1. Search for  + EC and ECEC processes in 112 Sn A.S. Barabash 1), Ph. Hubert 2), A. Nachab 2) and V. Umatov 1) 1) ITEP, Moscow, Russia 2) CNBG, Gradignan, France 1

2. Outline  Introduction  Experiment  Results  Conclusion

3. I. Introduction 2  +,  + EC and ECEC processes:  0 -transitions: (A,Z)  (A,Z-2) + 2e + e b + (A,Z)  (A,Z-2) + e + + X 2e b + (A,Z)  (A,Z-2) +  (2 ,e + e -,e -,…) + 2X  2 -transitions: (A,Z)  (A,Z-2) + 2e + + 2 e b + (A,Z)  (A,Z-2) + e + + 2 + X 2e b + (A,Z)  (A,Z-2) + 2 + 2X

4. Q value  2  + : Q' =  M – 4m e – 2  b (Q' max  0.8 MeV) (6 nuclei)   + EC: Q' =  M – 2m e –  b (Q' max  1.8 MeV) (22 nuclei)  ECEC: Q' =  M – 2  b (Q' max  2.8 MeV) (34 nuclei) [ Q(2  - )  3 MeV ]

5. ECEC(0 ) to the ground state  2e b + (A,Z)  (A,Z-2) + 2X +  brem + 2  + e + e - + e - int E ,.. =  M -  e1 -  e2 Suppression factor is ~ 10 4 (in comparison with EC  + (0 )) – M. Doi and T. Kotani, Prog. Theor. Phys. 89 (1993)139.

6. ECEC(0 ) Transition to the ground state. For the best candidates ( = 1 eV):  +  + (0 ) ~ 10 28 -10 30 y  + EC(0 ) ~ 10 26 -10 27 y ECEC(0 ) ~ 10 28 -10 31 y (One can compare these values with ~ 10 24 -10 25 y for 2  - -decay)

7. Resonance conditions  In 1955 (R.Winter, Phys. Rev. 100 (1955) 142) it was mentioned that if there is excited level with “right” energy then decay rate can be very high. (Q’-E* has to be close to zero. Q’-energy of decay to g.s., E*-energy of excited state)  In 1982 the same idea for transition to excited and ground states was discussed (M. Voloshin, G. Mizelmacher, R. Eramzhan, JETP Lett. 35 (1982)).  In 1983 (J. Bernabeu, A. De Rujula, C. Jarlskog, Nucl. Phys. B 223 (1983) 15) this idea was discussed for 112 Sn (transition to 0 + excited state). It was shown that enhancement factor can be on the level ~ 10 6 !

8. J. Bernabeu, A. De Rujula, C. Jarlskog, Nucl. Phys. B 223 (1983) 15 112 Sn  112 Cd [0 + (1871)] M = 1919.5±4.8 keV (old value) Q’(KK;0 + ) = M – E*(0 + ) – 2E K = = (-4.9 ± 4.8) keV T 1/2 (0)  3·10 24 y (for = 1 eV) (if Q’ ~ 10 eV) [ECEC(2) transition is strongly suppressed!!!] Nice signature: in addition to two X-rays we have here two gamma- rays with strictly fixed energy (617.4 and 1253.6 keV)

9. J. Bernabeu, A. De Rujula, C. Jarlskog, Nucl. Phys. B 223 (1983) 15 112 Sn 112 Cd(0 + ;1870 keV) The ECEC(0) mode is shown as a function of the degeneracy parameter Q-E

10. Resonance conditions  In 2004 the same conclusion was done by Z. Sujkowski and S. Wycech (Phys. Rev. C 70 (2004) 052501).  Resonance condition (using single EC(,) argument): E brems = Q’ res = E(1S,Z-2)-E(2P,Z-2) (i.e. when the photon energy becomes comparable to the 2P-1S level difference in the final atom) Q’-Q’res < 1 keV

11. Z. Sujkowski and S. Wycech

12. Decay-scheme of 112 Sn Here M = 1919.82±0.16 keV (PRL 103 (2009) 042501) Q’ = M - 2E b = 1866.42 keV Q’(E*) = Q’–1871.137(72)  - 4.71±0.23 keV

13. Isotope-candidates (transition to the excited state) NucleiA, %  M, keVE*, keV , keV E K *) E L2 *) 74 Se0.891209.7±2.3 1209.240±0.007 (new!) 1204.2 (2 + ) 2.5±0.1 (LL)11.11.23 78 Kr0.352846.4±2.02838.9 (2 + ?) 4.5±2.1 (LL)12.61.47 96 Ru5.522718.5±8.22700.2 (2 + ) -4.5±8.2 (KL) 2712.68 (?) 0±8.2 (LL) 202.86 106 Cd1.252770±7.22741.0 (4 + ) 1.1±7.2 (KL) 2748.2 (2,3  ) -5.6±7.2 (KL) 24.33.33 112 Sn0.971919.5±4.8 1919.82±0.16 (new!) 1871.137 (0 + ) -4.7±0.23 (KK) 1870.74(4 + ) -4.3±0.21 (KK) 26.73.73 130 Ba0.112617.1±2.02608.42 (?) -1.2±2.0 (LL) 2544.43 (?) 3.7±2 (KK) 34.55.10 136 Ce0.202418.9±132399.87 (1 +,2 + ?) 7.5±13 (LL) 2392.1 (1 +,2 + ?) - ??? -16±13 (KL) 2390.79(3  ) -14.6±13 (KL) 37.45.62 162 Er0.141843.8±5.61745.7(1 + ) -9.5±5.6 (KK) 1782.68(2 + ) -1±5.6 (KL) 53.88.58 *) E K and E L2 are given for daughter nuclei 2 + : suppression factor is ~ 10 4

14. g.s.-g.s. transitions 152 Gd (0.2%), 164 Er (1.56%), 180 W(0.13%) (There are only X-rays in this case)

15. 0 + G.S. -0 + G.S.  152 Gd- 152 Sm M = 54.6±3.5 keV  =0±3.5 keV K – 46.8 keV (KL case) L 1 = 7.73; L 2 = 7.31; L 3 = 6.71 keV  164 Er- 164 Dy M = 23.3±5.5 keV  =5.7±3.9 keV K – 53.78 keV (LL case) L 1 = 9.05; L 2 = 8.58; L 3 = 7.79 keV  180 W- 180 Hf M = 144.4±6.1 keV  =13.7±4.5 keV K – 65.34 keV KK -? L 1 = 11.27; L 2 = 10.74; L 3 = 9.56 keV 180 W- 180 Hf(2 + ;93.32 keV) M = 51.08±6.1 keV

16. Problems  There is no good theoretical description of the ECEC processes and “resonance” conditions  Accuracy of  M (and Q as a result) is not very good (~ 2- 10 keV) and has to be improved  Quantum numbers are not known in some cases [It is possible to improve the accuracy of  M to ~ 10-100 eV: 112 Sn:  M = 1919.82±0.16 keV, PRL 103 (2009) 042501; 74 Se:  M = 1209.240±0.007 keV, PRC 81 (2010) 032501R  M = 1209.169±0.049 keV, PLB 684 (2010) 17]

17. List of needed M measurements  Priority #1: 152 Gd- 152 Sm, 130 Ba- 130 Xe, 96 Ru- 96 Mo,  Priority #2: 164 Er- 164 Dy, 162 Er- 162 Dy, 136 Ce- 136 Ba, 106 Cd- 106 Pd

18. II. EXPERIMENT M = 1919.82 ± 0.16 keV  = 0.97%

19. SCHEME OF EXPERIMENT E = 2.0 keV (for 1332 keV) T = 3175.23 h Experiment is done in Modane Underground Laboratory, 4800 m w.e. 100 g of 112 Sn; Enrichment is 94.3%  5.05·10 23 nuclei 380 cm 3 low-background HPGe detector

20. 112 Sn (spectra)   Efficiency: 4.61% (617.5 keV) and 2.83% (1253.4 keV)

21. 112 Sn (spectra)

22. 112 Sn (results) Transition T 1/2, 10 20 y This work Previous work [1] T 1/2 th (2 ), y [2]  + ЕС(0 +2 ); g.s. > 0.97 > 0.56 3.8  10 24  +ЕС(0 +2 ); 2 + 1 > 7.02 > 2.79 2.3  10 32 ECEC(0 ) L 1 L 2 ; g.s. > 6.43 > 4.10 ECEC(0 ) K 1 L 2 ;g.s. > 8.15 > 3.55 ECEC(0 ) K 1 K 2 ;g.s. > 10.63 > 3.97 ECEC(0 ); 2 + 1 > 9.72 > 3.93 ECEC(0 ); 0 + 1 > 12.86 > 6.87 ECEC(0 ); 2 + 2 > 8.89 > 3.45 [1] A.S.B. et al., PRC 80 (2009) 035501; [2] P. Domin et al., NPA 753 (2005) 337.

23. 112 Sn (results-2) ECEC(0 ); 0 + 2 > 6.86 · 10 20 > 2.68·10 20 ECEC(0 ); 2 + 3 > 6.46 > 2.64 ECEC(0 ); 0 + 3 > 13.43 > 4.66 ECEC(2 ); 2 + 1 > 11.94 > 4.84 4.9  10 28 ECEC(2 ); 0 + 1 > 16.25 > 8.67 7.4  10 24 ECEC(2 ); 2 + 2 > 11.24 > 4.39 1.9  10 32 ECEC(2 ); 0 + 2 > 8.64 > 3.43 ECEC(2 ); 2 + 3 > 8.19 > 3.40 6.2  10 31 ECEC(2 ); 0 + 3 > 13.43 > 4.66 5.4  10 34

24. How to increase the sensitivity:  1 kg of 112 Sn, 1 y  ~ 10 22 y  200 kg of 112 Sn (using GERDA or MAJORANA), 10 y  ~ 10 26 y.

25. Comparison of existing experimental results for 112 Sn- 112 Cd(1871 Kev) transition  > 1.610 18 y (J. Dawson et al., 2008; 1.2 kg of natural Sn) > 0.9210 20 y (A.S.B. et al., 2008; 4 kg of natural Sn) > 0.810 19 y (J. Dawson et al., 2008; 1.2 kg of natural Sn)  > 1.310 19 y (M. Kidd et al., 2008; 3.9 g of 112 Sn)  > 4.710 20 y (A.S.B. et al., 2009; 50 g of 112 Sn)  > 1.310 21 y (A.S.B. et al., 2010; 100 g of 112 Sn)

26. Table. Best present limits on ECEC(0) to the excited state (for isotope-candidates with possible resonance conditions) Nuclear (natural abundance) E*(J  f )T 1/2, yExperiment, year 74 Se (0.89%)1204.20 (2 + )> 5.5·10 18 Modane (ITEP- Bordeaux), 2007 78 Kr (0.35%)2838.49 (2 + )> 1.2·10 21 *) Baksan (INR), 2010 96 Ru (5.54%)2700.21 (2 + ) 2712.68 (?) > 4.9·10 18 > 1.3·10 19 Gran Sasso (DAMA-Kiev), 2009 106 Cd (1.25%)2741.0 (4 + ) 2748.2 (2,3 - ) > 1.7·10 20 TGV-II, 2010 112 Sn (0.97%)1871.13 (0 + ) 1870.74 (4 + ) > 1.3·10 21 > 1.1·10 21 Modane (ITEP- Bordeaux), 2010 130 Ba (0.106%)2608.4 (?) 2544.43 (?) > 1.5·10 21 *) Geochemical, 2001 136 Ce (0.185%)2399.87 (1,2 + ) 2392.1 (1,2 + ) > 4.1·10 15 > 2.4·10 15 Gran Sasso (DAMA-Kiev), 2009 162 Er (0.14%)1745.7 (1 + ) - - *) Estimation from existing experimental data

27. CONCLUSION  New limits on the  + EC and ECEC processes for 112 Sn on the level 10 20 -10 21 y have been obtained (limits are in ~ 1.5-3 times better than previous results)  Possible resonance ECEC(0) transition 112 Sn- 112 Cd (1801.13 keV) has been investigated and limit 1.3·10 21 y was obtained  New M measurements are needed for other isotope- candidates  Quantum numbers have to be established for 2608.42 and 2544.43 keV levels in 130 Xe and 2712.68 kev in 96 Mo

28. BACKUP SLIDES

29. Last best achievements for such processes  ECEC(2 ): - T 1/2 ( 130 Ba) = (2.2 ± 0.5)·10 21 y (geochemical) - > 2.4·10 21 y ( 78 Kr, Baksan) - > 4.2·10 20 y ( 106 Cd, TGV-II) - > 5.9·10 21 y ( 40 Ca, DAMA-Solotvino)  2  + (0 +2 ), EC  + (0 +2 ), ECEC(0 ): > 10 20 -10 21 y ( 78 Kr, 106 Cd, 40 Ca; Baksan-Spain, DAMA-Solotvino) > 10 15 -10 19 y ( 120 Te, 108 Cd, 136 Ce, 138 Ce, 64 Zn, 180 W; COBRA, DAMA, Solotvino)