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

• D. Frekers

Charge-exchange reactions GT-transitions, ββ-decay and things beyond β β ν ν

• Chargex-reactions (3He,t) & (d,2He)
• highlights & features of 2νββ nuclear

matrix elements (NME)

76Ge, 82Se, 96Zr, 100Mo,136Xe

fragmentation – smallest/largest NME

• the 0νββ decay nuclear matrix elements

1st forbidden NME‘s and 2− states

• solar SNU rates and (3He,t) reaction

71Ga(3He,t), 82Se(3He,t)

• the A=96 system

the 96Zr (β−)  96Nb Q-value and a direct test of 0νββ NME

Outline

ν

30 min

12

19 21

10 T y

−

≈

β−β− decay

β−β− β−

EC

(Z,N) (Z+1,N-1) (Z+2,N-2)

(even-even) (even-even) (odd-odd)

neutron-rich 0+ 0+ never 0+

2νβ−β− decay: 0νβ−β− decay:

allowed 5-body

( )

2

ph-spc

NME

Γ = ×

any degree 3-body

( )

2

2

ph-spc

e

m

NME

ν

Γ = × ×

2 3 2 any degree 1 3-body

( )

2

ph-spc

ei i i

U m

NME

=

Γ = × × ∑

12

24

10 T y >

1 2

i i

diag( , , 1)

− Φ − Φ

= ⋅ U V e e

12 13 13 12 13 1 2 3 1 2 3 23 12 12 13 23 12 23 12 13 23 13 23 1 2 3 12 23 13 23 13 12 23 23 12 13 13 23 i e e e i i i i i

c c c s s e V V V V V V V c s c s s e c c s s s e c s V V V s s c c s e c s c s s e c c

δ δ δ α µ µ µ δ δ τ τ τ − − − − −

          = = − − −         − − −    

2 3 2 2 1 ei i i

NME U m

=

Γ ∝ ⋅ ∑

2 2 2 3 2 2 3 2 2 2 2 5 2 2 2 1

2.6 10 eV (0.05eV) 7.9 10 eV (0.009eV)

atm sol

m m m m m m

− −

∆ = − ≈ × ≈ ∆ = − ≈ × ≈

12 23 13

0.6 0.1 6 0.7 0.2 4 0.11 π π Θ = ± → ≈ Θ = ± → ≈ Θ =

recall: neutrino mass problem

2 extra Majorana-Phases

known quantities:

1) degenerate:

0.2

e

m eV

ν

≈

mν m1 m2 m3 2) normal hierarchy: mν m1 m2 m3

2 1 1

2 2 2 ( ) 2 ( ) 2 1

3 ( 0.5)

e

i i sol sol

m m m e e m

− Φ −Φ − −Φ

∝ ∆ × + + < ∆

δ ν

3) inverted hierarchy: mν m1 m2 m3

neutrino-mass-scenarios:

2 1

2 2 2 ( ) 2

3

e

i atm

m m e−

Φ −Φ

∝ ∆ × +

ν = ZERO!!

for: 1 13 2 1

3 9 ( ) 1 2

sol

m m π Θ ° Φ − Φ = = ∆ ฀

if inverted hierarchy could be established (LHC, SN-ν, precision-oscillation) THEN:

• r neutrino is a Dirac-particle

e

atm

m m

ν

≈ ∆

the best of all cases

Nucl.MatrixElements 2νβ−β− decay

q-transfer like in ordinary β-decay (q ~ 0.01 fm-1 ~ 2 MeV/c) i.e. only allowed transitions possible

Q

4 2 2 2 2 DGT 7 2 2 DGT

2 8 (Q,Z)

( ) F A C ( ) ( ) ( ) 2

G g C cos( ) M f( ) G M

• n

n

• b b

n n

ć ö ç ÷ ç ÷ G = Q ç ÷ ç ÷ p č ř = F

∝ ⋅

11 2

Q Z

• 2

MeV

−

≈

3

10

favorable:

• 1. high Q-value
• 2. large Z

unfavorable (but cannot be changed):

• 1. large neutron excess

(Pauli-blocking) exp p n

!!

p n

extracted from half-life

( ) ( )

2 DGT 1 2

1 1 Q (0 ) E(1 ) E E

(f) (i) g .s . k k m m k k g .s . k k ( ) (f) m g .s . m +

• m

m m m

M M GT M GT

• +

+

• n

+ bb

s t s t = +

• =

å å å å

to remember:

• 1. 2 sequential & „allowed“ β−-decays
• f „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,2He) or (3He,t) )

Nucl.MatrixElements 0νβ−β− decay

neutrino is a virtual particle q~0.5fm-1 (~ 100 MeV/c) (due to Heisenberg ) degree of forbiddeness is lifted

1 ~ q x D × D

e

( ) ( ) V A ( ) A

g G g M M m g

2 2 2 4 DF DGT

(Q,Z)

• n

n n n n b b

ć ö ç ÷ G =

• ç

÷ ç ÷ ç ÷ č ř

5 4

Q Z ∝ ⋅

!! 10 ≈

mass of 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

theory

NOT (easily) accessible via charge-exchange reactions

!!

Charge-exchange reactions

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

• (n,p),

!! q = 0

Q: what is the connection between „weak στ operator“ and the hadronic reaction A: dominance of the Vστ effective interaction at medium energies

2− 1+ 1+ 1+ 1+ 1+ 1+ 0+

dσ/dΩ (GT,q~0) ~j0(qR)2 ~(1- q2R2)

76Ge

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 ????

moderately

• blate/ prolate

(β2 ~ 0.1)

is the anti-correlation a property of deformation ??

76Ge

• blate

(β2 ~ −0.2)

76Se

82Se

N-Z=14

Resolution is the key !!! possibly useful for solar neutrino detection

Q 2 9 9 2 0+ Q 6 . 2 9 3 5–

h 3 . 5 3

Q C

E

6 . 7 9 0+

฀฀ ฀฀

฀฀ ฀฀ ฀฀

0.5 1.0 1.5 2.0 1 2 3 4 6 8 10 12 14 16 10-4 yield/(5 keV msr) Ex [MeV] 82Se(3He,t)82Br E = 420 MeV ∆E = 38 keV 0.0° < ฀lab < 0.5° 1.0° < θlab < 1.5° 2.0° < θlab < 2.5° IAS GTR 5

0.362 (3+) 0.421 (1+) 0.076 (1+) 0.543 (2−) 0.764 (2−) 1.233 (1+) 1.484 (1+) 2.087 (1+) 2.136 (1+) 2.498 (1+) 1.766 (1+,2−) ~65 Jπ=1+ states

9.5 10 2 4 6 8 IAS

3 isolated GT transition below 2 MeV- fragmentation recedes to GT resonance

82Se

96Zr

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

(d,2He)

B(GT+) = 0.3

Ex (MeV)

Fascination: With only 1 state:

. 19 1/2 exp. 19 1/2

(2 ) (2.1 0.4) 10 years (2 (2.3 0.2) 10 years (NEMO3-result)

calc

T T νββ νββ = ± ⋅ = ± ⋅

B(GT-) = 0.16

(3He,t)

=0.16

100Mo

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

HERE: almost the entire low-E GT strength is concentrated in the g.s.

100Mo

entire“low-energy“ GT strength is concentrated in a SINGLE STATE and with β− logft known

No need for GT giant resonance (g.s.) . (total)

DGT DGT

M M

ν ν

⋅

2 2

0 88 ฀

reduced fragmentation

• f GT strength

64Zn(εε, εβ+) 76Ge(β−β−) 82Se(β−β−) 96Zr(β−β−) 100Mo(β−β−)

136Xe

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

136Xe

What‘s the size of the NME?

2 21 1 2

T 2 2 10 yr .

n =

×

2

• 1

DGT

0 019 MeV

( )

M . ฀

n

− +

( ) ( )

2 m m

B 10 B GT GT

+

• »

×

all signs positive —>

( )

3 m

B 10 GT !!!!

+

• »

• A. Poves (simultaneous to our publication):

NO CANCELLATION !! there is no B(GT+) strength, except for lowest 1+ state

Shell model provides conclusive explanation for the deemed „pathologically“ long half-life of 136Xe. Expt‘l test: 136Ba(d,2He)136Cs 3x10-3

Recall:

136Xe is almost

doubly magic!!

136Xe β−β− 136Ba

expmt: 2νββ NME is exceptionally small question: how does the ME scale in the case of 0νββ decay? 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

gpp = 0.89 gpp = 0.96 gpp = 1.00 gpp = 1.05

1+ 2+3+ 4+ 5+6+7+ 8+ 1- 2- 3- 4- 5- 6- 7- 0- 40.0 30.0 20.0 10.0 0.0

• 10.0

Decomposition of MGT 2-

relative 2− strength to ~ 5 MeV Theory: The 2− strength makes up ~ 20-30% of the 0νββ ME!! Expmt:

136Xe exhibits largest 2− strength

0νββ ME enhanced?!?!

136Xe 100Mo

• J. Suhonen, Phys. Lett B607, 87 (2005)

35 !

Poves

(Poves)

solar neutrino rates via (3He,t)

71Ga(ν,e−) SNUs from 71Ga(3He,t)71Ge charge-ex reaction

5 10 15 20 25 30 35 1 2 3 4 5 102 x yield / (5 keV msr)

71Ga(3He,t)71Ge

E = 420 MeV ฀E = 45 keV

8 12 16 20 24 28 Ex[MeV]

8 16 24 32 9.0 IAS 103 x yield / (5 keV msr) 8.5

฀ c.m. = 0.3°

g.s., 1/2− 0.175, 5/2− 0.500, 3/2− 0.808, 1/2− 1.096, 3/2− 0.708, 3/2− 1.299, 3/2− 1.378, 5/2− 1.744, 3/2− 1.598, 5/2− 2.041 (5/2−) 2.806 (5/2−) 2.435 (5/2−) 2.352, 5/2−

90 100 110 120 1 2 3 4 5 6 7 8 Ex[MeV] SNU

71Ga(ν,e−) 122.4 3.4(stat) 1.1(sys) R = ± ±

฀c.m.[deg.]

71Ga(ν,e−) SNUs from (3He,t) charge-exchange reaction

prev‘ly:132 ± 18 DF et al, PRC91,2015

• stat. err. mostly due to CNO ν‘s

SNUs from SSM

solar neutrino rates via (3He,t)

82Se(ν,e−) SNUs from 82Se(3He,t)82Br charge-ex reaction

Advantages:

• low threshold
• enhanced sensitivity

to pp-neutrinos

• short life-time against

β-decay (35h)

• pp-ν‘s in „real time“
• γ-emission, easy to detect

82Se(3He,t) spectrum

B(GT) SNU

Total rate: 258 SNU Population of 1st 1+ state: 97% pp ν fraction: 76%

Future perspectives of chargex-reactions

11

• ββ-decay and nuclear matrix elements
• Resolution is key issue (RCNP gives the lead!)
• need 20 - 30 keV for (3He,t) & (d,2He)
• Need to explore proportionality between

chargex x-section and transitions (e.g. 2− states) in weak interaction (resol‘n is key)

• ν-physics and chargex-reactions
• Hadronic chargex and weak-interaction x-sections

are fortuitously connected -- exploit this!!

• solar neutrinos, SN-neutrinos, element synthesis
• Need to address quenching issue urgently!!
• Chargex in inverse kinematics plays a pivotal role

(BUT need resolution)

• EOS and chargex-reaction
• IAS and GT resonance data needed and useful

BUT:theories need to converge on their relevance

L ∆ ≠

71Ga(ν,e−)

122.4 3.4 1.1 SNU R = ± ±

82Se(ν,e−)

258.4 SNU R =

8

10 ml HF acid 48%

+ +

Zr silicate 100-500mg dissolved Zr

Isobar separation method (U of Calgary)

re-dissolved in acid ion-exchange chemistry purified Mo>10 ng with 4 M HCl

Zr

(∆96Mo/95Mo)=0.01%

ZrCl4 Zr & Mo

250°C & 3200 kPa separate Zr from Mo

measurable limit T1/2 < 15 × 1019 y

β

~

plasma mass spectrometer