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 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. JOURNAL DE PHYSIQUE Colloque C3, suppl6ment au n03, Tome 45, mars 1984 page C3-147 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=<E,>-EI is the difference between the energy of the initial state and some averaged energy of the intermediate states. The Gamow-Teller matrix element is given as usual by 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 <OF 11 u 11 l><lll o 11 01>= M and !?=E~+-E~~which can be taken from the expe- rimental data. In fact, in the single-5 Gamow-Teller transitions l+ + 0+ one has where the indexes 1 and 2 refer to the two branches of decay from the intermediate state 1+ to the initial and final O+ ground states. The resulting half-life is T~/~(BB)~,= (4.26~10'~)/( ]GI2 1') years The phase space integrals I* have been computed numerically, with the Coulomb correc -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 i n 4 4 3 8 6 6 4 6 2 2 2 2 2 2 2 2 3 3 ) 2 2 2 2 0 0 0 (yr 1/2 1.4xl0 1.8xl0 2.1xl0 l.lxlO 8.3x1 3.9xl0 3.7x1 x 7.3xl0 6.4xl0 6.5x1 2.5xl0 2 2 5 - v 2 5 5 2 3 0 0 3 4 h (KK) 3. 2.4 7. 0.9 0.31 10.3 12. 21. 1.3xl0 2.2xl0~ 4.4xl0~ m 3 4 8 0 9 4 8 1 4 9 3 0 / 1.2 1.4 3.3 3.6 3.1 2.1 4.9 4.5 5.5 5.3 0.4 T 6 4 6 4 4 4 z 4 2 2 2 Z z 2 3 2 4 2 ) 2 2 (yr - - - 1/2 1.7xl0 3.0xl0 2.8xl0 T 6.4xl0 2.2xl0 6.8xlO 5.2xlO 4.4xl0 1 2 1 9 _ - - v 2 " + ) 0 0 4 7 - - h - 1. 3. (K6 12. 16. 0.59x10 0.44xl0 0.70xl0~ 0.40xl0 m 0 2 7 0 6 1 9 3 - - / 0 - 1.5 1.7 1.2 2.9 2.6 3.6 3.3 T 0.1 1 3 0 7 ) 7 3 2 2 0 0 0 (yr - - - - - - - 1/2 T 2.61x1 7.07x1 2.86x1 9.55xl0 3 5 3 7 v - 2 - h - - - - - - (eV) 0.358xl0~ 0.39xl0 0.206xl0~ 0.835xl0~ m 4 0 4 4 - / - - - 0 - - - 1.6 1.4 1.0 0.7 T 2 4 6 0 2 9 3 3 m 6 5 9 s/ 1.9 1.5 1.3 1.8 2.2 2.9 3.5 3.0 2.1 2.3 4.2 l 2 3 2 3 3 3 3 3 2 2 - - - 2 1 I M 1 GT I 1.14xl0 1.14xl0~ 3.61xl0~ 7.22xl0~ 7.22xl0~ 2.28x10" 3.62xl0" 7.22xl0~ 4.55xl0" 4.55xl0 9.08xl0 2 6 1 5 4 4 1 3 4 5 - - 5. 5. 4. 4. 4. 5. 5. 5. 5. log(ft) 1 0 0 1 7 6 5 8 8 9 - - 4. 5. 5. 4. 4. 4. 5. 4. 4. log(ft) e e a a n r e d r d L E B B S C C K C n e e e r r , „ B Z C C K T F 2 78 68 48 58 138 162 64 36 48 50 56 56 58 120 136 5 3Q 130, 132 Nuclid 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.