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Double beta decay nuclear matrix elements in deformed nuclei
O. Moreno, R. Álvarez-Rodríguez,P. Sarriguren, E. Moya de Guerra
F. Šimkovic, A. Faessler
H. Müther
Past, present and future calculations within Tübingen-Madrid collaboration
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Introduction
Theoretical formalism
Results
Current work
Conclusions & outlook
Summary
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Introduction
Two succesive decays through intermediate virtual states.
Second order process in weak interaction energy denominator.
One of the most rare events in nature, T1/2 ~ 1019 – 1021 s.
Observed in 48Ca 76Ge 82Se 96Zr 100Mo 116Cd 128Te 130Te 150Nd.
Strong dependence on nuclear structure, in particular nuclear deformation.
AX
AY
AZ
2 2 decay
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Introduction
0 2 decay
Virtual emitted in the first decay is absorbed in the second decay.
For virtual neutrinos, (Majorana particles)
Also a very rare event, observation not yet confirmed.
Also strong dependence on nuclear structure
comparison with 22 nuclear matrix elements needed.
AX
AY
AZ
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Mean field+
pairing+
proton-neutroncorrelations
Theoretical formalism
def. HF (Skyrme)
BCS (expG)
pnQRPA . (ph+pp)
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Nuclear wavefunction: adiabatic + harmonic collective motionNuclear wavefunction: adiabatic + harmonic collective motion
Dynamics: Classical variational principleDynamics: Classical variational principle
Theoretical formalism
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HF & RPA equations:HF & RPA equations:
Theoretical formalism
(Pairing(PairingBCS)BCS)
(Skyrme (Skyrme interactions)interactions)
++
( )j j
j
Ee
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Theoretical formalism
136Xe
136Cs
136Ba
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ParentDaughter
expQexp
Qexp
Alvarez-Rodriguez et al. PRC 70 (2004) 064309
Results
HF (Sk3) + BCS
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Alvarez-Rodriguez et al. PRC 70 (2004) 064309
Results
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Alvarez-Rodriguez et al. PRC 70 (2004) 064309
Results
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Alvarez-Rodriguez et al. PRC 70 (2004) 064309
Alvarez-Rodriguez et al. PRC 70 (2004) 064309
Results
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1)1) Improvement of overlap between RPA Improvement of overlap between RPA intermediate virtual states.intermediate virtual states.
2)2) Introduction of a realistic residual Introduction of a realistic residual interaction giving rise to spin-isospin interaction giving rise to spin-isospin transitions (to be treated within RPA).transitions (to be treated within RPA).
3)3) Closure approximation.Closure approximation.
Current calculations
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1)1) Improvement of overlap between Improvement of overlap between RPA intermediate virtual states.RPA intermediate virtual states.
Current calculations I
136Xe
136Cs
136Ba
i fmm f ia BCS BCS
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1)1) Improvement of overlap between Improvement of overlap between RPA intermediate virtual states.RPA intermediate virtual states.
where
RPA phonon operators on initial (i) and final (f) nuclei
, , , ,
, , , ,
, , , ,
, , , ,
i f i f
i f
i f i f
i f
m m m m i f i f i fm m
m m m m i f i f i fm m
a X Y u v
b X Y u v
NEW
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1)1) Improvement of overlap between Improvement of overlap between RPA intermediate virtual states.RPA intermediate virtual states.
1 1
i fi f f im mm m mm O OO
F. Šimkovic, DBD06-ILIAS/N6 Collaboration meeting Valencia 2006
i fmm f iO m m
Unitarity test
1 † ?O O
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2) Introduction of a realistic residual interaction 2) Introduction of a realistic residual interaction giving rise to spin-isospin transitionsgiving rise to spin-isospin transitions
Two-body matrix element of a realistic interaction V (CD Bonn, Vlow k ,…):
Introducing JT coupling:
Gamow-Teller transitions
Current calculations II
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2) Introduction of a realistic residual interaction 2) Introduction of a realistic residual interaction giving rise to spin-isospin transitionsgiving rise to spin-isospin transitions
Change of basis: from original spherical harmonic oscillator w.f. to deformed HF w.f.:
Ready to be introduced in the RPA equations:
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3) Closure approximation3) Closure approximation
136Xe
136Cs
136Ba
Current calculations III
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3) Closure approximation3) Closure approximation
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3) Closure approximation3) Closure approximation
BCS overlap for parent and daughter nuclei with different deformation:
with
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3) Closure approximation3) Closure approximation
EM = GT closure
2v
Comparison 1+RPA – Closure to get energy denominator:
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• Theoretical 22 decay nuclear matrix elements are essential information to study 02 decays, which give new information on character.
• Our calculations through deformed RPA intermediate virtual states show:
- a reduction effect due to deformation differences between parent and daughter nuclei.
- a good agreement with single and double beta experimental data.
Conclusions
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• Current work includes:
- Improvement of RPA overlaps.
- Use of realistic spin-isospin residual interactions.
- Closure approximation.
• Get more accurate results on 22 and go to 02
Conclusions
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Conclusions
Atomic nucleus
Detector of NEMO3
02 experiment
3 m 10-14 m
The best laboratory to measure neutrino properties is not necessarily very big!
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Double beta decay nuclear matrix elements in deformed nuclei
O. Moreno, R. Álvarez-Rodríguez,P. Sarriguren, E. Moya de Guerra
F. Šimkovic, A. Faessler
H. Müther
Past, present and future calculations within Tübingen-Madrid collaboration
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APPENDIX
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Deformed Hartree-Fock with Skyrme forces
Single particle states (axially symmetric even-even nuclei)
Expansion into eigenfunctions of deformed h.o. (R,)
with
Pairing correlations in BCS approximation
and
Residual interactions consistent with the HF mean field
ph, pp
A simplified scheme
pnQRPA phonon operator for GT excitations
QRPA equations XK, Y
K
Transition amplitudes in the intrinsic frame
Average over nuclear volume
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Xe isotopes in 2 processes
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GT + GT +
GT –GT –
Gamow-Teller Gamow-Teller strength strength
distributionsdistributions
J = 0, 1(no 0+ 0+)
Tz = 1T = 0,1
HF + BCS(G)HF + BCS(G)+ QRPA+ QRPA
Results single Xe isotopes