Average and recommended half-life values for two neutrino double beta decay
aa r X i v : . [ nu c l - e x ] J a n Average and recommended half-life values for twoneutrino double beta decay
A.S. Barabash
Institute of Theoretical and Experimental Physics, B. Cheremushkinskaya 25, 117218Moscow, Russia
Abstract
All existing positive results on two neutrino double beta decay in differentnuclei were analyzed. Using the procedure recommended by the Particle DataGroup, weighted average values for half-lives of Ca, Ge, Se, Zr,
Mo,
Mo -
Ru (0 +1 ), Cd,
Te,
Xe,
Nd,
Nd -
Sm (0 +1 ) and Uwere obtained. Existing geochemical data were analyzed and recommendedvalues for half-lives of
Te, and
Ba are proposed. Given the measuredhalf-life values, nuclear matrix elements were calculated using latest (morereliable and precise) values for phase space factor. Finally, previous results(PRC 81 (2010) 035501) were up-dated and results for
Xe were added.
Keywords:
Double beta decay, Nuclear matrix elements, Ca, Ge, Se, Zr,
Mo,
Mo -
Ru (0 +1 ), Cd,
Te,
Te,
Xe,
Nd,
Nd -
Sm (0 +1 ), U and Ba
1. Introduction
At present, the two neutrino double beta (2 νββ ) decay process has beendetected in a total of 11 different nuclei. In
Mo and
Nd, this typeof decay was also detected for the transition to the 0 + excited state of thedaughter nucleus. For the case of the Ba nucleus, evidence for the twoneutrino double electron capture process was observed via a geochemicalexperiments. All of these results were obtained in a few tens of geochemicalexperiments and more than forty direct (counting) experiments as well asand in one radiochemical experiment. In direct experiments, for some nucleithere are as many as eight independent positive results (e.g.,
Mo). Insome experiments, the statistical error does not always play the primary
Preprint submitted to Nuclear Physics A July 9, 2018 ole in overall half-life uncertainties. For example, the NEMO-3 experimentwith
Mo has currently detected more than 219,000 2 νββ events [1], whichresults in a value for the statistical error of ∼ νββ decay remains quitehigh ( ∼ −
1) Nuclear spectroscopy . Now we know that some isotopes which were earlierconsidered to be stable are not, and decay via the double beta decay pro-cesses with a half-life period of ∼ − yr are observed. The valueswhich are presented here should be introduced into the isotope tables.
2) Nuclear matrix elements (NME) . First, it gives the possibility to im-prove the quality of NME calculations for two neutrino double beta decay, soone can directly compare experimental and calculated values. For example,so-called ” g A (axial-vector coupling constant) quenching” problem could besolved by comparison of exact experimental values of NMEs and results oftheoretical calculations (see discussions in Ref. [2, 3, 4, 5]. Second, it givesthe possibility to improve the quality of NME calculations for neutrinolessdouble beta decay. The accurate half-life values for 2 νββ decay are used toadjust the most relevant parameter of the quasiparticle random-phase ap-proximation (QRPA) model, the strength of the particle-particle interaction g pp [6, 7, 8, 9].
3) Research on the single state dominance (SSD) mechanism [10, 11] anda check of the ”bosonic” component of the neutrino hypothesis [12, 13] ispossible .In the present work, an analysis of all “positive” experimental resultshas been performed, and averaged or recommended values for isotopes arepresented.The first time that this work was done was in 2001, and the results werepresented at the International Workshop on the calculation of double betadecay nuclear matrix elements, MEDEX’01 [14]. Then revised half-life valueswere presented at MEDEX’05 and MEDEX’09 and published in Ref. [15]and [16, 17], respectively. In the present paper, new positive results obtainedsince end of 2009 and to the end of 2014 have been added and analyzed.The main differences from the previous analysis [17] are the following:2) The new experimental data obtained after the publication of Ref. [17]are included in the analysis: Ge [18],
Mo [19],
Mo -
Ru(0 +1 ) [20, 21], Cd [22],
Te [23],
Nd -
Sm (0 +1 ) [24] and Ba[25].2) Positive results obtained for
Xe [26, 27] are analyzed. This decaywas detected for the fist time in 2011 [28].3) To calculate NMEs new phase space factor values ( G ν ) from Ref.[29, 30] and [31, 32] are used.4) Considering possible changes of axial vector coupling constant g A (pos-sible quenching effect in nuclear medium) so-called effective NMEs are cal-culated, | M eff ν | = g A · | ( m e c · M ν ) | (in Ref. [17] the dimensionless nuclearmatrix elements | ( m e c · M ν ) | were calculated for g A = 1.254).
2. Present experimental data
Experimental results on 2 νββ decay in different nuclei are presented inTable 1. For direct experiments, the number of events and the signal-to-background ratio are presented.
3. Data analysis
To obtain an average of the ensemble of available data, a standard weightedleast squares procedure, as recommended by the Particle Data Group [76],was used. The weighted average and the corresponding error were calculated,as follows: ¯ x ± δ ¯ x = X w i x i / X w i ± ( X w i ) − / , (1)where w i = 1 / ( δx i ) . Here, x i and δx i are the value and error reported bythe i-th experiment, and the summations run over the N experiments.The next step is to calculate χ = P w i (¯ x − x i ) and compare it withN - 1, which is the expectation value of χ if the measurements are from aGaussian distribution. If χ / ( N −
1) is less than or equal to 1 and thereare no known problems with the data, then one accepts the results to besound. If χ / ( N −
1) is very large ( >> χ / ( N −
1) islarger than 1, but not greatly so, it is still best to use the average data, butto increase the quoted error, δ ¯ x in Equation 1, by a factor of S defined by S = [ χ / ( N − / . (2)3 able 1: Present, positive 2 νββ decay results. Here N is the number of useful events, T / is a half-life and S/B is the signal-to-background ratio. a ) For E e > . b ) after correction (see text); c ) for the SSD mechanism; d ) for E e > . e ) in both peaks. Nucleus N T / , yr S/B Ref., year Ca ∼
100 [4 . +2 . − . ( stat ) ± . syst )] · . +3 . − . · . +0 . − . ( stat ) ± . syst ) · Average value: 4 . + . − . · Ge ∼ . ± . · ∼ / . +0 . − . · ∼ / ∼
330 0 . +0 . − . · ∼ . . +0 . − . · ∼ . ∼ . ± . · ∼ . ∼ . ± . stat ) +0 . − . ( syst )] · ∼ . . +0 . − . · ∼ Average value: 1 . + . − . · Se 89.6 1 . +0 . − . · ∼ . ± . stat ) ± . syst )] · . ± . stat ) ± . syst )] · . ± . · (geochem.) [44], 1986 Average value: ( . ± . ) · Zr 26.7 [2 . +0 . − . ( stat ) ± . syst )] · . a ) [45], 1999453 [2 . ± . stat ) ± . syst )] · . ± . · (geochem.) [47], 1993(0 . ± . · (geochem.) [48], 2001 Average value: ( . ± . ) · able 1: continued. Mo ∼
500 11 . +3 . − . · . +3 . − . · . ± . stat ) ± . syst )] · b ) . +2 . − . · . +0 . − . ( stat ) ± . syst )] ·
10 [53], 1997800 [7 . ± . stat ) ± . syst )] · . ± . stat ) ± . syst )] · c )
40 [1], 2005 ∼
350 [7 . ± . stat ) ± . syst )] · ∼ d ) [19], 2014(2 . ± . · (geochem.) [55], 2004 Average value: ( . ± . ) · Mo - 133 e ) . +1 . − . · Ru (0 +1 ) 153 e ) [9 . +2 . − . ( stat ) ± . syst )] · . +1 . − . ( stat ) ± . syst )] · ∼ . +1 . − . ( stat ) ± . syst )] · ∼ . +1 . − . ( stat ) ± . syst )] · ∼ e ) [6 . +1 . − . ( stat ) ± . syst )] · ∼ /
10 [20], 2010239 e ) [7 . ± . stat ) ± . syst )] · Average value: 6 . + . − . · Cd ∼
180 2 . +0 . − . · ∼ / . ± . stat ) ± . syst )] · b ) . ± . stat ) +0 . − . ( syst )] · ∼ . ± . stat ) ± . syst )] · c )
10 [64], 201134927 [2 . ± . stat ) ± . syst )] · Average value: ( . ± . ) · Te ∼ . · (geochem.) [65], 1991(7 . ± . · (geochem.) [66], 1993(2 . ± . · (geochem.) [67], 2008(2 . ± . · (geochem.) [68], 2008 Recommended value: ( . ± . ) · able 1: continued 2. Te 260 [6 . ± . stat ) +2 . − . ( syst )] · . ± . stat ) ± . syst )] · ∼ · (geochem.) [65], 1991(27 ± · (geochem.) [66], 1993(9 . ± . · (geochem.) [67], 2008(8 . ± . · (geochem.) [68], 2008 Average value: ( . ± . ) · Xe ∼ . ± . stat ) ± . syst )] · ∼
10 [26], 201219042 [2 . ± . stat ) ± . syst )] · ∼
10 [27], 2014
Average value: ( . ± . ) · Nd 23 [18 . +6 . − . ( stat ) ± . syst )] · . +0 . − . ( stat ) ± . syst )] · . +0 . − . ( stat ) ± . syst )] · Average value: ( . ± . ) · Nd - 177 . d ) [1 . +0 . − . ( stat ) +0 . − . ( syst )] · . +0 . − . ( stat ) ± +0 . syst )] · ∼ Sm (0 +1 ) Average value: 1 . + . − . · U ( . ± . ) · (radiochem.) [73], 1991 Ba . + . − . · (geochem.) [74], 1996ECEC(2 ν ) ( . ± . ) · (geochem.) [75], 2001( . ± . ) · (geochem.) [25], 2009 Recommended value: ∼ δx i . In some cases, only the results obtainedwith high enough signal-to-background ratio were used. Ca There are three independent experiments in which 2 νββ decay of Cawas observed [33, 34, 35]. The results are in good agreement. The weightedaverage value is: T / = 4 . +0 . − . · yr . Ge Considering the results of six experiments, a few additional comments arenecessary, as follows:1) We use here final result of the Heidelberg-Moscow Collaboration, T / =[1 . ± . stat ) +0 . − . ( syst )] · yr [41].2) In Ref. [38], the value T / = 0 . +0 . − . · yr was presented. However,after a more careful analysis, this result has been changed [39]. In Ref. [39]a few values for half-life using different analysis methods were obtained. Iuse here the value obtained by fit the data using χ model, which take intoaccount shape of the spectrum (see Table 1). Unfortunately systematic errorwas not discussed and taken into account in this paper. This is why duringmy analysis I added typical systematic error for such sort of experiments( ± T / = [1 . +021 − . ( stat ) ± . syst )] · yr as aresult of Ref. [39].3) The results presented in Ref. [36] do not agree with the more recentexperiments [40, 41, 18]. Furthermore, the error presented in [36] appearsto be too small, especially taking into account that the signal-to-backgroundratio in this experiment is equal to ∼ /
8. It has been mentioned before [77]that the half-life value in this work can be ∼ . − T / = 1 . +0 . − . · yr . .3. Se There are three independent counting experiments and many geochemicalmeasurements ( ∼
20) for Se. The geochemical data are neither in goodagreement with each other nor in good agreement with the data from thedirect measurements. Typically, the accuracy of geochemical measurementsis at the level of 10% and sometimes even better. Nevertheless, the possibilityof existing large systematic errors cannot be excluded (see discussion in Ref.[78]). Thus, to obtain a present half-life value for Se, only the results ofthe direct measurements [1, 42, 43] were used. The result of Ref. [79] is thepreliminary result of [42]; hence it has not been used in our analysis. Theresult of work [42] is presented with very asymmetrical errors. To be moreconservative only the top error in this case is used. As a result, the weightedaverage value is: T / = (0 . ± . · yr . Zr There are two positive geochemical results [47, 48] and two results fromthe direct experiments of NEMO-2 [45] and NEMO-3 [46]. Taking into ac-count the comment in Sec. 3.3, I use the values from Refs. [45, 46] to obtaina present weighted half-life value for Zr of: T / = (2 . ± . · yr . Mo There are eight positive results from direct experiments and one resultfrom a geochemical experiment. I do not consider the preliminary result ofElliott et al. [50] and instead use their final result [53], plus I do not use thegeochemical result (again, see comment in Sec. 3.3). Finally, in calculatingthe average, only the results of experiments with signal-to-background ratiosgreater than 1 were used (i.e., the results of Refs. [51, 53, 1, 19]). In addition,I have used the corrected half-life value from Ref. [51] (see explanation in[17]). The following weighted average value for this half-life is then obtainedas: T / = (7 . ± . · yr . I do not consider the result of Ref. [80] because of a potentially high backgroundcontribution that was not excluded in this experiment. .6. Mo -
Ru ( +1 ; 1130.32 keV) The transition to the 0 +1 excited state of Ru was detected in seven inde-pendent experiments. The results are in good agreement, and the weightedaverage for the half-life using the results from [56, 57, 59, 60, 20, 21] is: T / = 6 . +0 . − . · yr . The result from [58] was not used here because we considered the result from[59] as the final result of the TUNL-ITEP experiment. Cd There are five independent positive results [35, 61, 63, 62, 22] that are ingood agreement with each other when taking into account the correspond-ing error bars. Again, I use here the corrected result for the half-life valuefrom Ref. [62]. The original half-life value was decreased by ∼
25% (seeexplanation in [17]). The weighted average value is: T / = (2 . ± . · yr . Te and Te For a long time, there were only geochemical data for these isotopes.Although the half-life ratio for these isotopes has been obtained with goodaccuracy ( ∼ T / of each nuclei are differentfrom one experiment to the next. One group of authors [65, 81, 82] gives T / ≈ . · yr for Te and T / ≈ · yr for Te, whereas anothergroup [44, 66] claims T / ≈ (2 . − . · yr and T / ≈ . · yr,respectively. Furthermore, as a rule, experiments with young samples ( ∼
100 million years) give results of the half-life value of
Te in the range of ∼ (0 . − . · yr, while old samples ( > ∼ (2 . − . · yr. Recently it was argued thatshort half-lives are more likely to be correct [67, 68]. Using different youngmineral results, the half-life values were estimated at (9 . ± . · yr[67] and (8 . ± . · yr [68] for Te and (2 . ± . · y [67] and(2 . ± . · yr [68] for Te.The first indication of a positive result for
Te in a direct experimentwas obtained in [69]. More accurate and reliable value was obtained recentlyin NEMO-3 experiment [23]. The results are in good agreement, and theweighted average value for half-life is T / = (6 . ± . · yr. T / ( Te) /T / ( Te) = (3 . ± . · − [66], one can obtain half-life value for Te, T / = (2 . ± . · yr. I recommend to use these last two results as the best present half-life valuesfor
Te and
Te, respectively. Xe The half-life value was recently measured in two independent experiments,EXO [28, 27] and Kamland-Zen [83, 26]. To obtain average value I use mostprecise results from these experiments, obtained in [26, 27] (see Table 1).The weighted average value is T / = (2 . ± . · yr. Nd This half-life value was measured in three independent experiments [70,53, 71]. The most accurate value was obtained in Ref. [71]. This valueis higher than in Ref. [53] and lower than in Ref. [70] ( ∼ σ and ∼ σ differences, respectively). Using Eq. (1), and three existing values, oneobtains T / = (8 . ± . · yr. Taking into account the fact that χ > T / = (8 . ± . · yr . Nd -
Sm ( +1 ; 740.4 keV) There are two independent experiments in which 2 νββ decay of
Nd tothe 0 +1 excited state of Sm was observed [72, 24] (the preliminary resultof Ref. [72] was published in Ref. [84]). The results are in good agreement.The weighted average value is: T / = 1 . +0 . − . · yr . U There is only one positive result but this time from a radiochemical ex-periment [73]: T / = (2 . ± . · yr . able 2: Half-life and nuclear matrix element values for two neutrino double beta decay(see Sec. 4). For Ba G ν value for ECEC transition is taken from [30]. a ) Obtainedusing SSD model.
Isotope T / (2 ν ), yr | M eff ν | ( G ν from [29]) ( G ν from [32]) recommendedvalue Ca 4 . +0 . − . · . +0 . − . . +0 . − . . ± . Ge 1 . +0 . − . · . +0 . − . . +0 . − . . ± . Se (0 . ± . · . +0 . − . . +0 . − . . ± . Zr (2 . ± . · . +0 . − . . +0 . − . . ± . Mo (7 . ± . · . +0 . − . . +0 . − . . +0 . a ) − . . ± . Mo- 6 . +0 . − . · . +0 . − . . +0 . − . Ru(0 +1 ) 0 . +0 . a ) − . . ± . Cd (2 . ± . · . +0 . − . . +0 . − . . +0 . a ) − . . ± . Te (2 . ± . · . +0 . − . . +0 . − . . ± . Te (6 . ± . · . +0 . − . . +0 . − . . ± . Xe (2 . ± . · . +0 . − . . +0 . − . . ± . Nd (8 . ± . · . +0 . − . . +0 . − . . ± . Nd- 1 . +0 . − . · . +0 . − . . +0 . − . . ± . Sm(0 +1 ) U (2 . ± . · . +0 . − . . +0 . − . . +0 . − . Ba, ∼ ∼ .
26 [30] ∼ . ν ) Ba (ECEC)
For
Ba positive results were obtained in geochemical measurementsonly. In geochemical experiments it is not possible to recognize the differentmodes. But I believe that exactly ECEC(2 ν ) process was detected becauseother modes are strongly suppressed (see, for example, estimations in [11,85, 86]). First positive result for Ba was mentioned in Ref. [74], in whichexperimental data from Ref. [87] were analyzed. In this paper positive resultwas obtained for one sample of barite ( T / = 2 . +3 . − . · yr), but for secondsample only limit was established ( T / > · yr). Then more accuratehalf-life values, (2 . ± . · yr [75] and (0 . ± . · yr [25], were11btained. However, the results are in strong disagreement. One can not useusual average procedure in this case. One just can conclude that half-lifeof Ba is ∼ yr. To obtain more precise and correct half-life value for Ba new measurements are needed.
4. NME values for two neutrino double beta decay
A summary of the half-life values are presented in Table 2 (2-nd column).From the measured half-life one can extract the experimental nuclear matrixelement using the relation [29] T − / = G ν · g A · ( m e c · M ν ) , (3)where T / is the half-life value in [yr], G ν is the phase space factor in[yr − ], g A is the dimensionless axial vector coupling constant and ( m e c · M ν )is the dimensionless nuclear matrix element. It is necessary to take intoaccount that there are various indications that in nuclear medium the matrixelements of the axial-vector operator are reduced in comparison with theirfree nucleon values. This quenching is often described as a reduction ofthe coupling constant g A from its free nucleon value of g A = 1 . g A ∼ . − . | M eff ν | = g A · | ( m e c · M ν ) | . And this value has been calculated for allmentioned above isotopes.The results of these calculations are presented in Table 2 (3-d and 4-th columns). To do the calculations I used the G ν values from Ref. [29]and [31, 32] , respectively (see Table 3). For Ba G ν value for ECECtransition was taken from [30]. These recent calculations pretend to be mostreliable and correct by this moment (see discussions in [29, 30, 31, 32]).Results of these calculations are in quite good agreement ( ∼ Te ( ∼ U. For
U two absolutely differentvalues 14 . · − yr − [29] and 98 . · − yr − [32]) were obtained. Itis clear that calculations for U have to be checked. For
Mo,
Mo-
Ru(0 +1 ) and Cd I used G ν calculated in Ref. [29] for SSD mechanism,in addition. Corresponding values for | M eff ν | are presented in Table 2 Ref. [32] was published as up-date of Ref. [31]. And, finally, I used in this work resultsof calculations from Ref. [32]. | M eff ν | are presented in Table 2 (5-th column) too. These valueswere obtained as an average of two values, specified in columns 3 and 4. Theerror of recommended values is chosen so that to cover all range of valuesfrom columns 3 and 4 (taking into account corresponding errors). For Mo,
Mo-
Ru(0 +1 ) and Cd I recommend to use values obtained using G ν for SSD mechanism.For the majority of isotopes we now have | M eff ν | with an accuracy of ∼ − Te and
Te it is ∼
13% and for
Nd-
Sm(0 +1 ) it is ∼ U ( ∼ Ba( ∼ U main uncertainty is connected with accuracy of G ν andfor Ba with accuracy of experimental data for the half-life.In a few recent publications [3, 4, 5] attempts to reproduce NME valuesfor two-neutrino double beta decay within various models were realized. Theconclusion was that renormalization (quenching) of g A is needed to reproducethe experimental data. So within Interacting Shell Model (ISM) approach [3]NMEs for Ca, Ge, Se,
Te,
Te and
Xe were calculated, using the g A ∼ . − .
94 (these values were obtained from data for a single beta decayor charge exchange reactions). As a result it was succeeded to obtain rathergood agreement between calculations and experimental data (nevertheless,NME calculated values for Se,
Te,
Te and
Xe exceed experimentaldata on ∼ − Mo,
Cd and
Te were adjusted to experimental values atthe expense of a choice of the corresponding g A values ( ∼ . − . g A has tobe ∼ . − .
71. The question of whether or not the quenching of g A is thesame in 2 νββ as in 0 νββ decay is the subject of debate, but it is clear thatthis question has to be carefully investigated because changes in g A leads tochanges in sensitivity to effective Majorana neutrino mass h m ν i in doublebeta decay experiments.I would like to note that in all these cases [3, 4, 5] when comparing withexperimental data the recommended T / (2 ν ) values from our previous work[17] were used. In the present work more precise experimental values for T / (2 ν ) and NME for many nuclei are obtained and, I believe, that will helpwith a solution of the g A problem in the future.13 able 3: Phase-space factors from Ref.[29], [32] and [30]. a ) Obtained using SSD model.
Isotope G ν (10 − yr − ) [29] G ν (10 − yr − ) [32] Ca 15550 15536 Ge 48.17 46.47 Se 1596 1573 Zr 6816 6744
Mo 3308 32314134 a )100 Mo-
Ru(0 +1 ) 60.55 57.0865 . a )116 Cd 2764 26883176 a )128 Te 0.2688 0.2149
Te 1529 1442
Xe 1433 1332
Nd 36430 35397
Nd-
Sm(0 +1 ) 4329 4116 U 14.57 98.51
Ba, ECEC(2 ν ) 15000 [30]
5. Conclusion
In summary, all positive 2 νββ -decay results were analyzed, and averagevalues for half-lives were calculated. For the cases of
Te and
Ba, the so-called recommended values have been proposed. Using these half-life values, | M eff ν | for two neutrino double beta decay were obtained. Finally, previousresults from Ref. [17] were successfully up-dated and new results for Xewere added. A summary is collected in Table 2. I strongly recommend theuse of these values as the most reliable presently.Notice that the accurate half-life values for 2 νββ decay could be used toadjust the most relevant parameter of the quasiparticle random-phase ap-proximation (QRPA) model, the strength of the particle-particle interaction g pp . In addition effective g A value could be established for 2 β decay. It willgive the possibility to improve the quality of NME calculations for neutrino-less double beta decay and, finally, to improve the quality of neutrino mass h m ν i estimations. 14 eferences [1] R. Arnold et al., Phys. Rev. Lett. 95 (2005) 182302.[2] A. Faessler et al., J. Phys. G 35 (2008) 075104.[3] E. Caurier, F. Nowacki, and A. Poves, Phys. Lett. B 711 (2012) 62.[4] J. Suhonen and O. Civitarese, Phys. Lett. B 725 (2013) 153.[5] J. Barea, J. Kotila, and F. Iachello, Phys. Rev. C 87 (2013) 014315.[6] V.A. Rodin et al., Nucl. Phys. A 766 (2006) 107; A 793 (2007) 213.[7] M. Kortelainen and J. Suhonen, Phys. Rev. C 76 (2007) 024315.[8] M. Kortelainen and J. Suhonen, Phys. Rev. C 75 (2007) 051303(R).[9] F. Simkovic, A. Faessler, V. Rodin, P. Vogel, and J. Engel, Phys. Rev.C 77 (2008) 045503.[10] F. Simkovic, P. Domin, and S.V. Semenov, J. Phys. G 27 (2001) 2233.[11] P. Domin et al., Nucl. Phys. A 753 (2005) 337.[12] A. Dolgov and A. Smirnov, Phys. Lett. B 621 (2005) 1.[13] A.S. Barabash et al., Nucl. Phys. B 783 (2007) 90.[14] A.S. Barabash, Czech. J. Phys. 52 (2002) 567.[15] A.S. Barabash, Czech. J. Phys. 56 (2006) 437.[16] A.S. Barabash, AIP Conf. Proc. 1180 (2009) 6.[17] A.S. Barabash, Phys. Rev. C 81 (2010) 035501.[18] M. Agostini et al., J. Phys. G 40 (2013) 035110.[19] L. Cardani et al., J. Phys. G 41 (2014) 075204.[20] P. Belli et al., Nucl. Phys. A 846 (2010) 143.[21] R. Arnold et al., Nucl. Phys. A 925 (2014) 25.1522] D. Poda et al., EPJ Web of Conf. 65 (2014) 01005.[23] R. Arnold et al., Phys. Rev. Lett. 107 (2011) 062504.[24] M.F. Kidd, J.H. Esterline, S.W. Finch, and W. Tornow, Phys. Rev. C90 (2014) 055501.[25] M. Pujol. B. Marty, P. Burnard, and P. Philippot, Geoch. Cosm. Act.73 (2009) 6834.[26] A. Gando et al., Phys. Rev. C 86 (2012) 021601(R).[27] J.B. Albert et al., Phys. Rev. C 89 (2014) 015502.[28] N. Ackerman et al., Phys. Rev. Lett. 109 (2011) 032505.[29] J. Kotila and F. Iachello, Phys. Rev. C 85 (2012) 034316.[30] J. Kotila and F. Iachello, Phys. Rev. C 87 (2013) 024313.[31] S. Stoica and M. Mirea, Phys. Rev. C 88 (2013) 037303.[32] M. Mirea, T. Pahomi, and S. Stoica, nucl-th/1411.5506.[33] A. Balysh et al., Phys. Rev. Lett. 77 (1996) 5186.[34] V.B. Brudanin et al., Phys. Lett. B 495 (2000) 63.[35] A.S. Barabash and V.B. Brudanin, Phys. At. Nucl. 74 (2011) 312.[36] A.A. Vasenko et al., Mod. Phys. Lett. A 5 (1990) 1299.[37] H.S. Miley, F.T. Avignone, R.L. Brodzinski, J.I. Collar, and J.H. Reeves,Phys. Rev. Lett. 65 (1990) 3092.[38] F.T. Avignone et al., Phys. Lett. B 256 (1991) 559.[39] F.T. Avignone, Prog. Part. Nucl. Phys. 32 (1994) 223.[40] A. Morales, Nucl. Phys. B (Proc. Suppl.) 77 (1999) 335.[41] C. Dorr and H.V. Klapdor-Kleingrothaus, Nucl. Instr. Meth. A 513(2003) 596. 1642] S.R. Elliott, A.A. Hahn, M.K. Moe, M.A. Nelson, and M.A. Vient, Phys.Rev. C 46 (1992) 1535.[43] R. Arnold et al., Nucl. Phys. A 636 (1998) 209.[44] T. Kirsten et al., in Proc. Int. Symp. ”Nuclear Beta Decay and Neutrino(Osaka’86)”, (World Scientific, Singapore, 1986), p.81.[45] R. Arnold et al., Nucl. Phys. A 658 (1999) 299.[46] J. Argyriades et al., Nucl. Phys. A 847 (2010) 168.[47] A. Kawashima, K. Takahashi, and A. Masuda, Phys. Rev. C 47 (1993)R2452.[48] M.E. Wieser and J.R. De Laeter, Phys. Rev. C 64 (2001) 024308.[49] H. Ejiri et al., Phys. Lett. B 258 (1991) 17.[50] S.R. Elliott, M.K. Moe, M.A. Nelson, and M.A. Vient, J. Phys. G 17(1991) S145.[51] D. Dassie et al., Phys. Rev. D 51 (1995) 2090.[52] M. Alston-Garnjost et al., Phys. Rev. C 55 (1997) 474.[53] A. De Silva, M.K. Moe, M.A. Nelson, and M.A. Vient, Phys. Rev. C 56(1997) 2451.[54] V.D. Ashitkov et al., JETP Lett. 74 (2001) 529.[55] H. Hidaka, C.V. Ly, and K. Suzuki, Phys. Rev. C 70 (2004) 025501.[56] A.S. Barabash et al., Phys. Lett. B 345 (1995) 408.[57] A.S. Barabash et al., Phys. At. Nucl. 62 (1999) 2039.[58] L. De Braeckeleer, M. Hornish, A. Barabash, and V. Umatov, Phys.Rev. Lett. 86 (2001) 3510.[59] M.F. Kidd et al., Nucl. Phys. A 821 (2009) 251.[60] R. Arnold et al., Nucl. Phys. A 781 (2007) 209.1761] H. Ejiri et al., J. Phys. Soc. of Japan 64 (1995) 339.[62] R. Arnold et al., Z. Phys. C 72 (1996) 239.[63] F.A. Danevich et al., Phys. Rev. C 68 (2003) 035501.[64] A.S. Barabash, Phys. Part. Nucl. 42 (2011) 613.[65] O.K. Manuel, J. Phys. G 17 (1991) S221.[66] T. Bernatowicz et al., Phys. Rev. C 47 (1993) 806.[67] A.P. Meshik et al., Nucl. Phys. A 809 (2008) 275.[68] H.V. Thomas, R.A.D. Pattrick, S.A. Crowther, D.J. Blagburn, and J.D.Gilmour, Phys. Rev. C 78 (2008) 054606.[69] C. Arnaboldi et al., Phys. Lett. B 557 (2003) 167.[70] V. Artemiev et al., Phys. Lett. B 345 (1995) 564.[71] J. Argyriades et al., Phys. Rev. C 80 (2009) 032501(R).[72] A.S. Barabash, P. Hubert, A. Nachab, and V.I. Umatov, Phys. Rev. C79 (2009) 045501.[73] A.L. Turkevich, T.E. Economou, and G.A. Cowan, Phys. Rev. Lett. 67(1991) 3211.[74] A.S. Barabash and R.R. Saakyan, Phys. At. Nucl. 59 (1996) 179.[75] A.P. Meshik, C.M. Hohenberg, O.V. Pravdivtseva, and Y.S. Kapusta,Phys. Rev. C 64 (2001) 035205.[76] J. Beringer et al. (Particle Data Group), Phys. Rev. D 86 (2012) 010001(p. 1266).[77] A.S. Barabash and V.I. Umatov, ITEP note, 1990 (unpublished).[78] O.K. Manuel, in Proc. Int. Symp. ”Nuclear Beta Decay and Neutrino(Osaka’86)””Nuclear Beta Decay and Neutrino(Osaka’86)”