1. Structure of the ECEC candidate daughter 112 Cd P.E. Garrett University of Guelph TRIUMF Excellence Cluster “Universe”, Technische Universität München

2. Rate of 0 ECEC Radiative Process Q res =|E(2P,Z-2)-E(1S,Z-2)|  f = radiative width of final atom Resonant enhancement when: Q – Q res = 0  M = mass difference of parent and daughter GS E K = K-shell electron binding energy E L = L-shell electron binding energy E ex = excitation energy in daughter nucleus

3. Theoretical Candidates Z. Sujkowski and S. Wycech, Physical Review C 70, 052501(R) (2004)

4. 112 Sn 0 + GS  112 Cd 1871 keV 0 + State MM 1919.5(4.6) E excitation 112 Cd1870.9 Q18.0(4.6) Q res [E(2P)-E(1S)]23.8 Q-Q res -5.8(4.6) Energies given in keV  Level energy and uncertainty based on  -ray singles measurements  Level energy quoted to 130 eV* or 190 eV**, but uncertainty could be much greater (up to ~ keV)  -rays are known to be doublets, which provides large uncertainty Z. Sujkowski and S. Wycech, Physical Review C 70, 052501(R) (2004) *A.H. Wapstra, G. Audi and C. Thibault, Nucl. Phys. A 729 (2003), p. 129 ** R.B. Firestone et al, Table of Isotopes, Vol. I, 8 th edition (1996)

5. Degenerate Levels – 1871 keV  Previous energy measurement attempts plagued by degenerate 4 + 1871 keV level  Levels decay to nearly same set of final states:  -rays doublets  Previous measurements used singles data. To resolve doublets, coincidence data is required. 0 617 1416 1224 1469 1871 0+0+ 2+2+ 4+4+ 0+0+ 2+2+ 4+4+ 1253 1312 2+2+ 455 558 402 Gamma Rays labelled in keV 1432 0+0+ 1871 0+0+ 402 558 1253 Investigate level energies through  -decay

6.  -decay studies at TRIUMF-ISAC with the 8  spectrometer  110 In(4.9hr 7 + g.s., 69min 2 + isomer), 112 In(15min 1 + g.s.), 112 Ag(3.1hr 2  g.s.)  spallation of Ta target with 40  A of 500 MeV protons surface ion or laser ion (TRILIS) source  Beam rates ~ 10 6 – 10 7 s  1 Tape Cassette Lead Sheilding

7. High sensitivity achieved with  -decay  112 Ag decay: 100  10 6 events in random- background subtracted  matrix  110 In decay: 850  10 6 events in random- background subtracted  matrix (mostly 7 + decay)

8. Example of sensitivity in  -decay to weak branches 0 617 1416 0+0+ 2+2+ 4+4+ 1312 2+2+ 1871 0+0+ 1253 Transitions in keV 360 2+2+ 2231 2+2+ 2156 286 5  10 -4  branch from 2231-keV level 112 Cd

9. 995 keV Gate: Transition to 4 + 1871 keV State 0 617 1416 1224 1469 1871 0+0+ 2+2+ 4+4+ 0+0+ 2+2+ 4+4+ 1253 1312 2+2+ 455 558 402 112 Ag  112 Cd 995 keV Gate Transitions in keV 995 1871 0+0+

10. 635 keV Gate: Transition to 0 + 1871 keV State 0 617 1416 0+0+ 2+2+ 4+4+ 1312 2+2+ 1871 0+0+ 1253 1469 2+2+ 402 Transitions in keV 635 1871 4+4+

11. Energy Calculation  -ray energies measured from coincidence data  Internal calibration with well known  rays from (n,n  ) measurements Garrett et al, PRC 64, 024316 (2001). –e.g. 617.516(21) keV (2 1 + → 0 1 + ), 1387.676(21) keV (3 1 - → 2 1 + )  Least squares fit method  Resolved problem of near degenerate states 0 + Level Energy: 1871.137(72) keV 4 + Level Energy: 1870.743(54) keV

12. 112 Sn 0 + GS  112 Cd 1871 keV State MM 1919.82(16) * E K + E L 26.7112 + 3.727 = 30.438 E excitation 112 Cd1871.137(72)** Q18.25(18) Q res [E(2P)-E(1S)]23.788(3) J. Rzadkiewicz, et al, Acta Phys. Pol. B 33 (1), 415-422 (2002). Q-Q res -5.54(18) keV Energies given in keV *Rahaman et al., PRL 103, 042501 (2009) **Green et al., PRC 80, 032502(R) (2009)

13. Nuclear Matrix Element  To determine mass, information needed regarding nuclear matrix element  Structure of 0 + 1871 keV state If measured from experiment   f, Q, Q res Nuclear matrix element 0 617 1416 1469 1871 0+0+ 2+2+ 4+4+ 2+2+ 4+4+ 1312 2+2+ Gamma Rays labelled in keV 1432 0+0+ 1871 0+0+ 402 558 1253 0 617 1416 1469 1871 0+0+ 2+2+ 4+4+ 2+2+ 4+4+ 1312 2+2+ Gamma Rays labelled in keV 1432 0+0+ 1871 0+0+ 402 1253 Previous WorkThis Work What is the nature of excited 0 + states?

14. Cd nuclei are paradigms for spherical vibrational, or U(5), nuclei  Spherical vibrators form one of the limits of the IBM – U(5) limit –Arima and Iachello (1975) cite 110,112 Cd, as having the smallest deviation from expected U(5) decay patterns –Kern (1995) survey also cited 110,112 Cd as “best” examples of U(5) nuclei  110–116 Cd pass all simple signature tests for spherical vibrators Arima&Iachello, Ann. Phys. 99, 253 (1976)

15. Complication from intruder configuration

16. 112 Cd – paradigm for vibrational U(5) nuclei Data explained well with strong mixing between intruder and normal phonon configurations

17. Lifetimes in 112 Cd from (n,n  ) reaction  Accelerator produced neutrons (Uni. of Kentucky)  Level lifetimes from Doppler shift attenuation method –small recoil velocity:   c –Doppler shifts can be large, several keV’s, or extremely small (on the order of 10’s eV), depending on lifetime of state  110 Cd, 112 Cd, 114 Cd, 116 Cd studied in detail  =1.00 ps -0.34 +1.00  =500 fs -80 +130  =2.20 ps -0.80 +3.20  =64(12) fs  =380(65) fs  =25(6) fs Corminboeuf PRL 84 4060 (2000), Corminboeuf PRC 63 014305 (2000), Garrett PRC 75 054310 (2007), Bandyopadhyay PRC 76 054308 (2007), Kadi PRC 68 031306(R) (2003)

18. 112 Cd – 0 + 3-phonon candidates 30 W.u. 0+0+ 2+2+ 2+2+ 0+0+ 90 W.u. Expected (HV) Non-observed transition – upper limit Intruder states 2-phonon states Relative B(E2) value (lifetime nor limit known) All values are B(E2)’s in W.u. unless indicated No suitable 0 + 3-phonon candidate, nor indication of 3-ph B(E2) strength, below 5  E 2+

19. Garrett et al, PRC 78, 044307 (2008) B A Cd 0 + systematics  Systematics in energy of 0 4 + level, combined with favored decay to intruder 2 + level, suggest an intruder assignment

20. 112 Cd – 2 + 3-phonon candidates B(E2  0 + )=17(5) B(E2  2 + )<1.9 B(E2  4 + )<0.4 0+0+ 2+2+ 4+4+ 2+2+ 0+0+ 2+2+ 30 W.u. 42 31 17 Expected (HV) All values are B(E2)’s in W.u. unless indicated

21. 112 Cd – 2 + 3-phonon candidates  B(E2  0 + )=23.2(50)+<0.7  B(E2  2 + )=0.4+<3.2  B(E2  4 + )<4.6 0+0+ 2+2+ 4+4+ 2+2+ 42 31 17 Expected (HV) Experimental values

22. Results from our  -decay studies to date force re-evaluation of Cd structure  Cd nuclei appear vibrational up to 2- phonon level  B(E2;0 +  2 + ) factor 2 weaker than expected  At 3-phonon level, systematically NO suitable candidates for 0 +, 2 + members –0 + levels: only possible collective transitions observed are to 2 + intruder level –2 + level: only collective decays to 0 + 2- phonon  Results from  -decay into 112 Cd show that the E2 strength from 0 + and 2 + 3-phonon members is not fragmented – it is entirely missing below 5 ħ   What mechanism would destroy 0 + and 2 + spin members of 3-phonon quintuplet and leave the remainder of the members?  Are the Cd nuclei really vibrational?  If the Cd are not vibrational, what are they?

23. Are the Cd nuclei quasi-rotational down to low-spin? Regan, PRL 90 152502(2003)

24. Spherical vibrational Cd nuclei appear to accommodate rotational bands Garrett and Wood, JPG 37, 064028 (2010)

25. proton spectrum Assigned 2 +  3  member based on strong B(E2) value to 3  octupole

26. Summary  Mass measurements with accurate determination of 0 4 + energy through  -decay study indicates 112 Sn  112 Cd unlikely candidate for resonant enhancement  Structure of initial/final states may hold surprises – and hence make accurate determination of ME’s difficult, even for “well understood” nuclei  Assumption of excited phonon vibrational states may be wrong description –If we can’t assume spherical vibrational nuclei, changes in deformation between parent-daughter may be more dramatic than previously thought –Using simple indicators, especially for states along yrast line, may lead to wrong conclusions about structure –Detailed spectroscopy, with wide variety of probes, required to unravel structure

27. Collaborators  University of Guelph –K.L. Green, J. Bangay, L. Bianco, G.A. Demand, A. Diaz-Varela, G.F. Grinyer, D. Jamieson, K.G. Leach, A.A. Phillips, M.A. Schumaker, C. Sumithrarachchi, C.E. Svensson, J. Wong  TRIUMF –G.C. Ball, D.S. Bandyopadhyay, A. Garnsworthy, G. Hackman, A.C. Morton, J.N. Orce, C.J. Pearson, S. Williams  St Mary’s University –R.A.E. Austin, S. Colosimo  Georgia Institute of Technology –W.D. Kulp, J.L. Wood  Simon Fraser University –D. Cross  University of Kentucky –S.W. Yates  Technical University Munich –T. Faestermann, R. Krücken  LMU Munich –R. Hertenberger, H.-F. Wirth

29. Neutrinoless Double Beta Decay  Decay rate: –G 0 (Q ,Z) = phase-space factor –|M 0 | = nuclear matrix element – = effective Majorana mass of e - neutrino –U ek is neutrino mixing matrix element for mass eigenstates m k  Violates lepton number conservation and (Majorana)  Signature: energy sum of  particles = Q value of reaction  Observation of process never confirmed  If processed observed and nuclear matrix element understood, then we can extract neutrino mass (Z,A)  (Z-2,A) + 2e + Challenge in  -decay is from reducing background to see signal Radiative ECEC suggested as possible alternative

30. 0 ECEC Radiative Process Most likely process: 2 e  captured in virtual process (resonant enhancement) − (Z-2,N+2)*: excited virtual atom with 2 e  holes − Radiates and one hole is filled, emitting observable K X- ray − Energy of radiative IB photon = Q value − Resonant enhancement: Q  E(2P)-E(1S) = E(K X-ray) − Nucleus in excited state, decays by  -ray emission Triple coincidence! (Z,N)(Z,N) (Z-2,N+2)* Resonant K h Photon  -ray(s) K X-ray

31. 2373-keV s 1/2  h 11/2 5 - G jl =1.2

32. ħω2ħω2 2ħω 2 3ħω 2 0 0+0+ 2+2+ 0,2,4 + 0,2,3,4,6 + E2 4ħω24ħω2 0,2,2,4,4,5,6,8 + Δn = ±1 Courtesy of M. Itoh and Y. Fujita Spherical Quadrupole Vibrations

33. Quadrupole harmonic oscillator  Use expectations of harmonic vibrator as a guide for 3-phonon states  Need lifetimes of low-spin, highly non-yrast states  (n,n  )  Need branching ratio measurements of low-energy branches in competition with high-energy branches   -decay Arrows = B(E2) values relative to 2 +  0 +

34. Comparison of lifetimes from (n,n  ) with other methods in 112 Cd  Lifetimes extracted with (n,n  ) compare well with those from Coulex (long lifetimes) and ( ,  ) (short lifetimes)

35. States in 112 Cd from 110 Cd(t,p)

36. New (d,p) data from Q3D@TU/LMU Munich

37. Results from Pd( 3 He,n)Cd reaction 0+20+2 0+30+3 0+20+2 0+30+3