„the uncertainty in the calculated nuclear matrix elements for neutrinoless double beta decay will...

„The uncertainty in the calculated nuclear matrix elements for neutrinoless double beta decay will constitute the principle

obstacle to answering some basic questions about neutrinos.“

Bahcall et al. Phys. Rev. D70 (2004) 033012

Theoretical Status of the Double Beta Decay

Amand Faessler, TuebingenTAUP2009, Wednesday, July first 2009

Oνββ-Decay (forbidden in Standard Model)

only for massive Majorana Neutrinos ν = νc

P

P

n n

Left

Left

ν Phase Space106 x 2νββ

TAUP2009, Wednesday, July first 2009

Neutrinoless Double Beta-

Decay Probability



QRPA Tuebingen 2008

QRPA and RQRPA (Tuebingen) with errors from Basis Size, exp. 2-Neutrino Decay, axial Coupling Constant gA = 1.25 and 1.00

and Short Range Correlations ( UCOM + Jastrow)


QRPA Tuebingen 2008

Blue triangles: Shell model of Strassburg and Madrid group only 4 to 5 single nucleon levels

Green Squares IBM2 of Barea and Iachello 2009


IBM2 Barea, Iachello 2009QRPA Tuebingen 2008SM Courier et al.

Rodin Saleh Kovalenko Faessler

Petr Vogel

Gutsche

SimkovicTAUP2009, Wednesday, July first 2009


Tuebingen Jyväskylä

Shell Model basis: 1f5/2, 2p3/2, 2p1/2, 1g9/2

SM+Spin-Orbit: 1f5/2, 2p3/2, 2p1/2, 1g9/2, 1f7/2, 1g7/2

1f5/2, 2p3/2, 2p1/2, 1g9/2, 1f7/2, 1g7/2, 1d5/2, 1d3/2, 2s1/2

Neutron-Neutron -> Proton-Proton relative

Angular Momentum for the Pair : Neutron x Neutron Proton x Proton



IBM Angular Momentum for the Pair : Neutron x Neutron Proton x Proton

0+

2+

Can one distiguish experimentally betweenQuasi-Particle Random Phase

(QRPA) and the Shell Model (SM)?


QRPAGT /2 ~ SMGT

QRPA Fermi/5 ~ SMFermihttp://Arxiv.org/abs/0906.1759 Rodin and Faessler: One can measure the Fermi contribution.

http://arxiv.org/abs/0906.1759


Can one distiguish experimentally betweenQuasi-Particle Random Phase

(QRPA) and the Shell Model (SM) ?

Due to TZ = 2 only the isotensor part of the „Coulomb interaction“ can contribute.

Since the strong Interaction commutes with Isospin, replace „Coulomb“ VC by the total Hamiltonian Htotal.


Can one distiguish experimentally between QRPA and SM ? Use Closure!

0+ + DIAS 0+


0+ Isobaric(i) Analog State

Can one distiguish experimentally between QRPA and SM ?

0+ + DIAS 0+


0+ Isobaric Analog State

Can one distiguish experimentally between QRPA and SM ?

(p,n); (3He,3H)(n,p); (d,2p); (3H, 3He)

Overconstraining the 2by adjusting gpp und gA

to -, EC and 2 for 116Cd and 100Mo (Bari+Tuebingen)

-

EC

1+

0+

116Cd 100Mo

0+


1+1+

Solid points: Overconstrained results large and small basis.Open circle QRPA 3 basis sets and gA = 1.00.

Only theoretical 1errors.


Renormalized QRPA 0 Half Lives calculated in TUE with the Bonn CD force and Jastrow

correlations for quenched gA = 1.00; errors from 2 experiments

for <m> = 50 meV 76Ge 76Se T(1/2) [years] = (1.10+-0.13)* 1027

82Se 82Kr T(1/2) [years] = (3.50+-0.42)* 1026

100Mo 100Ru T(1/2) [years] = (3.33+-0.45)* 1026

128Te 128Xe T(1/2) [years] = (7.35+-1.00)* 1027

150Nd 150Sm T(1/2) [years] = (3.55+-0.50)* 1025


But 150Nd + 150Sm is deformed!

Kay, Schiffer et al. Phys. Rev. C79 (2009) 021301

Proton removal reactions: v2

76Ge(d,3He)75Ga; 76Se(d,3He)

Proton additon reactions: u2

76Ge(3He,d)77As; 76Se(3He,d)

f7/2

p3/2

p1/2

f5/2

g9/2

28

40

5076

32Ge44

p = 0.10

7634Se42

p= 0.16 Neutron vacancy u2

Proton occupancy v2

Double Beta Decay System 76Ge 76Se.


Ge – Seexperiment

Se – Geexperiment

Fn

Fp


Adjutment of the Neutron Levels to reproduce the Occupation of Schiffer et al. from Simkovic, Faessler and Vogel : Phys. Rev. C79(2009) 015502 and also Suhonen and Civitarese: Phys. Lett. B668 (2008) 277

50

40


Omega

1/2

3/2

5/2

7/29/2

g 9/2

p 1/2

f 5/2

1/2

3/2

5/21/2

1/2

3/2p3/2

Deformation 2

Single neutron energies for N = 42

jN = 28

Deformation affects the occupation Probabilities of neutrons mainly.

Parity < 0; deformed mixed: p1/2, p3/2 ,f5/2> 0: g9/2

exp exp

2 = 0.12 = 0.16

2 = 0.232 = 0.26


Summary: Neutrino Mass from Exp. Klapdor et al. Mod. Phys. Lett.

A21,1547(2006) ; 76Ge T(1/2; 0) = (2.23 +0.44 -0.31) x 1025 years; 6

Theory with R-QRPA and gA = 1.25 (Tuebingen)<m()> = 0.22 [eV] (exp+-0.02;theor+-0.01) Bonn CD, Consistent Brückner Correlations <m()> = 0.24 [eV] (exp+-0.02; theor+-0.01) Argonne, Consistent Brückner Correlations Shell Model 4 to 5 levels (Strassburg + Madrid): <m()> ~ 0.45 [eV] Jastrow CorrelationsTHE END


„the uncertainty in the calculated nuclear matrix elements for neutrinoless double beta decay will...

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