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

Introduction

Theoretical formalism

Results

Current work

Conclusions & outlook

Summary

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

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

Mean field+

pairing+

proton-neutroncorrelations

Theoretical formalism

def. HF (Skyrme)

BCS (expG)

pnQRPA . (ph+pp)

Nuclear wavefunction: adiabatic + harmonic collective motionNuclear wavefunction: adiabatic + harmonic collective motion

Dynamics: Classical variational principleDynamics: Classical variational principle

Theoretical formalism

HF & RPA equations:HF & RPA equations:

Theoretical formalism

(Pairing(PairingBCS)BCS)

(Skyrme (Skyrme interactions)interactions)

++

( )j j

j

Ee

Theoretical formalism

136Xe

136Cs

136Ba

ParentDaughter

expQexp

Qexp

Alvarez-Rodriguez et al. PRC 70 (2004) 064309

Results

HF (Sk3) + BCS

Alvarez-Rodriguez et al. PRC 70 (2004) 064309

Results

Alvarez-Rodriguez et al. PRC 70 (2004) 064309

Results

Alvarez-Rodriguez et al. PRC 70 (2004) 064309

Alvarez-Rodriguez et al. PRC 70 (2004) 064309

Results

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

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

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

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

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

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:

3) Closure approximation3) Closure approximation

136Xe

136Cs

136Ba

Current calculations III

3) Closure approximation3) Closure approximation

3) Closure approximation3) Closure approximation

BCS overlap for parent and daughter nuclei with different deformation:

with

3) Closure approximation3) Closure approximation

EM = GT closure

2v

Comparison 1+RPA – Closure to get energy denominator:

• 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

• 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

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!

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

APPENDIX

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

Xe isotopes in 2 processes

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