1. 1 TCP06 Parksville 8/5/06 Electron capture branching ratios for the nuclear matrix elements in double-beta decay using TITAN ◆ Nuclear matrix elements in double-beta decay. ◆ Present uncertainties ◆ Measurement of electron-capture branching ratios. ◆ A new method using TITAN D. Frekers, J. Dilling, I. Tanihata and TITANEC collaboration

2. 2 TCP06 Parksville 8/5/06 Double Beta Decay ◆ Two-neutrino decay (2  ) This decay is allowed by the standard model and has been observed. Calculations of the nuclear matrix elements are the main issues to understanding the decay rates. ◆ Zero-neutrino decay (0  ) This mode of decay is forbidden by the standard model. Requires the neutrino to be a Majorana particle with a mass. Recent observations of the neutrino oscillation suggest the non-zero mass of the neutrino and thus this decay mode may exist. New generation experiments for detecting this mode of decay are in progress. Majorana neutrino mass would be determined if this mode of decay is observed and reliable estimation of the nuclear matrix elements are available.

3. 3 TCP06 Parksville 8/5/06 Rate of a 2  decay Q: decay Q value G F : Fermi coupling constant Q c : Cabibbo angle F - : Coulomb factor for  - decay f(Q): phase space factor C: Relativistic correction [Allowed by the standard model]

4. 4 TCP06 Parksville 8/5/06 Nuclear matrix element for 2  decays Gamow-Teller transitions to all available states. Fermi-type transitions are negligible due to the isospin conservation.

5. 5 TCP06 Parksville 8/5/06 Rate of 0  decay (Neutrinoless decay) [Forbidden by the standard model] Both Gamow-Teller and Fermi transitions are involved. U ei : mixing matrix m i : mass eigenvalues of neutrinos

6. 6 TCP06 Parksville 8/5/06 Matrix elements of 0  decay R lk : proton neutron distance in the nucleus E a : energy parameter related to the excitation energy

7. 7 TCP06 Parksville 8/5/06 Theoretical approaches to the matrix elements ◆ Weak-coupling shell model based on G-matrix nucleon- nucleon interactions W.C Haxton and G.J. Stephenson, Jr., Part. Nucl. Phys 12 (1984) 409. E. Caurier et al., Phys. Rev. Lett. 77 (1996) 1954. But not available for all double beta-decay candidates. ◆ Quasiparticle Random phase approximation (QRPA) J. A. Halbleib and R. A. Solensen, Nucl. Phys. A 98 (1967) 542. J. Suhonen, Phys. Lett. B 607 (2006) 87.

8. 8 TCP06 Parksville 8/5/06 ◆ One can test the precession of calculations by comparing calculations to measured two-neutrino decay rate. The operator involved in the 2 decay mode is the Gamow- Teller operator that connects the initial and final states via virtual transitions to J  =1 + states in the intermediate nucleus, only. ◆ The neutrinoless mode, on the other hand connect to all states in the intermediate nucleus. ◆ For this reason, comparison in 2 is not a direct test of the precision of the 0 rate calculation, but can be taken as a necessary condition for the reliability of the calculation. M. Bhattacharya et al., Phys. Rev. C 58 (1998) 1247.

9. 9 TCP06 Parksville 8/5/06 Theoretical situation (QRPA) ◆ Both decay modes can be described with ONE parameter, g pp, that is the particle-particle coupling part of the proton-neutron two-body interaction. ◆ g pp is fixed by the experimental 2  decay half life (g pp ~1) ◆ 0  decay is insensitive to g pp. ◆ So just trust us!! Only 1 + is sensitive to g pp However…

10. 10 TCP06 Parksville 8/5/06 The case of A=116 J. Suhonen, Phys. Lett. B 607 (2005) 87. 116 Cd Single state dominance One can obtain the transition strength of M EC and M  separately. Exp.  - Exp. EC (direct mea.) Exp. EC ( 3 He,t) M. Bhattacharya et al. Phys. Rev. C 58 (1998) 1247. H. Akimune et al., Phys. Lett. B 394 (1997) 23.

11. 11 TCP06 Parksville 8/5/06 Experimental data also show inconsistency ◆ Direct measurement of Electron capture (M EC =0.69) Extremely small branching compared with  - decay. (~0.023%) ◆ Nucleon transfer reactions (M EC =0.18) Uncertainty between the proportionality of between B(GT) and the ( 3 He,t) charge exchange cross section.

12. 12 TCP06 Parksville 8/5/06 Difficulty in electron capture branching ratio ◆ Measurement should be made by detecting Kx-rays after capture of electrons under the back ground of x-rays and  rays associated with  - decays. ◆ Neutron activation method,… Reaction with accelerated beam and tape transport system. Kx-rays after shake off by electrons. Bremsstrahlung from electrons. Beta delayed gamma emission. Impurity of decay sample.

13. 13 TCP06 Parksville 8/5/06 A New Method at TITAN ◆ Observation of x-ray from decays of trapped ions. No material around the decaying nuclei. All electrons are swept away by the magnetic field. No impurity

14. 14 TCP06 Parksville 8/5/06 ISAC Facility at TRIUMF M. Bhattacharya et al., PRC 58 (1998)1247. TITAN

15. 15 TCP06 Parksville 8/5/06 TITAN Mass measurement mode TITAN EC measurement mode

16. 16 TCP06 Parksville 8/5/06 EBIT (Electron Beam Ion Trap) ◆ Use it without the electron gun. (Penning trap mode) ◆ 7 ports for X-ray detection

17. 17 TCP06 Parksville 8/5/06 100 Tc case as an example ◆ Optimization High detection efficiency of 17.5 keV X-rays Low efficiency for  rays. High rejection of e - ■ Detector thickness ■ Be window thickness ■ Magnetic field strength T 1/2 =15.8 s

18. 18 TCP06 Parksville 8/5/06 Simulated spectra ( 100 Tc) X-ray spectrum by a Si detector (2mm thick) 8x10 8 decays @0.002% branching ratio with  -ray anticoincidence with 90% rejection rate. Additional background for 1.5x10 8 decays.

19. 19 TCP06 Parksville 8/5/06 Simulated spectra ( 100 Tc) X-ray spectrum by a Si detector (2mm thick) 8x10 7 decays @0.1% branching ratio and no  -ray anti-coincidence rejection, or 8x10 8 decays @0.01% branching ratio with  -ray anticoincidence with 90% rejection rate.

20. 20 TCP06 Parksville 8/5/06 Summary ◆ Radioactive beam facilities and ion traps provides a new possibility for a precise determination of an extremely small branching ratio of electron capture. ◆ It will give the best test ground for nuclear models of double beta decay. It thus provides information on the matrix elements of 0  decays. ◆ Please refer to the paper by D. Frekers, J. Dilling, and I. Tanihata submitted to publication for detailed discussion of other cases of double beta decays. Thank you