Nuclear Matrix Elements for Resonant 0ECEC Processes · Various 0ν2β Decay Modes of 106Cd 106 46...
Transcript of Nuclear Matrix Elements for Resonant 0ECEC Processes · Various 0ν2β Decay Modes of 106Cd 106 46...
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
I. Intro
0ν2β Decays of 106Cd
Jouni Suhonen (JYFL, Finland) TAUP’11 2 / 21
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
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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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
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
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 , . . .
Jouni Suhonen (JYFL, Finland) TAUP’11 8 / 21
Rate of Resonant 0νECEC Decay
ln 2T1/2
= gECEC[MECEC]2〈mν〉
2Γ
(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))
Jouni Suhonen (JYFL, Finland) TAUP’11 9 / 21
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)
Jouni Suhonen (JYFL, Finland) TAUP’11 10 / 21
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)
Jouni Suhonen (JYFL, Finland) TAUP’11 11 / 21
II. Status of 0νECEC Searches
Accessing R0νECEC Half-Lives
Jouni Suhonen (JYFL, Finland) TAUP’11 12 / 21
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=?)
Jouni Suhonen (JYFL, Finland) TAUP’11 13 / 21
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
Jouni Suhonen (JYFL, Finland) TAUP’11 14 / 21
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
Jouni Suhonen (JYFL, Finland) TAUP’11 15 / 21
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
Jouni Suhonen (JYFL, Finland) TAUP’11 16 / 21
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)
Jouni Suhonen (JYFL, Finland) TAUP’11 17 / 21
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
Jouni Suhonen (JYFL, Finland) TAUP’11 18 / 21
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
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)
Jouni Suhonen (JYFL, Finland) TAUP’11 20 / 21
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