Study of nuclear matrix elements of two-neutrino double-beta decay - PowerPoint PPT Presentation

Study of nuclear matrix elements of two-neutrino double-beta decay by (p,n) and (n,p) reactions (p,n) and (n,p) reactions Oct 12 2009 Oct 12, 2009 K Y k K. Yako Department of Physics, University of Tokyo

Collaborators: K. Miki , H. Sakai, K. Miki, S. Noji, K. Y., Department of Physics, University of Tokyo K. Hatanaka, M. Kato, H. Matsubara, H. Okamura, A. Tamii, RCNP, Osaka University T. Uesaka, T. Kawabata, S. Sakaguchi, Y. Sasamoto, Y. Shimizu CNS, University of Tokyo T. Wakasa, Y. Tameshige, M. Dozono, E. Ihara, Y. Maeda, Department of Physics, Kyushu University M. Sasano , K. Sekiguchi, K. Suda, H. Kuboki, RIKEN K. Muto, Department of Physics, Tokyo Institute of Technology D Frekers D. Frekers, Department of Physics Münster University Department of Physics, Münster University M.B. Greenfield, Division of Natural Sciences International Christian University Division of Natural Sciences, International Christian University T. H. Okabe, Haian Zheng, IIS, University of Tokyo

Two-neutrino double beta decay 2 νββ decay − → + + + ν (A,Z+1) daughter ( A , Z ) ( A , Z 2 ) 2 e 2 （ A,Z ） e • second order weak process parent • rarest process confirmed so far intermediate • if thoroughly understood, • if thoroughly understood (A Z+2) (A,Z+2) it helps analysis of 0 νββ decay rate. Half lives … not understood well Suhonen et al., PR300(1998)123 Half-life and matrix element ： Nucleus Exp T 1/2 (y) Calc T 1/2 (y) 48 Ca ~ 4.3 x 10 19 (1.3 – 6.0) x 10 19 ( ) − 2 1 ν = ν ν 2 2 2 T G M 76 Ge ~ 1.4 x 10 21 ( (0.8 – 1.4) x 10 21 ) 1 / 2 DGT 82 Se ~ 0.9 x 10 20 (0.1 – 1.1) x 10 20 f O m m O i ∑ − − ν = GT GT 2 M 96 Zr ~ 2.1 x 10 19 (3.0 – 11) x 10 19 − + DGT E ( M M ) / 2 m m i f f 100 M 100 Mo ~ 8.0 x 10 18 8 0 10 18 (1.7 – 32) x 10 18 (1 7 32) 10 18 ∑ ± = σ GT operator: O j t ± GT 116 Cd ~ 3.3 x 10 19 (5.1 – 10) x 10 19 j ± = 2 GT strength: B ( GT ) j O i 128 Te ~ 2.5 x 10 24 (0.6 – 37) x 10 24 ± GT 130 Te ~ 0.9 x 10 21 (0.3 – 2.7) x 10 21 150 Nd ~ 7.0 x 10 18 (6.7 – 27) x 10 18

Model adjustments Effective interaction is adjusted so that the model reproduces… • M 2v M Exp QRPA (Rodin) Single β - & β + rates • 76 Ge 76 Se 76 Ge 76 Se cy n Vacan Further constrants… • Occupation numbers p Neutron 0g9/2 of “valence” nucleons: 0f5/2 (d,p), (p,d), 1p ( α , 3 He), ( 3 He, α ) Kay, Schiffer et al., 2009 extra ground-state correlation is necessary. • Distribution of GT(1 + ) transition strengths: → charge exchange reactions

B(GT) in low-lying states GT strengths: (p,n) type (p, ) yp G Grewe et al., PRC76(2007)054307 t l PRC76(2007)054307 ( 3 He,t) (n,p) type 48 Sc (d, 2 He) 48 Ca = 4276 keV = × 19 T 4 10 y 48 Ti 1 / 2 Low lying states Low lying states … high resolution measurements 48 Ca( 3 He,t) @ 140A MeV (RCNP) ( , ) @ ( ) 48 Ti(d, 2 He) @ 90A MeV (KVI)

“Contribution” of low-lying states Grewe et al., PRC76(2007)054307 ν “upperlimit” matrix element: 2 M + f f O O m m m m O O i i ∑ ∑ − − 2 ν = GT GT GT GT M − + E ( M M ) / 2 m m i f + + − B B ( ( GT GT ) ) B B ( ( GT GT ) ) ∑ 2 ν = M + − + E ( M M ) / 2 m m i f No sign info & additive sum → upper limit Decay measurement : Balysh et al., PRL77(1996)5186 +2.4 (stat) ± 1 4(sys)) x 10 19 y (4 3 (4.3 (stat) ± 1.4(sys)) x 10 19 y - 1.1 ν 2 NEMO3 (Vala et al., NPB188(2009)62) M + +0.5 (4.4 (4.4 ± 0.4) x 10 ± 0.4) x 10 19 y y - 0.4 0 4 M 2v → 0.045 MeV -1

Same as Horoi et al. Current understanding by shell model PRC75(2007)034303 Shell model calculation Shell model … reasonable. … reasonable. (full fp) (full fp) • GXPF1A Exp • Q F = 0 6 Q F 0.6 ν 2 M M “ “upperlimit” li it” + decay Enough data? Enough data? … not necessarily.

Aim • If your strategy is to check or constrain the theoretical GTGR calculations, you need the full snapshots of the B(GT) ? ? distribution. distribution • B(GT +/- ) distributions were studied up to the studied up to the continuum, in the (p,n) intermediate nuclei, 48 Sc, 116 In. (n,p) • Measurement 48 Sc 48 Ca – E beam = 300 MeV E = 300 MeV – θ = 0 ° ~12 ° 48 Ca(p n) 48 Sc Ca(p,n) Sc 116 Cd(p n) 116 In Cd(p,n) In 48 Ti 48 Ti 48 Ti(n,p) 48 Sc 116 Sn(n,p) 116 In

(p,n) & (n,p) at 300 MeV Advatages • Simple reaction mechanism • 300 MeV: 1. Effective interaction favors Spin-flip 1 Eff ti i t ti f S i fli transitions over Non-Spin-flip ones ( ( ) ) t t στ t / / t τ ⇒ GT transitions are most clearly seen. 2. Distortion effects are smallest ( ). t 0 0 ⇒ analysis with DWIA is reliable. 3. Tensor interaction is smallest ( ). T t τ ⇒ Proportionality relation is reliable. P ti lit l ti i li bl cross section strength tensor FraneyLove FraneyLove … Multipole decomposition analysis works M lti l d iti l i k best.

(p,n) & (n,p) facilities at RCNP (p,n) facility Ring Cyclotron K = 400 AVF Cyclotron K = 120 NPOL (n,p) facility LAS

• 48 Ca target • 48 Ca target 48 Ca(p,n) measurement 17 mg/cm 2 , 98% 17 mg/cm 2 , 98% • energy resolution • energy resolution 410 keV 410 keV • angular range • angular range angular range angular range 0 – 40 deg 0 – 40 deg NPOL3 NPOL3 NPOL3 1 x 1 m 2 1 x 1 m 2 1 x 1 m 2 n n 5 cm t plastic 5 cm t plastic 5 cm t plastic 5 cm plastic 5 cm plastic 5 cm plastic scintillators scintillators scintillators Δ t: 230 ps Δ t: 230 ps Δ t: 230 ps Δ t: 230 ps Δ t: 230 ps Δ t: 230 ps

(n,p) measurement (n,p) 実験施設 K.Y. et al., NIMA592(2008)88 （ n,p ） facility • 2x10 6 neutrons/s b by 7 Li(p,n) 7 Li( ) • 0-12deg …covered by 3 angular settings of LAS

48 Ti target Alford et al., NPA514(1990)49 48 Ti(n,p) at TRIUMF (1990, Alford et al.) • metal 48 Ti: thin … low statistics – Data at 3 angles Oxygen … not ideal for MD analysis not ideal for MD analysis • 48 TiO 2 : contribution of oxygen 48 Ti at E x > 6 MeV x 6 MeV 1. metallothermic reduction （ IIS UT, Okabe Gr. ） TiO 2 + 2Ca = Ti + 2CaO 48 TiO 2 13g → 48 Ti 5g (70%) purity: 98.7% purity: 98.7% 2 ． solidification by pressure 3 x 300 mg/cm 2 2 x 3 cm 2 3 x 300 mg/cm , 2 x 3 cm （ c.f. Alford et al.: 130mg/cm 2 ）

48 Ti(n,p) spectra • angular range 0 -12 deg 0 12 deg • energy resolution 1 2 M V 1.2 MeV • statistical accuracy 1--3% / 2MeV ・ 1deg • systematic uncertainty • systematic uncertainty 4%

48 Ti(n,p) angular dist. Multipole decomposition analysis E x = 15 MeV MDA ∑ ∑ σ θ ≈ σ θ exp calc ( , E ) a ( , E ) π π cm x cm x J J ph ph ; ; J J π DWIA J π + − − − + + − Δ = = L 0 , 1 , 2 , 3 [ J 1 , ( 0 , 1 , 2 ), ( 2 , 3 ), 4 ] DWIA inputs (DW81) DWIA inputs (DW81) • NN interaction: t-matrix by Franey & Love @325 MeV • optical model parameters: • optical model parameters: Global optical potential (phenomenological, Cooper et al.) • one-body transition density: b d t iti d it pure 1p-1h configurations Particle: Particle: 1f 2p 1g 2d 3s or 1h11/2 1f, 2p, 1g, 2d, 3s, or 1h11/2 Hole: 1p, 1d, 2s, or 1f radial wave functions radial wave functions … W.S. / H.O. W S / H O

Examples of angular distribution The DWIA description of GT transition is good. The description of Δ L=2 is reasonable. (f7/2,f7/2) The Δ L>3 component does not contribute much at 0 °

Reliability of σ ( θ ) in the continuum • Transitions with “stretched” configurations g … studied experimentally. DW81 (shallow binding) gives excellent description excellent description. • Others (0p 1/2 ,1s 1/2 ) (0p 1/2 ,1s 1/2 ) -1 … DW81 (shallow binding) CRDW (continuum Ichimura) CRDW (continuum, Ichimura) • 16 O(p,p’) 16 O (T=1, 0 - ; 12.8 MeV) at 295 MeV

Decomposed angular distributions [ 48 Ti(n,p)] Miki section 1.0 MeV 9.0 17.0 cross s MeV) b / sr / M erential 11.0 19.0 3.0 MeV (mb ble diffe Doub 0 5 10 0 5 10 0 5 10 0 5 10 0 0 5 10 5 10 Scattering angle (deg) Δ L=0 Δ L=0 Δ L=1 Δ L=1 Δ L=2 Δ L=2 Δ L=3 Δ L=3

Decomposed spectra Sasano/Miki

Proportionality relation σ d σ ω = o ˆ F ( q , ) B ( GT ) ( 0 ) Δ = Ω GT L 0 d kinematical GT unit cross section correction by DWIA y σ ˆ = 4.69 ± 0.35 mb/sr GT Sasano, PRC79(2009)024602 σ Is a good quantity? ˆ GT …depends on transition density. σ ˆ A-dependence of GT (p,n) @ 300 MeV

Proportionality test by shell model Sasano (A.U.) 48 Ca(p,n) 48 Sc 48 Ti(n,p) 48 Sc Exercise by using: • 48 Ca-- 48 Ti system y s section • Shell model calc. (n ≤ 4) • Standard DWIA calc. unit cross Deviations are small 0.01 1 0.01 1 for large B(GT) for large B(GT) u B(GT - ) B(GT + ) for both sides. exact exact exact exact .) ion (A.U. averaged averaged σ Average ( ) ˆ fferent GT could work. ouble diff ross sect σ ˆ works in this case. GT Do cr E x (MeV) E x (MeV)