M 0 for 48 Ca from charge-exchange reactions Vadim Rodin DBD11, - PowerPoint PPT Presentation

M 0 ν for 48 Ca from charge-exchange reactions Vadim Rodin DBD11, Osaka, 16 / 11 / 2011

Introduction Nuclear 0 νββ -decay (¯ ν = ν ) strong in-medium modification of the basic process dd → uue − e − (¯ ν e ¯ ν e ) e - Light neutrino n p _ exchange mechanism ν A,Z A,Z+2 ν p n continuum e - virtual excitation 2 - of states of all multipolarities 1 - in (A,Z + 1) nucleus 1 + 0 + GT amplitudes to 1 + states 0 + (A,Z+1) — from charge-exchange reactions 0 + (A,Z) (H. Ejiri, D. Frekers, H. Sakai, R. Zegers, et al.) (A,Z+2)

World status of M 0 ν , light neutrino mass mechanism (R)QRPA (Tü) | QRPA (Jy) 8 SM IBM-2 PHFB GCM+PNAMP 6 0 ν | | M | 4 | | 2 0 48 Ca 82 Se 96 Zr 100 Mo 110 Pd 124 Sn 130 Te 150 Nd 160 Gd 76 Ge 94 Zr 98 Mo 104 Ru 116 Cd 128 Te 136 Xe 154 Sm QRPA: (Tü) F. Šimkovic, A. Faessler, V.R., P. Vogel and J. Engel, PRC 77 (2008); 150 Nd, 160 Gd with deformation: D. Fang, A. Faessler, V.R., F. Šimkovic, PRC 82 (2010); PRC 83 (2011) (Jy) J. Suhonen, O. Civitarese, NPA 847 (2010) SM E. Caurier, J. Menendez, F. Nowacki, A. Poves, PRL 100 (2008) & NPA 818 (2009) IBM-2 J. Barea and F. Iachello, PRC 79 (2009); PHFB P.K. Rath et al. , PRC 82 (2010); GCM + PNAMP T. R. Rodriguez and G. Martinez-Pinedo, PRL 105 (2010)

Measuring M 0 ν F Can one measure nuclear matrix elements of neutrinoless double beta decay? V.R., A. Faessler, PRC 80 , 041302(R) (2009) [arXiv:0906.1759 [nucl-th]] PPNP 66 , 441 (2011); arXiv:1012.5176 [nucl-th]

j D I AS i j T T � 2 i 0 0 � ^ T j I AS i j T T � 1 i 0 0 ^ V C � + ^ ^ T T + j 0 i i j T T i 0 0 + j 0 i f j T � 2 T � 2 i 0 0

Measuring M 0 ν F � ˆ b = 1 W 0 ν ˆ � T − , [ ˆ T − , ˆ � P ν ( r ab ) τ − V C ] a τ − F = e 2 ab ( 1 − τ ( 3 ) a )( 1 − τ ( 3 ) V C = e 2 C = e 2 b ) 1 b − τ a τ b Isospin lowering operator ˆ Coulomb interaction ˆ , isotensor Coulomb ˆ V ( 2 ) ( τ ( 3 ) a τ ( 3 ) T − = � � � a ; 3 ) a τ − 8 r ab 8 r ab a � b ab

Measuring M 0 ν F � ˆ b = 1 W 0 ν ˆ � T − , [ ˆ T − , ˆ � P ν ( r ab ) τ − V C ] a τ − F = e 2 ab ( 1 − τ ( 3 ) a )( 1 − τ ( 3 ) V C = e 2 C = e 2 b ) 1 b − τ a τ b Isospin lowering operator ˆ Coulomb interaction ˆ , isotensor Coulomb ˆ V ( 2 ) ( τ ( 3 ) a τ ( 3 ) T − = � � � a ; 3 ) a τ − 8 r ab 8 r ab a � b ab � ˆ T − , [ ˆ T − , ˆ e 2 M 0 ν F = � 0 + � | 0 + V C ] f | i � � ˆ T − � 2 | T 0 T 0 � ≈ � T 0 − 2 T 0 − 2 | V C � ˆ T − � 2 | T 0 T 0 � = � T 0 − 2 T 0 − 2 | ˆ V C | T 0 T 0 − 2 � × � T 0 T 0 − 2 |

Measuring M 0 ν F F = − 2 M 0 ν � f | ˆ s | ˆ ω s � 0 + T − | 0 + s �� 0 + T − | 0 + ¯ i � e 2 s ω s = E s − ( E 0 + i + E 0 + f ) / 2 ¯ � ˆ � ˆ � ˆ T − , [ ˆ T − , ˆ T − , [ ˆ T − , ˆ T − , ˆ � � � V C ] H tot ] H str = 0 used assuming = H tot = ˆ ˆ K + ˆ H str + ˆ V C F ≈ − 2 M 0 ν f | ˆ T − | IAS �� IAS | ˆ ω IAS � 0 + T − | 0 + e 2 ¯ i � � ˆ ≈ 1 T − � 2 | 0 + f | ˆ e 2 � 0 + V C | DIAS �� DIAS | i �

Measuring M 0 ν F Measure the ∆ T = 2 isospin-forbidden matrix f | ˆ element � 0 + T − | IAS � charge-exchange ( n , p )-type reaction � IAS | ˆ T + | 0 + f � ∼ 0 . 001 Challenge: � IAS | ˆ T − | 0 + i � M 0 ν M 0 ν F ( QRPA ) GT ≈ 3 ÷ 5 ≈ − 2 . 5 and M 0 ν M 0 ν F ( S M ) F

48 Ca → 48 Ti IAS of 48 Ca ( T = 4 , T z = 3 ) in 48 Sc 1. is located at E x = 6.678 MeV ( ¯ ω IAS ≈ 8.5 MeV) under threshold of particle emission 2. 100% γ -decay to 1 + state at E x = 2.517 MeV ( E γ = 4.160 MeV) 3. a single state — no fragmentation (too low density of T = 3 0 + states around the IAS) Example Reaction: 48 Ti(n,p) 48 Sc(IAS)

48 Ca → 48 Ti IAS ↓

48 Ca → 48 Ti

48 Ca → 48 Ti � IAS | ˆ = − e 2 M 0 ν T + | 0 f � 1 F ω IAS R · � IAS | ˆ 2 ¯ N − Z T − | 0 i � 2 � � � IAS | ˆ T + | 0 f � QRPA: M 0 ν ≈ 2 · 10 − 6 F = 0 . 6 ⇒ � � � � � IAS | ˆ T − | 0 i � � � � � d 2 σ pn d Ω dE ≈ 10 mb / (sr MeV), E p = 134 MeV (B.D.Anderson et al., PRC 31 (1985)) ⇒ d 2 σ np d Ω dE ≈ 20 nb / (sr MeV) E p → 0 . 5 E p ⇒ σ np → 4 σ np σ F ∝ E − 2 Unit cross section: ˆ p

Reaction analysis Basic requirements for a charge-exchange probe Measure cross section ≡ Know � IAS | ˆ T + | 0 + f � ???

Reaction analysis Any hadronic probe adds isospin to nuclear system (weak interaction probe would be ideal) to probe small admixture of | DIAS � to | 0 + f � ⇒ must be forbidden to connect in reaction main components of | IAS � and | 0 + f � ( ∆ T = 2 ) Only T = 1 2 probes (( n , p ), ( t , 3 He),. . . )

Reaction analysis f → IAS ) ∝ � IAS | ˆ σ np ( 0 + T + | 0 + f � ??? ˆ T − | 0 + i � = | T 0 T 0 � ; | IAS � = 2 T 0 | 0 + i � + α | T 0 − 1 T 0 − 1 � √ ( ˆ T − ) 2 | 0 + f � = | T 0 − 2 T 0 − 2 � + β | T 0 − 1 T 0 − 2 � + γ 4 T 0 ( 2 T 0 − 1 ) | 0 + i � √ = | DIAS �

Reaction analysis 48 Ca, 5 � ω s.p. space, QRPA σ np ( γ DIAS → IAS ) is 100 times larger than for the other mechanisms via admixtures of IVMR Assumptions: 2 , r 2 � � IVMR s | ˆ ˆ R − = � σ pn ( 0 + � R − | 0 + � i → IVMR s ) = σ 0 R 2 τ − a i � � � a a � and i → IVMR ) ≈ σ pn ( 0 + i → IAS ) σ pn ( 0 + 10

Conclusions • M 0 ν F can be related to ∆ T = 2 isospin admixture of the DIAS in the final g.s. and can be extracted from measured Fermi m.e. � IAS | ˆ T + | 0 f � • can help to discriminate between nuclear structure models (di ff erence in M 0 ν F as much as the factor of 5) • Choice of a target: well-isolated IAS of 48 Ca in 48 Sc (weak Coulomb mixing applies) Reaction: 48 Ti(n,p) 48 Sc(IAS) Estimates: σ np ≈ 20 nb / (sr MeV) and σ np ∝ � IAS | ˆ T + | 0 f �

Conclusions • Role of spread of IAS in heavy nuclei to be investigated Supported by: DFG TR27 “Neutrinos and beyond”

Backup

Backup

Spread of IAS Why no fragmentation of IAS of 48 Ca? Density of 0 + states around IAS back-shifted Fermi-gas (BSFG) model: ρ ( U , J , π ) = 1 2 F ( U , J ) ρ ( U ) √ 1 1 exp( 2 F ( U , J ) = 2 J + 1 � − J ( J + 1 ) aU ) � ρ ( U ) = 2 σ 2 exp ( U + t ) 5 / 4 , √ σ a 1 / 4 2 σ 2 12 2 U = at 2 − t , U = E − δ, the level density parameter a ; the spin cut-o ff parameter σ 2 = I rigid � 2 t ≈ 0 . 015 A 5 / 3 t ; the backshift δ ( > 0 even-even, ≈ 0 odd-A, < 0 odd-odd);

Spread of IAS 46 Sc a = 5 . 96 MeV − 1 , δ = − 2 . 37 MeV (W. Dilg et al. NPA 217 (1973)) E x = 6.8 MeV → ρ ( 0 + ) + ρ ( 0 − ) ≈ 59 MeV − 1 but at E x = 3 MeV → ρ ( 0 + ) + ρ ( 0 − ) ≈ 5 MeV − 1 (no J = 0 state is listed in ENSDF for 48 Sc for E x < 3 MeV). 46 Sc a = 5 . 74 MeV − 1 , δ = − 1 . 9 MeV (RIPL-2) E x = 6.8 MeV → ρ ( 0 + ) + ρ ( 0 − ) ≈ 33 MeV − 1 at E x = 3 MeV → ρ ( 0 + ) + ρ ( 0 − ) ≈ 3 MeV − 1

Spread of IAS 46 Sc a = 5 . 96 MeV − 1 , δ = − 2 . 37 MeV (W. Dilg et al. NPA 217 (1973)) E x = 6.8 MeV → ρ ( 0 + ) + ρ ( 0 − ) ≈ 59 MeV − 1 but at E x = 3 MeV → ρ ( 0 + ) + ρ ( 0 − ) ≈ 5 MeV − 1 (no J = 0 state is listed in ENSDF for 48 Sc for E x < 3 MeV). 46 Sc a = 5 . 74 MeV − 1 , δ = − 1 . 9 MeV (RIPL-2) E x = 6.8 MeV → ρ ( 0 + ) + ρ ( 0 − ) ≈ 33 MeV − 1 at E x = 3 MeV → ρ ( 0 + ) + ρ ( 0 − ) ≈ 3 MeV − 1 76 As IAS at E x = 8 . 24 MeV a = 10 . 81 MeV − 1 , δ = − 1 . 45 MeV (W. Dilg et al. NPA 217 (1973)) → ρ ( 0 + ) + ρ ( 0 − ) ≈ 7000 MeV − 1

Spread of IAS