AN ESTIMATION OF THE RATES OF (TWO-NEUTRINO) DOUBLE BETA DECAY AND RELATED PROCESSES J. Abad, A. Morales, R. Núñez-Lagos, A. Pacheco
To cite this version:
J. Abad, A. Morales, R. Núñez-Lagos, A. Pacheco. AN ESTIMATION OF THE RATES OF (TWO- NEUTRINO) DOUBLE BETA DECAY AND RELATED PROCESSES. Journal de Physique Collo- ques, 1984, 45 (C3), pp.C3-147-C3-150. 10.1051/jphyscol:1984328. jpa-00224042
HAL Id: jpa-00224042 https://hal.archives-ouvertes.fr/jpa-00224042 Submitted on 1 Jan 1984
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AN ESTIMATION OF THE RATES OF (TWO-NEUTRINO) DOUBLE BETA DECAY AND RELATED PROCESSES
J. Abad, A. Morales, R. ~df;ez-~a~osand A.F. Pacheco
mstituto de ~&caNuclear y Altas Energiias, Universidad de Zaragoza, Zaragoza, Spain
Rdsumd - La desintdgration double-bdta, la capture dlectronique avec dmission de positrons et la capture dlectronique double (tou'ours avec Bmission de dew neu- trinos) ont dtB calculdes en supposant que l'dtat 1' le plus bas du noyau intermd- diaire est dominant. En utilisant les valeurs expdrimentales pour les Bldments de matrice de dgsintdgration bQta simple et les ddnominateurs d'dnergie, on obtient des rBsultats qui ne ddpendent pas des calculs de physique nuclsaire. Les rBsultats pour la dssintdgration double-b6ta sont en accord avec les donndes gdochimiques rBcentes. D'autres prddictions sont 2 la portde des possibilitGs actuelles de dBtection.
Abstract - The (two-neutrino) double beta decay, the electron capture with positron emission and the doubleelectroncapture decay rates are estimated for se- veral nuclides by assuming the dominance of the lowest 1+ state of the intermediate isobar. By using single-8 decay matrix elements and energy denominators as experi- mental imputs we get values independently of nuclear physics calculations. The re- sults for double 8- decay are in agreement with the recent geochemical values. Other predictions are within the present experimental sensitivity.
The recent years have witnessed a great deal of work /1/ in the field of double be- ta decay because of its relevance for the question of the,(Plajorana) neutrino mass which might be inferred if the lepton number violating neutrinoless double beta de- cay would take place. From the theoretical point of view there exists alarming dis- crepancies /2/ between the conventional (28)-decay theory and the geochemical measu- rements /3,4,5/. Although it is commonly accepted that the uncertainties in the computations arise mainly from the nuclear matrix elements it is troubling to note that recent improved calculations with the state-of-the-art shell model techniques have exacerbated these discrepancies /2,6/. Moreover, the proper treatment /2,7/ of the Coulomb correction amounts also to an increase of the absolute rates, i.e.,each new refinement seems to go in the wrong direction. In the direct experiments there exists, so far, one "positive" result 181, in the 82~ecase, which is in contradic- tion with the corresponding geochemical result 161. On the other hand, there are two geochemical experiments /3,4/ measuring the famous Tellurium ratio which give incompatible results of far reaching consequences /2,4,7/.
Should the geochemical results /4,5/ be correct one is faced to the uneasy situation of having theoretical absolute rates considerably larger than the experimental ones and, which is worse, all the theoretical improvements make the rates even larger. One might give up some of the approximations usually made in computing the rates, like for instance, the closure approximation employed when performing the sum over the intermediate nuclear states /6,9/ or to look for alternative mechanisms in order to reduce the theoretical rates /lo/. In Ref 6, devoted to the Te isotopes, the sum over the intermediate 1+ states is performed for excitation energies up to about 20 MeV, inserting LheahedXcdty campcLted single 8- and f.?+ decay amplitudes from the 0+ ground states to the various I+ intermediate states, instead of using the (28)-decay amplitudes conventionally surmned up by closure. With the nuclear states described in a BCS pairing model they obtain even higher rates than those previously computed
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984328 C3-148 JOURNAL DE PHYSIQUE
/2/. In Ref. 9 the sum over the intermediate states is saturated by keeping only %he lowest-lying 1+ state, inserting the expenimentae matrix elements of the single 8- and 6+ decay amplitudes from the 1+ to the 0+ ground states. This very naive and drastic a roach, as noted also in Ref. 6, already yields the observed 26-decay rates in the E58Te, 130~8and 82Se cases, as given by the geochemical data. These results may cast some doubts about the reliability of the geochemical measurements or the closure approximation, or both.
In the present paper we briefly review our results /9/ and extend them to other two- neutrino processes related to the double beta decay, i.e. double positron emission, e- -+ e+ conversion and double electron capture Ill/.
In the conventional (26)* decay theory the (two-neutrino) decay rate in O+ + 0+ transitions is given by 1 ~(68);, = (96a7)- (GFcos8) 4~4rn9 lMGT 1 2~$(years)-1
A=1.25 and S=
GT It is straightforward to check that if one assumes the dominance of the 1' lowest- lying intermedia5e state,+one woukd obta&n, instead of MGT and S, respectively the quantities
-tion --- factors F* as suggested by Haxton et a1 121. Table 1 shows the half-life pre- Nuclide (log ft)l (log ft)2 'I,s/m laGTI2 I TlI2(years)
TABLE 1 + (eV)2v (K6 )2v (KK)2v
2 Nuclide log(ft)1 log(ft)2 IM I s/m T /m T1/2(yr) T /m T1/2(yr) T /m x1/2(yr) 1 GT1 0 h 0 h 0 h
64„ 3 9 34 26 3QZn 5.0 5.3 7.22xl0~ 2.13 - - - 0.13 0.70xl0~ 6.4xl0 2.11 0.315 7.3xl0
27 78Kr 4.8 5.5 7.22xl0~3 2.35 1.64 0.835xl0~3 7.07x10 3.61 12.0 2.2xl024 5.58 12.0 6.4xl024 36Kr 27 22 22 4.9 4.4 7.22xl0~3 1.44 0.206xl0~3 2.86x10 3.39 16.0 6.8xlOzz 5.34 21.0 6.5x10 48Cd 1.39
4.8 4.4 9.08xl0-2 4.23 0.43 4.4xl0~5 2.5xl028 48Cd ------24 4.7 4.1 2.28x10"l 2.29 1.70 0.59x10" -1 5.2xlOZ4 3.64 2.42 1.4xl023 50Sn - - -
120Te 4.5 5.1 3.62xl0"2 2.92 - - - 1.26 0.40xl0-2 4.4xl026 3.19 0.93 1.8xl024 52 130,, 30 23 5.1 5.4 4.55xl0"3 1.86 1.04 0.358xl0~5 2.61x10 2.97 3.7 3.0xl024 4.90 10.35 8.3x10 56Ba 132 B 4.55xl0-3 3.50 1.48 2.2xl0~2 3.9xl026 56Ba ------23 136Ce 4.6 5.5 1.14xl0-2 1.92 0.70 0.39xl0-7 9.55xl031 2.62 1.4 2.8xl024 4.54 7.4 3.7x10 58Le
138Ce 1.14xl0~2 1.23 1.3xl0-2 2.1xl026 58Ce - - 3.04 ------
162Fr 5.0 5.6 3.61xl0~3 1.56 1.50 0.44xl0_1 1.7xl026 3.39 3.3 l.lxlO24 68Er - - -
n i C3-150 JOURNAL DE PHYSIQUE dictions for (24)5v decay in some nuclides where the 1+ intermediate-state-dominan- ce-hypothesis is applicable. As it was said above the results are in fair agreement with the geochemical data for the 128~e,130Te and 82~e(28)- decay cases.
In much the same way the I+ dominance approach can be applied to the (two neutrino) e-+e+ conversion process (Kf3)2v whose rate is given conventionally 1121, by 1 = (24a5)- (~cose~)*A4 I Y (0) 1 1~~~12m6~2 (years)-' r(~B)2, where To+m- Ee+ I pe+ 14+dEe+ lo E:~E:~ dEvl(K~+L~+K 2 2 2L 2) - 1 K,= (s+B,-~+E v 1)-'+(S+E~++E~~) , L~=( s+B~-+E v2 ) -'+(S+E~++E~l) - 1 BK is the binding energy of the K electron and S has the same meaning as above. By inserting the experimental 3 and 3 instead of MGT and S, one gets the e-+e+ half-li- fe from the expression T~,~(KB+)Zv=(3.53~1021) /(a3Z3 [%I years where the atomic wave function has been approximated, as usual, by 1 Y (o)~~=(~z)~~~IT-~ As far as the (two-neutrino) double electron capture (KK)zV is concerned, the ,&+ do- minance hypothesis amounts, as in previous cases, to replace the experimental M and 3 instead of and S in the conventional rate /13/ r (KK) 2v=(~T~)-~(GCO~~~) 414m3 I Y (0) 1 * IllGT 121) (years.)-' where 0d~vl~:l~~2(~~+~?j+~3~3)/3, K3=(S-ni+BK+Evl)-1 , L~=(s-~+B~+E~~)-~
The half-life is given by (~~)~~=(1.82x10~~)/(a~~~12121~) years T1/2 The parameters entering the above formulae and the predicted half-lives for proces- ses(~~)$~,(~$92, and (KK)2\, are given in table 2.
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