nuclear structure , the double beta decay and the neutrino mass

Nuclear Structure, the Double Beta Decay and the Neutrino Mass

Amand Faessler University of Tuebingen

1. Occupation probabilities for 76Ge 76Se. F. Simkovic, A. Faessler, P. Vogel: Phys.Rev C 79

(2009) 015502; O. Moreno, E. Moya de Guerra, P. Sarriguren, A. Faessler: Phys. Rev. C81(2010) 041303

2. Which neutron pairs contribute to the Double Beta Decay ? A. Escuderos, A. Faessler, V. Rodin, F. Simkovic arXiv: 1001.3519 (2010)

Oνββ-Decay (forbidden in Standard Model)

P

P

n n

Left

Left

ν Phase Space

106 x 2νββ

Amand Faessler, Tuebingen

e1

e2

= c Majorana Neutrino

Neutrino must have a Mass

Neutrinoless Double Beta-

Decay Probability

Amand Faessler, Tuebingen

Amand Faessler, Tuebingen

1. From which Neutrons come the two Protons?

J. Schiffer et al. Phys. Rev. Lett. 100 (2008)112501Double Beta Decay: 76

32Ge44 7634Se42

f7/2

p3/2

p1/2

f5/2

g9/2

Fp

Fn

28

40

50

7632Ge44(d,p) or (,3He)

7634Se42(p,d) or (He,)

Neutron Holes below 50

Saxon-Woods + BCS

Saxon-Woods (Bertsch)+ BCS

Selfconsistent Hartree-Fock-Bogoliubov with Skyrme3 (Sk3) Moreno, Moya de Guerra, Sarriguren and Faessler

Phys. Rev. C81(2010) 041303• Neutron Two Body Spin-Orbit Force is to small : V. O.

Nesterenko , J. Kvasil, P. Vesely, W. Kleinig, P. G. Reinhard, V. Yu. Ponomarev: Spin-flip M1 giant resonaces as a challenge for the Skyrme forces: J. Phys. G37(2010)064034

• Skyrme3W0 = 120 200 [MeV fm5]

NeutronSk3 Sk3

Amand Faessler, Tuebingen

1g1g7/2

1g9/2

Amand Faessler, Tuebingen

Protons and Neutrons above the 28 Shell

7632Ge44 76

34Se42

2and Running Sum of Double Gamow-Teller Distributions for 76Ge 76Se

Amand Faessler, Tuebingen

From experimental Charge Exchange Reactions (Madey et al (p,n) and Frekers et al. (d,2He))

(p,n) (d,2He)

76Ge76Se

76As

1+

0+

0+

Amand Faessler, Tuebingen

0.0

New points in this work: The neutron occupation probabilities (Schiffer et al.)

are reproduced by Sk3. Sk3 reproduces 2. Old Sk3 by a factor 1/8 to small. Sk3 running sum = Gamow-Teller strength

distribution (R. Madey et al. and E. W. Grewe et al. ). Root mean square radii of 76Ge and 76Se with Sk3

76Ge Sk3: 4.09 (SK3: 4.12)theor 4.08 fm exp ; 76Se Sk3: 4.14 (Sk3: 4.17)theor 4.14 fmexp ;

The total binding energy for 76Ge with Sk3 Theor.: 662.0 MeVtheor Exp.: 661.6 MeVexp .

Amand Faessler, Tuebingen

2. Which Angular Momentum J Neutron Pairs contribute to the

Neutrinoless Double Beta decay?

• Quasi-Particle Random Phase Approach (QRPA; Tübingen).

• Shell Model (Poves et al. : Nucl. Phys. A818 (2009) 139).

• Angular Momentum Projected Hartee-Fock-Bogoliubov (Tübingen; P. K. Rath et al.).

• Interacting Boson Model (Barea and Iachello).Amand Faessler, Tuebingen

Amand Faessler, Tuebingen

a) QRPA all the Ring digrams:

Ground State: 0, 4, 8, 12 , … quasi- particles (seniority)

b) The Shell Model Ground state: 0, 4, 6, 8, ….

Problem for SM: Size of the Single Particle Basis.

Basis Size Effect for 82Se on the Neutrinoless Double Beta Decay.

Amand Faessler, Tuebingen

4levels (Shell Model): 1p3/2, 0f5/2, 1p3/2, 0g9/2

6levels: 0f7/2, 1p3/2, 0f5/2, 1p3/2, 0g9/2, 0g7/2

9levels:0f7/2, 1p3/2, 0f5/2, 1p3/2, 0g9/2, 0g7/2, 1d5/2, 2s1/2, 1d3/2

4levels: Ikeda Sum rule 50 %

Contribution of Higher Angular Momentum Pairs in Projected HFB.

Only even Angular Momentum Pairs with Positive Parity can contribute.

IBM: = 0+ and 2+ Pairs

HFB 0

Amand Faessler, Tuebingen

QRPA (TUE), Shell Model (Madrid-Strassburg), IBM2, PHFB

Amand Faessler, Tuebingen

Neutrino Mass from Experiment Klapdor et al. 76Ge Mod. Phys. Lett. A21,1547(2006) ; T(1/2; 0) = (2.23 +0.44 -0.31) x 1025 years; 6

Matrix Elements: QRPA Tuebingen

• <m()> = 0.24 [eV] (exp+-0.02; theor+-0.01) [eV]

Amand Faessler, Tuebingen

Summary1) Increased neutron two-body Spin-Orbit Force

Skyrme3 plus Deformation reproduces Schiffer occupation probabilities, 2, the running sum of 2, root mean square radii and total binding energies.

2) Different approaches give different contributions for the different angular momentum neutron pairs (QRPA ~ Shell model).

THE ENDAmand Faessler, Tuebingen

Ikeda Sumrule

Amand Faessler, Tuebingen

• Single nucleon basis (SM): p3/2, f5/2, p1/2, g9/2;

Fit to 2 gpp = 2.3; Only 50% 0f Ikeda sum rule;

No collective GTR; Main M1-strength: 7 MeV to low; • f7/2, p3/2, f5/2, p1/2, g9/2, g7/2; fit 2gpp = 0.9;

100% of Ikeda sum rule; GTR correct;

• f7/2 500 MeV, p3/2, f5/2, p1/2, g9/2, g7/2 500MeV

Fit 2 2.3; Sum to 600 MeV: 100% Ikeda SR; Sum to 10 MeV: 50% Ikeda SR; No collective GTR; Low energies as for four levels.

Different Seniority Contributions s for 82Se and 128Te in QRPA and the Shell Model

Amand Faessler, Tuebingen

M0   s=0     s= 4, (6), 8,… total ISR%82Se 4lev QRPA      6.7         -5.6           1.1 5082Se 4lev SM 7.8 -5.8 2.082Se 5lev SM 2.582Se 6lev   QRPA 10.7          -6.6            4.1 10082Se 9lev   QRPA 11.9           -7.6            4.3 100128Te 5lev QRPA 9.7 -8.3 1.4 60128Te 5lev SM 10.6 -8.4 2.2128Te 6lev SM 2.7128Te 7lev QRPA 13.7 -10.3 3.4 100 128Te 13lev QRPA 16.8 -13.0 3.8 100

Additive Contributions of 0, 4, 6, … Quasi-Particle States in the SM (Poves et al.).

Amand Faessler, Tuebingen

128Te

82SeNot in QRPA

Increasing Admixtures in the Ground State

Contributions to the neutrinoless matrix elements for different nuclei, basis sets and seniorities and

the exhaustion of the Ikeda Sum Rule.

Amand Faessler, Tuebingen