D. Frekers, Univ. Münster, TRIUMF-Vancouver ββ-decay matrix elements & charge-exchange reactions (some surprises in nuclear physics??

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1 D. Frekers, Univ. Münster, TRIUMF-Vancouver ββ-decay matrix elements & charge-exchange reactions (some surprises in nuclear physics??) KVI: (d, 2 He) reactions GT + RCNP: (3He,t) reactions GT - (TRIUMF: EC rates with ion-traps)

2 OUTLINE 1) some basics about ν s and nuclear ββ matrix elements 2) understanding the nuclear physics of 2vββ -decay charge-exchange reactions (d, 2 He) and ( 3 He,t) 48 Ca 64 Zn 76 Ge 82 Se 96 Zr 100 Mo 116 Cd 128/130 Te 136 Xe 150 Nd CANDLES COBRA GERDA NEMO NEMO MOON/NEMO COBRA CUORE EXO, KamLAND-ZEN SNO+ 3) possibilities towards the nuclear physics of 0vββ-decay. 4) wish list and issues for theorists to deal with

3 β β decay (even-even) 0 + (Z,N) neutron-rich 2νβ β decay: 0νβ β decay: EC β β never body (Z+1,N-1) ph-spc Γ= ( ) 3-body (odd-odd) allowed β NME 0 + (even-even) (Z+2,N-2) 3 2 Γ= 2 ( ph-spc ) mueimi NME 2 2 any degree i= 1 eν 2

4 Quick reminder of neutrino mass problem i Φ i Φ U = V e e diag( 1, 2, 1) 2 iδ Ve1 Ve2 Ve3 c12c13 c13s12 s13e iδ iδ Vαi = Vμ1 Vμ2 Vμ3 = c23s12 c12s13s23e c12c23 s12s13s23e c13s23 V i i 1 V 2 V δ δ τ τ τ3 s12s23 c13c23s13e c12s23 c23s12s13e c13c23 known quantities: 3 i= 1 2 ei Γ NME U m Θ = 0.6 ± 0.1 π 6 12 Θ = 0.7 ± 0.2 π 4 23 Θ < atm ev (0.05eV) Δ m = m m sol ev (0.009eV) Δ m = m m i 2 2 extra Majorana phases

5 Neutrino mass scenarios: 1) degenerate: m ν m 1 m 2 m 3 m ν e 0.2eV best of all cases 2 2) normal hierarchy: 2 1 2( i Φ2 Φ1) 2( i δ Φ1) mν Δ m ( 0.5) e sol + e + < e Δm m m sol ν 3 = zero!! for: m 1 m 2 3m π 3m Θ 1 13 = 0 ( Φ2 Φ 1) = = 1 Δm 2 sol 2 3) inverted hierarchy: m ν m 1 m 2 m 3 e 2 2 2( i 2 1) Δ atm 3 + m m e Φ Φ ν if inverted hierarchy were determined (by LHC or spectral distortion of SN-neutrinos) THEN: mν Δmatm e or the neutrino is a Dirac particle 2

6 NME 2νβ β decay q-transfer like ordinary β-decay (q ~ 0.01 fm -1 ~ 2 MeV/c) only allowed decays possible

7 2 2 C GF g ν A ( 2ν ) 2 Γ = cos( DGT Q ( ) 7 C ) M ( ) f( ) β β Θ F 8π 2 = G 2ν (Q,Z)!! M 4 ( 2ν ) DGT 2 Q 11 Z 2 favorable: 1. High Q-value 2. High Z exp 10 3 MeV 1 N Z -2 Unfavorable: 1. high neutron excess (because of Pauli-Blocking) p n

8 A layman s sketch of thepauli-blocking remember: GT requires Δħω=0!! Extreme case: (p,n) completely open (n,p) completely blocked Soft surface case: (p,n) still largely open (n,p) still largely blocked yet probabilities could be finite but tiny

9 M ( 2ν ) DGT = (f) + + (i) 0g.s. σkτk 1m 1m σkτ 0 k k k g.s. 1 (f) + m 2 Q ββ(0 g.s. ) + E(1 m) E0 = m m ( + ) ( -) m M GT M GT E m To note: 1. two sequential & allowed β -decays of Gamov-Teller type 2. first- oder higher order forbidden decays negligible 3. Fermi transitions don t contribute (because different isospin-multiplet) accessible thru charge- exchange reactions in (n,p) and (p,n) direction ( e.g. (d, 2 He) or ( 3 He,t) )

10 NME 0νβ β decay neutrino enters as virtual particle, q~0.5fm -1 (~ 100 MeV/c) degree of forbiddeness weakened

11 !! 0ν 0ν 4 (Q,Z) ( β β ) A 2 ( ) g 0ν V ( 0ν) DGT DF g A Γ = G g M M m 2 ν e 2 Q 5 Z 4 10!! To note: 1. first- or higher order forbidden transitions important theory indepnt. of (A,Z) (except for magic nuclei) Mass of Majorana-ν! 2. Fermi transitions important 3. Pauli-blocking largely lifted 4. high Q-value, high Z important NOT accessible thru charge-exchange reactions

12 Neutrinoless Double Beta Decay Nuclear Matrix Elements V.Rodin, A. Faessler, F. Šimkovic, P. Vogel, PRC 68 (2003) ;

13 Back to 2νββ decay and charge-exchange reactions

14 - (n,p), 300

15 - (n,p),

16 The message after many years of expmlt studies of 2νββ!! -NME 1. In all cases the low-energy part of the GT-excitation makes up most of the NME. 2. The GT giant resonance has little to no effect on the NME (Pauli-blocked from the 2 nd leg). 3. A large difference of the nuclear shape between mother and grand-daughter leads to a suppression of the NME (case: 76 Ge). 4. There are some very special and simple cases ( 96 Zr, 100 Mo) 5. What is the effect of a 2n-pair in 128,130 Te? 6. What is wrong with 136 Xe why is it so stable?

17 76 Ge the most important ββ-decaying nucleus

18 0.54

19 an anticorrelation of strength (very similar to 48 Ca) some B(GT) in the bckgnd!!!!!!! An effect of the difference of deformation?? 76Se: oblate (β 2 ~ 0.2) 76Ge: moderately oblate/ prolate (β 2 ~ 0.1)

20 about 60!! individual levels up to 5 MeV!!!

21 triplet of states: 0.044, 0.082, 0.12 MeV Correlate states within the expmtl resolution

22 0.14 Correlated states make up 55% of 2νββ-ME DGT =0.09 MeV-1 M DGT Adding correlation with undifferentiated bckgnd makes up ~100% of 2νββ-ME DGT = MeV-1 T 1/2 = ( ) x yr M DGT

23 taken from F. Simkovic et al. (cf also P. Sarriguren et al., PRC67,44313 (2003)) Intrinsic deformation seems to affect the 2νββ-ME, however, it is the difference of deformation between mother and daughter and not their absolute values which counts. Exp lly the deformation seems to manifest itself in a state-by-state mismatch, rather than an overall reduction of B(GT) s.

24 96 Zr the most neutron-rich Zr-isotope N-Z=16

25 (d, 2 He) ( 3 He,t) Ex (MeV) B(GT + ) = 0.3 B(GT - ) = 0.15 T Fascination: With this 1 level only: (2 νββ ) = (2.4 ± 0.3) 10 years calc. 19 1/ 2 T (2 νββ = (2.2 ± 0.4) 10 years (NEMO3-result) exp. 19 1/ 2

26 100 Mo Important for ββ-decay solar neutrino detector (Q=-168 kev) SN-neutrino detector SN-neutrino temperature

27 entire low-energy GT - strength is concentrated in ONE singlestateonly, theg.s. GOOD!!! for SN-ν temp ure meas nt B(GT) =0.32 logft (EC) = 4.54 In perfect agreement with Ejiri et al. (1998): B(GT) = 0.33

28 64 Zn(εε, εβ+) 76 Ge(β β ) 82 Se(β β ) 96 Zr(β β ) 100 Mo(β β ) reduced spreading of GT strength

29 What about 128 Te 130 Te 136 Xe

30

31 128Te 130Te (slightly more fragmented)

32 128Te 130Te (slightly more fragmented) also predicted by

33 136Xe

34 How big is the matrix element? ν T yr ( ) M 2 ν 3 DGT 5 10 scenario-1 all positive sign > m ( ) 3 GT + ( ) m GT B 10 B unlikely scenario-2 sign(clst-1) = - sign (clst-2) likely

35 Chargex reactions are a powerful tool to determine the 2νββ NME (d, 2 He) (t, 3 He) GT + leg & ( 3 He,t) GT- leg high resolution is essential. The difference between the intrinsic deformation of mother and daughter nucleus seems to cause state-by-state mismatch of B(GT) s How big is the effect on the 0νββ NME?? In all cases the low energy part of the GT distribution seems to be most relevant for the 2ν decay even Single-State-Dominance for 96 Zr und 100 Mo Wouldthisbetrueforthe0νββ decay as well? Radioactive beam facilites and ion traps can provide nice tools for getting access to 0ν-ββ decay matrix elements What is the importance of Nordheim states?? they are strongly excited in CEX and μ-x

36 My personal wish list and unresolved issues: 1. Need a more modern reaction theory and appropriate reaction code 2. Need updated NN t-matrix fits (we use Love and Franey 81) and have them implemented into a reaction theory code 3. Need theories, which can predict 0νββ matrix elements and which can be tied to experimental data/observables along the way (presently, g.s. β-decay and EC-decay rates are utterly wrong!!) 4. Need to understand more quantitavely the physics, which cause certain matrix element to have a different sign eff g A 5. Need to address more agressively the GT-quenching issue ( ) (experimentally and theoretically)

37 eff g A The -problem or the quenching of the Ikeda sumrule ( ) ( + ) = 3( ) S β S β N Z can this be attacked?? Recall: ( ) 1 ( eff ) 4 eff A A A T ~ g g 0.7g 1/2

38 Reasons for GT quenching nuclear structure but then quenching should depend on the underlying nuclear structure non-nucleonic degrees of freedom quenching should not strongly depend on the underlying nuclear structure (but rather on nucl. density)

39

40

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42 76Ge

43 96Zr

44 100Mo

45 g A - quenching as a fctn. of nucl. density (long & short range effect due to 2B-currents) un-quenching of g A un-quenching of g A as a function of momentum transfer

46 To prove the theory, need: 1) a heavy target consisting of neutrons only 2) a diluted nuclear density!! maybepossiblewith: 1) 132 Sn or even better 132+x Sn 2) check nuclear density by exciting pygmy resonances 3) perform (p,n) type reaction to excite GT giant resonance. 3(N-Z) = 96+3x. What is the quenching???

47 In the next round get the 0νββ NME s & who knows? may be Nature is indeed kind