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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, T 1/2 ~ 10 19 – 10 21 s. Observed in 48 Ca 76 Ge 82 Se 96 Zr 100 Mo 116 Cd 128 Te 130 Te 150 Nd. Strong dependence on nuclear structure, in particular nuclear deformation. AXAX AYAY AZAZ 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 s trong dependence on nuclear structure comparison with 2 2 nuclear matrix elements needed. AXAX AYAY AZAZ
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Mean field + pairing + proton-neutron correlations Theoretical formalism def. HF (Skyrme) BCS ( exp G) pnQRPA . ( ph + pp )
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Nuclear wavefunction: adiabatic + harmonic collective motion Dynamics: Classical variational principle Theoretical formalism
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HF & RPA equations: Theoretical formalism(PairingBCS) (Skyrme interactions) +
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Theoretical formalism 136 Xe 136 Cs 136 Ba
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Parent Daughter exp Q exp 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)Improvement of overlap between RPA intermediate virtual states. 2)Introduction of a realistic residual interaction giving rise to spin-isospin transitions (to be treated within RPA). 3)Closure approximation. Current calculations
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1)Improvement of overlap between RPA intermediate virtual states. Current calculations I 136 Xe 136 Cs 136 Ba
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1)Improvement of overlap between RPA intermediate virtual states. where RPA phonon operators on initial (i) and final (f) nuclei NEW
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1)Improvement of overlap between RPA intermediate virtual states. F. Šimkovic, DBD06-ILIAS/N6 Collaboration meeting Valencia 2006 Unitarity test
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2) Introduction of a realistic residual interaction giving rise to spin-isospin transitions Two-body matrix element of a realistic interaction V (CD Bonn, V low k,…): Introducing JT coupling: Gamow-Teller transitions Current calculations II
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2) Introduction of a realistic residual interaction giving 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 approximation 136 Xe 136 Cs 136 Ba Current calculations III
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3) Closure approximation
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BCS overlap for parent and daughter nuclei with different deformation: with
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3) Closure approximation E M = GT closure 2v Comparison 1 + RPA – Closure to get energy denominator:
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Theoretical 2 2 decay nuclear matrix elements are essential information to study 0 2 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 2 2 and go to 0 2 Conclusions
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Atomic nucleus Detector of NEMO3 0 2 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 X K , 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 – Gamow-Teller strength distributions J = 0, 1 (no 0+ 0+) T z = 1 T = 0,1 HF + BCS(G) + QRPA Results single Xe isotopes
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