D. Frekers Charge-exchange reactions GT-transitions, -decay and - PowerPoint PPT Presentation

D. Frekers Charge-exchange reactions GT-transitions, ββ -decay and β ν Flux @ 1 AU [cm -1 s -1 MeV -1 )] for lines [cm -1 s -1 ] 1012 pp 1010 things beyond 13N 108 15O β ν 106 17F 8B 104 7Be pep hep 102 0.1 0.2 0.5 1 2 5 10 20 neutrino energy [MeV]

Outline  Chargex-reactions ( 3 He,t) & (d, 2 He)  highlights & features of 2νββ nuclear matrix elements (NME) 76 Ge, 82 Se, 96 Zr, 100 Mo, 136 Xe fragmentation – smallest/largest NME  the 0νββ decay nuclear matrix elements 1 st forbidden NME‘s and 2 − states ν  solar SNU rates and ( 3 He,t) reaction 71 Ga( 3 He,t), 82 Se( 3 He,t) 30 min  the A=96 system the 96 Zr ( β− )  96 Nb Q-value and a direct test of 0νββ NME

β − β − decay never 0 + EC (odd-odd) 0 + (Z+1,N-1) (even-even) β − (Z,N) β − β − neutron-rich 0 + (even-even) (Z+2,N-2) 2 2νβ − β − decay: Γ = × ( ) NME ph-spc − ≈ 19 21 allowed T 10 y 5-body 12 2 2 2 2 3 × ∑ 0νβ − β − decay: Γ = Γ = × × × 2 m ( ( ) ) NME NME U m ph-spc ph-spc ν e ei i = > 24 any degree any degree i 1 3-body 3-body T 10 y 12

recall: neutrino mass problem 2 3 ⋅ ∑ 2 Γ ∝ 2 NME U m ei i = i 1 − Φ − Φ i i = ⋅ U V e e 2 extra Majorana-Phases diag( 1 , 2 , 1)  − δ  i   c c c s s e V V V  12 13 13 12 13  e 1 e 2 e 3   − δ − δ   = = − − i − i   V V V V c s c s s e c c s s s e c s α µ µ µ i 1 2 3 23 12 12 13 23 12 23 12 13 23 13 23     − δ − δ   − i − − i   V V V s s c c s e c s c s s e c c τ τ τ   1 2 3 12 23 13 23 13 12 23 23 12 13 13 23 Θ = ± → ≈ π 0.6 0.1 6 12 known quantities: Θ = ± → ≈ π 0.7 0.2 4 23 Θ = 0.11 13 − ∆ 2 = 2 − 2 ≈ × 3 2 ≈ 2 m m m 2.6 10 eV (0.05eV) atm 3 2 − ∆ 2 = 2 − 2 ≈ × 5 2 ≈ 2 m m m 7.9 10 eV (0.009eV) sol 2 1

neutrino-mass-scenarios: 1) degenerate: ≈ m 0.2 eV ν e m ν the best of all cases m 1 m 2 m 3 2 2 3 m − Φ −Φ − δ −Φ 2) normal hierarchy: ∝ ∆ 2 × + 2 ( i ) + < 2 ( i ) 1 m m e 2 1 ( 0.5) e 1 ν sol ∆ e m sol m 3 m ν for: = ZERO!! π 3 m Θ ° Φ − Φ = = 1 m 2 ฀ 9 ( ) 1 m 1 13 2 1 ∆ 2 m sol 2 2 e − Φ −Φ ∝ ∆ 2 × + 2 ( i ) 3) inverted hierarchy: m m 3 2 1 ν atm e if inverted hierarchy could be established m 2 m ν m 1 (LHC, SN- ν , precision-oscillation) THEN: ≈ ∆ m m ν atm m 3 e or neutrino is a Dirac-particle

N ucl. M atrix E lements 2νβ − β − decay q-transfer like in ordinary β -decay (q ~ 0.01 fm -1 ~ 2 MeV/c) i.e. only allowed transitions possible

!! 4 ć ö 2 C G g ç ÷ n n ( ) 2 2 2 F A ç ÷ G = Q Q F cos( ) M f( ) ç ÷ - - - C ( ) DGT b b ( ) 7 ç ÷ č ř p 2 8 2 n n 2 ( 2 ) = G (Q,Z) M DGT 10 3 ≈ − -2 exp MeV Q Z 11 2 ∝ ⋅ extracted from half-life favorable: 1. high Q-value 2. large Z unfavorable (but cannot be changed): 1. large neutron excess (Pauli-blocking) p p n n

- + + - (f) (i) å å s t s t 0 1 1 0 g .s . k k m m k k g .s . k k n ( 2 ) å = M DGT + (f) 1 + - Q (0 ) E(1 ) E m bb g .s . m 0 2 ( ) ( ) + - M GT M GT m m å = E m m to remember: 1. 2 sequential & „allowed“ β − -decays of „Gamow-Teller“ type 2. „1, 2, 3, ... forbidden“ decays negligible 3. Fermi–transitions do no contribute (because of different isospin-multiplets) Can be determined via charge- exchange reactions in the (n,p) and (p,n) direction ( e.g. (d, 2 He) or ( 3 He,t) )

N ucl. M atrix E lements 0νβ − β − decay neutrino is a virtual particle q~0.5fm -1 (~ 100 MeV/c) D q × D x (due to Heisenberg ) ~ 1 degree of forbiddeness is lifted

!! 2 2 ć ö g 2 ç ÷ n n n n 0 0 4 ( 0 ) ( 0 ) V G = - ç G (Q,Z) g M ÷ M m - - n A ç ÷ DGT DF b b ç ÷ ( ) č ř g e A mass of theory Q Z 5 4 10 ∝ ⋅ ≈ Majorana- ν ! !! largely independent of (A,Z) (except near magic nuclei) to remember: 1. „higher-fold forbidden“ transitions possible 2. Fermi–transitions important 3. „Pauli-blocking“ largely lifted 4. large Q-value, high Z important NOT (easily) accessible via charge-exchange reactions

Charge-exchange reactions ∆ E/E ~ 5 x10 -5 ~ 25 keV at 420 MeV ( 3 He)

Q : what is the connection between „weak στ operator“ and the hadronic reaction A : dominance of the V στ effective interaction at medium energies - (n,p), q = 0 !!

2 − 1 + 1 + 1 + d σ /d Ω (GT,q~0) ~j 0 (qR) 2 ~(1- q 2 R 2 ) 1 + 1 + 1 + 0 +

76 Ge N-Z=10 Resolution is the key !!!

almost 70 !! resolved single states up to 5 MeV identified as GT 1+ transitions !!!

~ 70 !! single states up to 5 MeV !!! ???? anti-correlation ???? is the anti-correlation a property of deformation ?? 76 Ge 76 Se moderately oblate oblate/ prolate ( β 2 ~ − 0.2) ( β 2 ~ 0.1)

82 Se 3 5 . 3 0 h 0+ 5 – ฀฀ ฀฀ Q 3 0 9 2 . 6 Q 2 9 9 2 ฀฀ ฀฀ ฀฀ Q C 9 7 . 6 E N-Z=14 0+ Resolution is the key !!! possibly useful for solar neutrino detection

82 Se 10-4 yield/(5 keV msr) 2.0 8 0.076 (1 + ) 0.421 (1 + ) 1.233 (1 + ) 1.484 (1 + ) 82Se(3He,t)82Br 2.087 (1 + ) 2.136 (1 + ) 2.498 (1 + ) IAS IAS E = 420 MeV 6 ∆ E = 38 keV 1.5 4 1.766 (1 + ,2 − ) 0.0° < ฀ lab < 0.5° 0.362 (3 + ) 0.543 (2 − ) 0.764 (2 − ) 1.0° < θ lab < 1.5° 2 2.0° < θ lab < 2.5° 1.0 0 10 9.5 GTR 0.5 ~65 J π =1 + states 0 0 1 2 3 4 5 6 8 10 12 14 16 Ex [MeV] 3 isolated GT transition below 2 MeV- fragmentation recedes to GT resonance

96 Zr N-Z=16 Remember: B(GT) tot = 3(N-Z) ~ 50! B(F) = (N-Z)

(d, 2 He) ( 3 He,t) =0.16 E x (MeV) B(GT-) = 0.16 B(GT+) = 0.3 Fascination: With only 1 state: νββ = ± ⋅ . 19 calc (2 ) (2.1 0.4) 10 years T 1/2 νββ = ± ⋅ exp. 19 (2 (2.3 0.2) 10 years (NEMO3-result) T 1/2

100 Mo N-Z=16 useful as SN neutrino detector (sensitive to ν temperature in SN)

HERE: almost the entire 100 Mo low-E GT strength is concentrated in the g.s. entire“low-energy“ GT strength is concentrated in a SINGLE STATE and with β − log ft known ν ν ⋅ 2 2 ฀ M (g.s.) 0 88 . M (total) DGT DGT No need for GT giant resonance

64 Zn( εε, ε β + ) 76 Ge( β − β − ) 82 Se( β − β − ) 96 Zr( β − β − ) reduced fragmentation of GT strength 100 Mo( β − β − )

136 Xe N-Z=28 question: why so stable !!!

136 Xe

What‘s the size of the NME? n = 2 21 × . T 2 2 10 yr − + 1 2 n ( ) 2 -1 ฀ M . 0 019 MeV DGT all signs positive —> ( ) ( ) + - - 2 » × B GT 10 B GT m m ( ) + - 3 » GT !!!! B 10 m

A. Poves (simultaneous to our publication): NO CANCELLATION !! there is no B(GT + ) strength, except for lowest 1 + state 3x10 -3 Recall: 136 Xe is almost doubly magic!! Shell model provides conclusive explanation for the deemed „pathologically“ long half-life of 136 Xe. Expt‘l test: 136 Ba(d, 2 He) 136 Cs

β−β− 136 Ba 136 Xe 2νββ NME is exceptionally small expmt: how does the ME scale in the case of 0νββ decay? question: could it be that: 2νββ ME is suppressed AND 0νββ ME is enhanced ???

Experiments towards the 0νββ NMEs Here: 2 - states and occupation vacancy numbers via chargex reactions

40.0 Decomposition of MGT 30.0 20.0 136 Xe 10.0 0.0 1+ 2+3+ 4+ 5+6+7+ 8+ 0- 1- 2- 3- 4- 5- 6- 7- 35 ! 2 - 100 Mo gpp = 0.89 gpp = 0.96 -10.0 gpp = 1.00 gpp = 1.05 Theory: The 2 − strength makes up relative 2 − strength to ~ 5 MeV ~ 20-30% of the 0νββ ME!! Expmt: 136 Xe exhibits largest 2 − strength J. Suhonen, Phys. Lett B607, 87 (2005) 0νββ ME enhanced ?!?!

(Poves) Poves

Flux @ 1 AU [cm -1 s -1 MeV -1 )] for lines [cm -1 s -1 ] 1012 pp 1010 solar neutrino 13N 108 15O 106 rates via ( 3 He,t) 17F 8B 104 7Be pep 102 hep 0.1 0.2 0.5 1 2 5 10 20 neutrino energy [MeV] 71 Ga( ν  ,e − ) SNUs from 71 Ga( 3 He,t) 71 Ge charge-ex reaction