Nuclear Matrix Elements for Resonant 0ECEC Processes · Various 0ν2β Decay Modes of 106Cd 106 46...

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Nuclear Matrix Elements for Resonant 0ν ECEC Processes Jouni Suhonen Department of Physics University of Jyväskylä TAUP’11, Munich, Germany, 5-9 September, 2011 Contents: Intro: 0ν 2β Decays of 106 Cd Status of R0ν ECEC Searches Jouni Suhonen (JYFL, Finland) TAUP’11 1 / 21

Transcript of Nuclear Matrix Elements for Resonant 0ECEC Processes · Various 0ν2β Decay Modes of 106Cd 106 46...

Page 1: Nuclear Matrix Elements for Resonant 0ECEC Processes · Various 0ν2β Decay Modes of 106Cd 106 46 Pd 60 0+ gs 2+ 1 511.86 keV 2+ 2 1128.0 keV 0+ 1 4+ 1133.7 keV 1229.2 keV 0 + 2766.26

Nuclear Matrix Elements for Resonant 0νECECProcesses

Jouni Suhonen

Department of PhysicsUniversity of Jyväskylä

TAUP’11, Munich, Germany, 5-9 September, 2011

Contents:

Intro: 0ν2β Decays of106Cd

Status of R0νECECSearches

Jouni Suhonen (JYFL, Finland) TAUP’11 1 / 21

Page 2: Nuclear Matrix Elements for Resonant 0ECEC Processes · Various 0ν2β Decay Modes of 106Cd 106 46 Pd 60 0+ gs 2+ 1 511.86 keV 2+ 2 1128.0 keV 0+ 1 4+ 1133.7 keV 1229.2 keV 0 + 2766.26

I. Intro

0ν2β Decays of 106Cd

Jouni Suhonen (JYFL, Finland) TAUP’11 2 / 21

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Various 0ν2β Decay Modes of 106Cd

10646Pd60

0+gs

2+1

511.86 keV

2+2

1128.0 keV0+

1

1133.7 keV4+1229.2 keV

0+2766.26 keV

XK XK

1+1

10647Ag59

0+1

10648Cd58R0νECEC

0νβ+β+, 0νβ+EC

0νβ+EC Q = 2770(7) keV

Qβ− = 202 keV

Multiple-commutator model

(MCM =ccQRPA+pnQRPA)

MCM

pnQRPA

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Neutrinoless Double Positron/EC Decays

0νβ+β+ Decay

p

n

(Z − 2, N)

(Z − 2, N)

p

n

e+ e+

Final nucleus (Z − 2, N + 2)

Initial nucleus (Z, N)

νe = νe

0νβ+EC Decay

p

n

(Z − 2, N)

(Z − 2, N)

p

n

e+

e−bound

H

Final nucleus (Z − 2, N + 2)

Initial nucleus (Z, N)

νe = νe

Jouni Suhonen (JYFL, Finland) TAUP’11 4 / 21

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Rates of 0νβ+β+ and 0νβ+EC DecaysDecay rates:

ln 2Tα1/2(0

+)= gα

0ν(0+)[M(0ν)′]2〈mν〉

2 , α = β+β+, β+EC ,

gα0ν(0+) is the phase-space factor

Effective neutrino mass:

〈mν〉 =∑

j=light

λCPj |Uej|

2mj

Standard NME:

M(0ν)′ =( gA1.25

)2[

M(0ν)GT −

(

gVgA

)2

M(0ν)F + M

(0ν)T

]

,

where gA = 1.25 corresponds to the bare-nucleon value of theaxial-vector coupling constant.

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Page 6: Nuclear Matrix Elements for Resonant 0ECEC Processes · Various 0ν2β Decay Modes of 106Cd 106 46 Pd 60 0+ gs 2+ 1 511.86 keV 2+ 2 1128.0 keV 0+ 1 4+ 1133.7 keV 1229.2 keV 0 + 2766.26

Two-Neutrino Double Electron Capture

p

n

(Z − 2, N)

(Z − 2, N)

p

n

e−bound

νe

e−bound

νe

H H ′

Final nucleus (Z − 2, N + 2)

Initial nucleus (Z, N)

Jouni Suhonen (JYFL, Finland) TAUP’11 6 / 21

Page 7: Nuclear Matrix Elements for Resonant 0ECEC Processes · Various 0ν2β Decay Modes of 106Cd 106 46 Pd 60 0+ gs 2+ 1 511.86 keV 2+ 2 1128.0 keV 0+ 1 4+ 1133.7 keV 1229.2 keV 0 + 2766.26

Neutrinoless Double Electron Capture

Radiative 0νECEC

p

n

(Z − 2, N)

(Z − 2, N)

p

n

e−bound

e−bound

H H ′

Final nucleus (Z − 2, N + 2)

Initial nucleus (Z, N)

γ

νe = νe

Resonant 0νECEC

p

n

(Z − 2, N)

(Z − 2, N)

p

n

e−bound

e−bound

H H ′

Final nucleus (Z − 2, N + 2)∗

Initial nucleus (Z, N)

νe = νe

Jouni Suhonen (JYFL, Finland) TAUP’11 7 / 21

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Single-Hole States in Atoms

Hydrogen atom

E [eV]

r [A]

1s1/2

2s1/2, 2p1/2, 2p3/2

3s1/2, 3p1/2, 3p3/2, 3d3/2, 3d5/2

E1

14E1

19E1

−10.0

10.00.0

Cadmium atom

E [keV]

0

−10

−20

1s1/2

2s1/22p1/2

2p3/2

3s1/2 3p1/2

n = 1 ↔ K , n = 2 ↔ L , n = 3 ↔ M , . . .

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Rate of Resonant 0νECEC Decay

ln 2T1/2

= gECEC[MECEC]2〈mν〉

(Q− E)2 + Γ2/4, Q−E = degeneracy parameter

phase-space factor

gECEC(0+) =

GF cos θC√2

«4 g4A4π2

m6eN 2

0,−1 ,

where N0,−1 is the normalization of the relativistic K-shell(1s1/2) Diracwave function for a uniformly charged spherical nucleusQ = M(Z,A) −M(Z− 2,A) = difference between the initial and finalatomic massesE = E∗ + EH + EH′ + EHH′ = nuclear excitation energy + electron bindingΓ = Γ∗ + ΓH + ΓH′ = nuclear and atomic radiative widthsNUCLEARMATRIX ELEMENT:MECEC = 1

RAM(0ν)′ , RA = 1.2A1/3 fm

Enhancement factors of 106 possible (J. Bernabeu, A. De Rujula, and C. Jarlskog, Nucl.

Phys. B 223 (1983) 15 ; Z. Sujkowski and S. Wycech, Phys. Rev. C 70 (2004) 052501(R))

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Page 10: Nuclear Matrix Elements for Resonant 0ECEC Processes · Various 0ν2β Decay Modes of 106Cd 106 46 Pd 60 0+ gs 2+ 1 511.86 keV 2+ 2 1128.0 keV 0+ 1 4+ 1133.7 keV 1229.2 keV 0 + 2766.26

Computed Half-Life Estimates

Tβ+β+

1/2 = Tβ+β+

0 (〈mν〉[eV])−2, Tβ+β+

0 (0+

gs) =

(1.93 − 2.20) × 1027yr (UCOM)

(3.11 − 3.24) × 1027yr (Jastrow)

Tβ+EC1/2 = Tβ+EC

0 (〈mν〉[eV])−2, Tβ+EC

0 (0+

gs) =

(1.35− 1.54) × 1026yr (UCOM)

(2.18− 2.28) × 1026yr (Jastrow)

Tβ+EC0 (0+

2−ph) =

(9.81− 12.20) × 1028yr (UCOM)

(8.32− 10.70) × 1028yr (Jastrow)

TECEC1/2 = TECEC

0x2 + 26.21(〈mν〉[eV])2

, TECEC0 (0+

1−ph) =

(3.02− 8.08) × 1022yr (UCOM)(3.56− 9.69) × 1022yr (Jastrow)

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Half-Life Estimate for 106Cd

Decay width of the two-hole state: Γ = 10.24 eV

1024

1025

1026

1027

1028

1029

1030

1031H

alf-life

(yr)

100 101 102 103

x (eV)

〈mν〉 = 1.0 eV

〈mν〉 = 0.3 eV

〈mν〉 = 0.05 eV

T1/2 = ln 2 (x/Γ)2+1/4gECEC[MECEC]2〈mν〉2

Γ, x = |Q− E| (degeneracy parameter)

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Page 12: Nuclear Matrix Elements for Resonant 0ECEC Processes · Various 0ν2β Decay Modes of 106Cd 106 46 Pd 60 0+ gs 2+ 1 511.86 keV 2+ 2 1128.0 keV 0+ 1 4+ 1133.7 keV 1229.2 keV 0 + 2766.26

II. Status of 0νECEC Searches

Accessing R0νECEC Half-Lives

Jouni Suhonen (JYFL, Finland) TAUP’11 12 / 21

Page 13: Nuclear Matrix Elements for Resonant 0ECEC Processes · Various 0ν2β Decay Modes of 106Cd 106 46 Pd 60 0+ gs 2+ 1 511.86 keV 2+ 2 1128.0 keV 0+ 1 4+ 1133.7 keV 1229.2 keV 0 + 2766.26

Estimate for the R0νECEC Half-Life of 106Cd

Γ = 10.24 eV ; MECEC0ν = 1.98− 3.48 for the decay to the potential 0+

Q value measured in SHIPTRAP (GSI, Darmstadt) (M. Gonsharov et al., Phys. Rev.

C 84 (2011) 028501)

Q − E = 8.39 keV for KK capture to (0+?)= −0.33(41)keV(!) for KL3 capture to (2,3)− (NME=?)

For the decay to the potential 0+:

T1/2 =(2.11− 5.70) × 1030

(〈mν〉[eV])2years

Conclusion: Decay rate to 0+ much suppressed by the rather largedegeneracy parameterQ− E

Possible resonance for the negative-parity states (NME=?)

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Page 14: Nuclear Matrix Elements for Resonant 0ECEC Processes · Various 0ν2β Decay Modes of 106Cd 106 46 Pd 60 0+ gs 2+ 1 511.86 keV 2+ 2 1128.0 keV 0+ 1 4+ 1133.7 keV 1229.2 keV 0 + 2766.26

Resonant 0νECEC Decay of 112Sn

11248Cd64

0+1

2+1

617.516 keV

0+4

1924.3 keV

XK XK

1+1

11249In63

0+1

11250Sn620νECEC

Q = 1919.82(16) keV

Qβ− = 658 keV

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Page 15: Nuclear Matrix Elements for Resonant 0ECEC Processes · Various 0ν2β Decay Modes of 106Cd 106 46 Pd 60 0+ gs 2+ 1 511.86 keV 2+ 2 1128.0 keV 0+ 1 4+ 1133.7 keV 1229.2 keV 0 + 2766.26

Half-Life Estimate for 112Sn

Γ = few tens of eV ; MECEC0ν = 4.76 (unitless NME)

Q value measured in JYFLTRAP (S Rahaman, V.-V. Elomaa, T. Eronen, J. Hakala, A.

Jokinen, A. Kankainen, J. Rissanen, J. Suhonen, C. Weber, and J. Äystö, Phys. Rev. Lett. 103 (2009)

042501)

Q− E = −4.5 keV for KK capture= 18.2 keV for KL1 capture= 40.9 keV for L1L1 capture

Hence:

T1/2 >5.9 × 1029

(〈mν〉[eV])2years

Conclusion: Decay rate much suppressed by the rather largedegeneracy parameter Q− E

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Page 16: Nuclear Matrix Elements for Resonant 0ECEC Processes · Various 0ν2β Decay Modes of 106Cd 106 46 Pd 60 0+ gs 2+ 1 511.86 keV 2+ 2 1128.0 keV 0+ 1 4+ 1133.7 keV 1229.2 keV 0 + 2766.26

Resonant 0νECEC Decay of 74Se

7432Ge42

0+1

2+1

595.88 keV

2+2

1204.31 keV

XL XL

2−17433As41

0+1

7434Se400νECEC

Q = 1209.171(49) keV

Qβ− = 1353.1 keV

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Page 17: Nuclear Matrix Elements for Resonant 0ECEC Processes · Various 0ν2β Decay Modes of 106Cd 106 46 Pd 60 0+ gs 2+ 1 511.86 keV 2+ 2 1128.0 keV 0+ 1 4+ 1133.7 keV 1229.2 keV 0 + 2766.26

Half-Life Estimate for 74Se

Γ = few tens of eV ; MECEC0ν < 0.0160 (unitless NME)

Q value measured in JYFLTRAP (V.S. Kolhinen, V.-V. Elomaa, T. Eronen, J. Hakala,

A. Jokinen, M. Kortelainen, J. Suhonen and J. Äystö, Phys. Lett. B 684 (2010) 17)

Q− E = 2.23 keV for L2L3 capture (most favorable)

Hence:

T1/2 ≈5× 1043

(〈mν〉[eV])2years

Conclusion: Decay rate much suppressed both by the rather largedegeneracy parameter Q− E and the very small NMEfor the 2+

f final state. The same occurs for the 2νβ−β− decay(see M. Aunola and J. Suhonen, Nucl. Phys. A 602 (1996) 133)

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Page 18: Nuclear Matrix Elements for Resonant 0ECEC Processes · Various 0ν2β Decay Modes of 106Cd 106 46 Pd 60 0+ gs 2+ 1 511.86 keV 2+ 2 1128.0 keV 0+ 1 4+ 1133.7 keV 1229.2 keV 0 + 2766.26

Resonant 0νECEC Decay of 136Ce

13656Ba80

0+1

2+1

818.50 keV

0+4

2390.20 keV

XK XK 1+1

13657La79

0+1

13658Ce780νECEC

Q = 2378.53(27) keV

Qβ− = 460 keV

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Page 19: Nuclear Matrix Elements for Resonant 0ECEC Processes · Various 0ν2β Decay Modes of 106Cd 106 46 Pd 60 0+ gs 2+ 1 511.86 keV 2+ 2 1128.0 keV 0+ 1 4+ 1133.7 keV 1229.2 keV 0 + 2766.26

Half-Life Estimate for 136Ce

Γ = 13.81 eV ; MECEC = 0.250 (unitless NME)

Q value measured in JYFLTRAP(V.S. Kolhinen, T. Eronen, D. Gorelov, J.

Hakala, A. Jokinen, A. Kankainen, J. Rissanen, J. Suhonen and J. Äystö, Phys. Lett. B

697 (2011) 116)

Q− E = −11.67 keV for KK capture= 19.78 keV for KL1 capture= 51.24 keV for L1L1 capture

Hence:

T1/2 >2.26 × 1033

(〈mν〉[eV])2years

Conclusion: Decay rate much suppressed by the rather largedegeneracy parameter Q− E and the rather small NME

Jouni Suhonen (JYFL, Finland) TAUP’11 19 / 21

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Concise List of Other Cases

Transition Jπf Q− E [keV] At. orb. Ref.96Ru → 96Mo 2+ 8.92(13) L1L3 [1]

0+? −3.90(13) L1L1 Q from [1]102Pd → 102Ru 2+ 75.26(36) KL3 [2]144Sm → 144Nd 2+ 171.89(87) KL3 [2]152Gd → 152Sm 0+

gs 0.91(18) KL1 [3]156Dy → 156Gd 1− 0.75(10) KL1 [4]

0+ 0.54(24) L1L1 [4]2+ 0.04(10) M1N3 [4]

162Er → 162Dy 2+ 2.69(30)keV KL3 [1]168Yb → 168Er (2−) 1.52(25)keV M1M3 [1]

[1] S. Eliseev et al., Phys. Rev. C 83 (2011) 038501 (SHIPTRAP, GSI)[2] M. Goncharov et al., Phys. Rev. C 84 (2011) 028501 (SHIPTRAP, GSI)[3] S. Eliseev et al., Phys. Rev. Lett. 106 (2011) 052504 (SHIPTRAP, GSI)[4] S. Eliseev et al., Phys. Rev. C 84 (2011) 012501(R) (SHIPTRAP, GSI)

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Conclusions and Outlook

Conclusions:

Most R0νECEC decays are NOT OBSERVABLE due to badly fulfilledresonance condition and/or tiny NME.Possible exceptions are:

Decay of 106Cd to (2, 3)− state (NME is unknown)

Decay of 152Gd for which one gets the estimate (S. Eliseev et al., Phys.Rev. Lett. 106 (2011) 052504)

T1/2 ≈1026

(〈mν〉[eV])2years

Decays of 156Dy to 1−, 0+ and 2+ states (NMEs are unknown)

Outlook (and recommendations):

Reliable calculation of the NMEs of the above-mentioned specialcases of R0νECEC should be pursued.

Jouni Suhonen (JYFL, Finland) TAUP’11 21 / 21