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

Aug 28, 2023 •41 likes •411 views

D. Frekers Charge-exchange reactions GT-transitions, bb -decay and b n Flux @ 1 AU [cm -1 s -1 MeV -1 )] for lines [cm -1 s -1 ] 10 12 pp 10 10 things beyond 13 N 10 8 15 O b n 10 6 17F 8B 10 4 7 Be pep 10 2 hep 0.1 0.2 0.5 1 2 5

  1. D. Frekers Charge-exchange reactions GT-transitions, bb -decay and b n Flux @ 1 AU [cm -1 s -1 MeV -1 )] for lines [cm -1 s -1 ] 10 12 pp 10 10 things beyond 13 N 10 8 15 O b n 10 6 17F 8B 10 4 7 Be pep 10 2 hep 0.1 0.2 0.5 1 2 5 10 20 neutrino energy [MeV]

  2. Outline  Cha Charge gex-reac eactions tions ( 3 He,t He,t) ) & & (d, (d, 2 He) He)  highlights & features of 2nbb nuclear matrix elements (NME) 76 Ge, 82 Se, 96 Zr, 100 Mo, 136 Xe fragmentation – smallest/largest NME  the the 0nbb decay decay nuc nuclear lear ma matr trix ix elements elements 1 st forbidden NME‘s and 2 - states n  so solar lar SNU SNU rates tes and and ( 3 He,t) He,t) reac eaction tion 71 Ga( 3 He,t), 82 Se( 3 He,t)  the the A=96 A=96 sy system stem the 96 Zr ( b- )  96 Nb Q-value and a direct test of 0nbb NME

  3. b - b - decay never 0 + EC (odd-odd) 0 + (Z+1,N-1) (even-even) b - (Z,N) b - b - neutron-rich 0 + (even-even) (Z+2,N-2) 2 2nb - b - decay:    NME ( ) ph-spc -  19 21 allowed T 10 y 5-body 12 2 2 2 2 3   0nb - b - decay:        2 m ( ( ) ) NME NME U m ph-spc ph-spc n e ei i   24 any degree any degree i 1 3-body 3-body T 10 y 12

  4. recall: neutrino mass problem 2 3   2   2 NME U m ei i  i 1 -  -  i i   U V e e 2 extra Majorana-Phases diag( 1 , 2 , 1)  -   i   c c c s s e V V V  12 13 13 12 13  e 1 e 2 e 3   -  -      - - i - i   V V V V c s c s s e c c s s s e c s     i 1 2 3 23 12 12 13 23 12 23 12 13 23 13 23     -  -    - i - - i   V V V s s c c s e c s c s s e c c      1 2 3 12 23 13 23 13 12 23 23 12 13 13 23       0.6 0.1 6 12 known quantities:       0.7 0.2 4 23   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

  5. neutrino-mass-scenarios: 1) degenerate:  m 0.2 eV n e m n the best of all cases m 1 m 2 m 3 2 2 3 m -  - -  - 2) normal hierarchy:   2   2 ( i )   2 ( i ) 1 m m e 2 1 ( 0.5) e 1 n sol  e m sol m 3 m n = ZERO!! for:  3 m    -    1 m 2 9 ( ) 1 m 1 13 2 1  2 m sol 2 2 e -  -   2   2 ( i ) 3) inverted hierarchy: m m 3 2 1 n atm e if inverted hierarchy could be established m n m 2 m 1 (LHC, SN- n , precision-oscillation) THEN:   m m n atm m 3 e or neutrino is a Dirac-particle

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

  7. !! 4 2 C G g ( ) 2 2 2 F A Q cos( ) M f( ) C ( ) DGT ( ) 7 2 8 2 2 ( 2 ) G M (Q,Z) DGT 10 3 -  -2 exp MeV Q 11 Z 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

  8. (f) (i) 0 1 1 0 g .s . k k m m k k g .s . k k ( 2 ) M DGT (f) 1 Q (0 ) E(1 ) E m g .s . m 0 2 + - M GT M GT m m E m m to remember: 1. 2 sequential & „allowed“ b - -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) )

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

  10. !! 2 2 g 2 0 0 4 ( 0 ) ( 0 ) V G (Q,Z) g M M m A DGT DF ( ) g e A mass of theory Q Z 5 4 10    Majorana- n ! !! 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

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

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

  13. 2 - 1  1  1  d σ /d Ω (GT,q~0) ~j 0 (qR) 2 ~(1- q 2 R 2 ) 1  1  1  0 

  14. 76 Ge N-Z=10 Resolution is the key !!!

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

  16. ~ 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 ( b 2 ~ - 0.2) ( b 2 ~ 0.1)

  17. 82 Se 3 5 . 3 0 h 5 – 0+ b - b - Q 3 0 9 2 . 6 Q 2 9 9 2 b - b - b - Q C 9 7 . 6 E N-Z=14 0+ Resolution is the key !!! possibly useful for solar neutrino detection

  18. 82 Se 10-4 yield/(5 keV msr) 2.0 8 0.076 (1  ) 0.421 (1  ) 1.233 (1  ) 1.484 (1  ) 2.087 (1  ) 2.136 (1  ) 2.498 (1  ) 82 Se( 3 He,t) 82 Br IAS IAS E = 420 MeV 6  E = 38 keV 1.5 4 1.766 (1  ,2 - ) 0.0° < q lab < 0.5° 0.362 (3  ) 0.543 (2 - ) 0.764 (2 - ) 1.0° < q lab < 1.5° 2 2.0° < q lab < 2.5° 1.0 0 10 9.5 GTR 0.5 ~65 J  =1  states 0 0 1 2 3 4 5 6 8 10 12 14 16 E x [MeV] 3 isolated GT transition below 2 MeV- fragmentation recedes to GT resonance

  19. 96 Zr N-Z=16 Remember: B(GT) tot = 3(N-Z) ~ 50! B(F) = (N-Z)

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

  21. 100 Mo N-Z=16 useful as SN neutrino detector (sensitive to n temperature in SN)

  22. 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 b - log ft known n  n 2 2 M (g.s.) 0 88 . M (total) DGT DGT No need for GT giant resonance

  23. 64 Zn( ee, e b + ) 76 Ge( b - b - ) 82 Se( b - b - ) 96 Zr( b - b - ) reduced fragmentation of GT strength 100 Mo( b - b - )

  24. 136 Xe N-Z=28 question: why so stable !!!

  25. 136 Xe

  26. What‘s the size of the NME? 2 21 T 2 2 10 . yr -  1 2 ( 2 ) -1 M . 0 019 MeV DGT all signs positive — > 2 B GT 10 B GT m m 3 GT !!!! B 10 m

  27. 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

  28. 136 Xe b-b- 136 Ba expmt: 2nbb NME is exceptionally small question: how does the ME scale in the case of 0nbb decay? could it be that: 2nbb ME is suppressed AND 0nbb ME is enhanced ???

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

  30. 40.0 Decomposition of MGT 30.0 20.0 136 Xe 10.0 0.0 1+ 2+3+ 4+ 5+6+7+8+ 1- 2- 3- 4- 5- 6- 7- 0- 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 0nbb ME!! Expmt: 136 Xe exhibits largest 2 - strength J. Suhonen, Phys. Lett B607, 87 (2005) 0nbb ME enhanced ?!?!

  31. (Poves) Poves

  33. Flux @ 1 AU [cm -1 s -1 MeV -1 )] for lines [cm -1 s -1 ] 10 12 pp 10 10 solar neutrino 13 N 10 8 15 O 10 6 rates via ( 3 He,t) 17F 8B 10 4 7 Be pep hep 10 2 0.1 0.2 0.5 1 2 5 10 20 neutrino energy [MeV] 71 Ga( n  ,e - ) SNUs from 71 Ga( 3 He,t) 71 Ge charge-ex reaction

  34. 71 Ga( n  ,e - ) SNUs from ( 3 He, t ) charge-exchange reaction 10 2 x yield / (5 keV msr) 35 10 3 x yield / (5 keV msr) 32 IAS 30 24 0.175, 5/2 - 0.500, 3/2 - 0.808, 1/2 - 1.096, 3/2 - 1.378, 5/2 - 1.744, 3/2 - 2.352, 5/2 - g.s., 1/2 - 16 25 8 3.570 (1/2 -, 3/2 - ) 20 2.041 (5/2 - ) 2.435 (5/2 - ) 2.806 (5/2 - ) 0.708, 3/2 - 1.299, 3/2 - 1.598, 5/2 - 0 9.0 8.5 3.077 15 10 71 Ga( 3 He, t ) 71 Ge E = 420 MeV 5 D E = 45 keV Q c.m. = 0.3° 0 0 1 2 3 4 5 8 12 16 20 24 28 E x [MeV] 71 Ga( n  ,e - ) SNU 120 R    110 122.4 3.4(stat) 1.1(sys) SNUs from SSM 100 stat. err. mostly due to CNO n ‘s 90 0 1 2 3 4 5 6 7 8 Ex[MeV] prev‘ly:132 ± 18 DF et al, PRC91,2015

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