0.38}\left(syst\right)\right]\cdot {10}^{18d)}$	80	[31], 2019
		Average value: $\left(6.88\pm 0.25\right)\cdot {\mathrm{𝟏𝟎}}^{\mathrm{𝟏𝟖}}$

Table 2. Table 1: continued.

100Mo -	$133{}^{e)}$	${6.1}_{-1.1}^{+1.8}\cdot {10}^{20}$	1/7	[32], 1995
100Ru ($0_1^{+}$)	$153{}^{e)}$	$\left[{9.3}_{-1.7}^{+2.8}\left(stat\right)\pm 1.4\left(syst\right)\right]\cdot {10}^{20}$	1/4	[33], 1999
	19.5	$\left[{5.9}_{-1.1}^{+1.7}\left(stat\right)\pm 0.6\left(syst\right)\right]\cdot {10}^{20}$	$\sim 8$	[34], 2001
	35.5	$\left[{5.5}_{-0.8}^{+1.2}\left(stat\right)\pm 0.3\left(syst\right)\right]\cdot {10}^{20}$	$\sim 8$	[35], 2009
	37.5	$\left[{5.7}_{-0.9}^{+1.3}\left(stat\right)\pm 0.8\left(syst\right)\right]\cdot {10}^{20}$	$\sim 3$	[36], 2007
	$597{}^{e)}$	$\left[{6.9}_{-0.8}^{+1.0}\left(stat\right)\pm 0.7\left(syst\right)\right]\cdot {10}^{20}$	$\sim 1/10$	[37], 2010
	$239{}^{e)}$	$\left[7.5\pm 0.6\left(stat\right)\pm 0.6\left(syst\right)\right]\cdot {10}^{20}$	$\sim 2$	[38], 2014
		Average value: ${6.7}_{-0.4}^{+0.5}\cdot {\mathrm{𝟏𝟎}}^{\mathrm{𝟐𝟎}}$
116Cd	$\sim 180$	${2.6}_{-0.5}^{+0.9}\cdot {10}^{19}$	$\sim 1/4$	[39], 1995
	174.6	$\left[2.9\pm 0.3\left(stat\right)\pm 0.2\left(syst\right)\right]\cdot {10}^{19b)}$	3	[40], 1996
	9850	$\left[2.9\pm 0.06{\left(stat\right)}_{-0.3}^{+0.4}\left(syst\right)\right]\cdot {10}^{19}$	$\sim 3$	[41], 2003
	4968	$\left[2.74\pm 0.04\left(stat\right)\pm 0.18\left(syst\right)\right]\cdot {10}^{19d)}$	12	[42], 2017
	93000	$\left({2.63}_{-0.12}^{+0.11}\right)\cdot {10}^{19}$	1.5	[43], 2018
		Average value: $\left(2.69\pm 0.09\right)\cdot {\mathrm{𝟏𝟎}}^{\mathrm{𝟏𝟗}}$
128Te		$\left(2.41\pm 0.39\right)\cdot {10}^{24}$ (geochem.)		[44], 2008
		$\left(2.3\pm 0.3\right)\cdot {10}^{24}$ (geochem.)		[45], 2008
		Recommended value: $\left(2.25\pm 0.09\right)\cdot {\mathrm{𝟏𝟎}}^{\mathrm{𝟐𝟒}𝐟)}$
130Te	260	$\left[6.1\pm 1.4{\left(stat\right)}_{-3.5}^{+2.9}\left(syst\right)\right]\cdot {10}^{20}$	1/8	[47], 2003
	236	$\left[7.0\pm 0.9\left(stat\right)\pm 1.1\left(syst\right)\right]\cdot {10}^{20}$	1/3	[48], 2011
	$\sim$ 33000	$\left[8.2\pm 0.2\left(stat\right)\pm 0.6\left(syst\right)\right]\cdot {10}^{20}$	0.1-0.3	[49], 2017
	$\sim$ 20000	$\left[7.9\pm 0.1\left(stat\right)\pm 0.2\left(syst\right)\right]\cdot {10}^{20}$	$>$1	[50], 2019
		Average value: $\left(7.91\pm 0.21\right)\cdot {\mathrm{𝟏𝟎}}^{\mathrm{𝟐𝟎}}$
	$\sim$ 19000	$\left[2.165\pm 0.016\left(stat\right)\pm 0.059\left(syst\right)\right]\cdot {10}^{21}$	10	[51], 2014
136Xe	$\sim$ 100000	$\left[2.21\pm 0.02\left(stat\right)\pm 0.07\left(syst\right)\right]\cdot {10}^{21}$	10	[52], 2016
		Average value: $\left(2.18\pm 0.05\right)\cdot {\mathrm{𝟏𝟎}}^{\mathrm{𝟐𝟏}}$
150Nd	23	$\left[{18.8}_{-3.9}^{+6.9}\left(stat\right)\pm 1.9\left(syst\right)\right]\cdot {10}^{18}$	1.8	[53], 1995
	414	$\left[{6.75}_{-0.42}^{+0.37}\left(stat\right)\pm 0.68\left(syst\right)\right]\cdot {10}^{18}$	6	[27], 1997
	2214	$\left[9.34\pm 0.22{\left(stat\right)}_{-0.60}^{+0.62}\left(stat\right)\pm 0.63\left(syst\right)\right]\cdot {10}^{18}$	4	[54], 2016
		Average value: $\left(8.4\pm 1.1\right)\cdot {\mathrm{𝟏𝟎}}^{\mathrm{𝟏𝟖}}$
		Recommended value: $\left({9.34}_{-0.64}^{+0.67}\right)\cdot {\mathrm{𝟏𝟎}}^{\mathrm{𝟏𝟖}}$
150Nd -	$177.5{}^{e)}$	$\left[{1.33}_{-0.23}^{+0.36}{\left(stat\right)}_{-0.13}^{+0.27}\left(syst\right)\right]\cdot {10}^{20}$	1/5	[55], 2009
	21.6	$\left[{1.07}_{-0.25}^{+0.45}\left(stat\right)\pm 0.07\left(syst\right)\right]\cdot {10}^{20}$	1.2	[56], 2014
150Sm ($0_1^{+}$)		Average value: ${1.2}_{-0.2}^{+0.3}\cdot {\mathrm{𝟏𝟎}}^{\mathrm{𝟐𝟎}}$
238U		$\left(2.0\pm 0.6\right)\cdot {\mathrm{𝟏𝟎}}^{\mathrm{𝟐𝟏}}$ (radiochem.)		[57], 1991

Table 3. Table 2: Present, positive two neutrino double electron capture results. Here, N is the number of useful events, S/B is the signal-to-background ratio. In case of 78 Kr and 124 Xe T 1 / 2 subscript 𝑇 1 2 T_{1/2} for 2 ​ K ​ ( 2 ​ ν ) 2 𝐾 2 𝜈 2K(2\nu) capture is presented (this is ∼ similar-to \sim 75-80% of E ​ C ​ E ​ C ​ ( 2 ​ ν ) 𝐸 𝐶 𝐸 𝐶 2 𝜈 ECEC(2\nu) ). ) a {}^{a}) See text.

130Ba		${2.1}_{-0.8}^{+3.0}\cdot {\mathrm{𝟏𝟎}}^{\mathrm{𝟐𝟏}}$ (geochem.)		[58], 1996
$ECEC\left(2\nu \right)$		$\left(2.2\pm 0.5\right)\cdot {\mathrm{𝟏𝟎}}^{\mathrm{𝟐𝟏}}$ (geochem.)		[59], 2001
		$\left(0.60\pm 0.11\right)\cdot {\mathrm{𝟏𝟎}}^{\mathrm{𝟐𝟏}}$ (geochem.)		[60], 2009
		Recommended value: $\left(2.2\pm 0.5\right)\cdot {\mathrm{𝟏𝟎}}^{\mathrm{𝟐𝟏}}$
78Kr	15	$[{1.9}_{-0.7}^{+1.3}(\mathrm{𝐬𝐭𝐚𝐭}\pm 0.3\left(\mathrm{𝐬𝐲𝐬𝐭}\right)]\cdot {\mathrm{𝟏𝟎}}^{\mathrm{𝟐𝟐}}$		[61], 2017
$2K\left(2\nu \right)$
		Recommended value: $\left({1.9}_{-0.8}^{+1.3}\right)\cdot {\mathrm{𝟏𝟎}}^{\mathrm{𝟐𝟐}}$ (?)${}_{}{}^a)$	15
124Xe	126	$[1.8\pm 0.5(\mathrm{𝐬𝐭𝐚𝐭}\pm 0.1\left(\mathrm{𝐬𝐲𝐬𝐭}\right)]\cdot {\mathrm{𝟏𝟎}}^{\mathrm{𝟐𝟐}}$	0.2	[62], 2019
$2K\left(2\nu \right)$
		Recommended value: $\left(1.8\pm 0.5\right)\cdot {\mathrm{𝟏𝟎}}^{\mathrm{𝟐𝟐}}$

Full text

1 INTRODUCTION

In the present work, a critical analysis of all positive experimental results has been performed, and averaged (or recommended) values for all isotopes are presented.

The first time this work was done was in 2001, and the results were presented at MEDEX’01 [1]. Then revised half-life values were presented at MEDEX’05 [2], MEDEX’09 [3, 4] and MEDEX’13 [5, 6]. In the present paper, new positive results obtained since 2015 have been added and analyzed.

2 PRESENT EXPERIMENTAL DATA

Experimental results on $2\nu\beta\beta$ decay and $ECEC(2\nu)$ in different nuclei are presented in Table 1 and Table 2, respectively. For direct experiments, the number of useful events and the signal-to-background ratio are presented. The results of geochemical experiments for 82Se, 96Zr, 100Mo and 130Te are not presented in Table 1, since these data were not used in the calculation of average values (see the discussion in [4, 6]).

3 DATA ANALYSIS

To obtain an average of the ensemble of available data, a standard weighted least-squares procedure, as recommended by the Particle Data Group [7], was used (see also [6]). In case of 76Ge only results from [16, 17] (as most precise and reliable) were used to obtain the average half-life value. In case of 100Mo I used results from [27, 29, 30, 31] only for the same reason. Due to the wide variation in results for 150Nd, I recommend using the result obtained in the NEMO-3 experiment as the most reliable estimate of the half-life of 150Nd by this moment.

It has to be stressed that for 238U, 124Xe and 78Kr ”positive” result was obtained in the only experiment. This is why confirmation of these results in independent experiments is needed. And one has to be very careful using indicated half-life values. Most questionable situation is for 78Kr. Number of detected events is quite small and analysis of experimental data is very complicated. If obtained result is correct it means that in case of 78Kr we have a deal with highest value of Nuclear Matrix Element (NME) among all nuclei for which 2$\nu$ decay was observed (NME for 78Kr is $\sim$ 2 times higher than in case of 100Mo, which has the highest value of NME). In principle it is possible, but looks a little bit strange.

4 ACKNOWLEDGMENTS

This work was partly supported by Russian Scientific Foundation (grant No. 18-12-00003)