Weak decay of 5 Λ He and 12 Λ C : experimental results RIKEN H. Outa 10. Oct HYP2006(Mainz) for KEK-PS E462 / E508 collaborations Osaka Univ. a, KEK b, GSI c, Seoul Univ. d, Tohoku Univ. e, Univ.of Tokyo f, Tokyo Inst. Tech. g, KRISS h, RIKEN i S. Ajimura a, K.Aoki b, A.Banu c, H. C. Bhang d, T. Fukuda b,O. Hashimoto e, J. I. Hwang d, S. Kameoka e, B. H. Kang d, E. H. Kim d, J. H. Kim d, M. J. Kim d, T. Maruta f, Y. Miura e, Y. Miyake a, T. Nagae b, M. Nakamura f, S. N. Nakamura e,H. Noumi b, S. Okada g, Y. Okayasu e, H. Outa b, H. Park h,P. K. Saha b, Y. Sato b, M. Sekimoto b, T. Takahashi e,H. Tamura e, K. Tanida i, A. Toyoda b, K. Tsukada e,T. Watanabe e, H. J. Yim d Γ π _ Γ π _ (  → ｐ + π － ) Γ π 0 Γ π 0 (  → ｎ + π ０ ) Γ p Γ p (  +“ ｐ ”→ ｎ + ｐ ) Γ n Γ n (  +“ ｎ ”→ ｎ + ｎ ) Γ 2N (ΛNN →NNN) Mesonic q ～ 100MeV/c Non-Mesonic (NMWD) q ～ 400MeV/c 1/  HY =Γ tot ΓmΓm Γ nm Weak decay mode of  hypernucleus Study of the mechanism of baryon-baryon weak interaction 1

Contents of the present talk Γ(Λn→nn)/Γ(Λp→np) ratio n/p spectra from A=5,12 S. Okada et al. PLB 597 (2004) A= 5 B.H. Kang et al. PRL 96 (2006) A=12 M.J. Kim et al. PLB 641 (2006) 28 [ M. Kim, poster session ] Asymmetry parameter T. Maruta et al. nucl-ex/ [ T.Maruta, parallel session A2] Mesonic & non-mesonic decay widths [ S. Okada, poster session ] S. Kameoka et al. Nucl. Phys. A754 (2005) 173c-177c S. Okada et al. Nucl. Phys. A754 (2005) 178c-183c Two nucleon-induced NMWD (ΛNN→NNN) [H.Bhang, parallel session A2] Γ π _ Γ π _ (  → ｐ + π － ) Γ π 0 Γ π 0 (  → ｎ + π ０ ) Γ p Γ p (  +“ ｐ ”→ ｎ + ｐ ) Γ n Γ n (  +“ ｎ ”→ ｎ + ｎ ) Γ 2N (ΛNN →NNN) Mesonic q ～ 100MeV/c Non-Mesonic (NMWD) q ～ 400MeV/c 1/  HY =Γ tot ΓmΓm Γ nm Weak decay mode of  hypernucleus 2

 n /  p Theoretical N N N Λ Direct Quark mechanism Meson Exchange mechanism Λ N NN π,K,η,ρ,ω,K * 0.93±0.55 (Szymanski et al.) Exp. (for 5  He)  n /  p ratio : The most important observable used to study the isospin structure of the NMWD.  n /  p ratio puzzle Γ p Γ p (Λ+“ ｐ ”→ ｎ + ｐ ) Γ n Γ n (Λ+“ ｎ ”→ ｎ + ｎ )  n /  p ～ 0.1 Λ N NN W S π One Pion Exchange (OPE) Simple theoretical model Tensor-dominant  requires the final Nn pair to have isospin 0. 3

n n n p p p p p n n n p rescattering Final state interaction (FSI) effect Experimental difficulties in single nucleon measurement Difficulty in detecting neutrons.  There is no experiment to observe both of the protons and neutrons simultaneously with high statistics. Final state interaction (FSI) effect  not well established Distinguish between the FSI and ”  NN  nNN” process  NN→NNN (2N-induced process) Λ N N N W π N N (One of the theoretical model) 4

n p n p  n n p n p n p n p n Coincidence NMWD The present experiment KEK-PS E462/E508 Angular correlation 1) Angular correlation ( back-to-back, cos  <-0.8 ) Energy correlation 2) Energy correlation ( Q ～ E(N1)+E(N2) ～ 152MeV ) Angular correlation 1) Angular correlation ( back-to-back, cos  <-0.8 ) Energy correlation 2) Energy correlation ( Q ～ E(N1)+E(N2) ～ 152MeV ) NMWD : ΛN→NN * cosθ< － 0.8 * E(N1)+E(N2) cut Direct measurement of the  n /  p ratio Select ΛN→NN events w/o FSI effect & ΛNN→NNN. Select light hypernuclei to minimize FSI effect, 5  He and 12  C 5

π+π+ K+K+ Target: 6 Li, 12 C Excitation-energy spectra for 6  Li and 12  C 6.2×10 4 events 4.6×10 4 events decay counter 5  He 6  Li (g.s.)  5  He + p The ground state of 6  Li is above the threshold of 5  He + p. 5  He 6

Charged particle ： ・ TOF (T2→T3) ・ tracking （ PDC ） Neutral particle ： ・ TOF (target→NT) ・ T3 VETO p n π K Decay counter Setup (KEK-PS K6 & SKS) Decay arm N: 20cm×100cm×5cm T3: 10cm×100cm×2cm T2: 4cm×16cm×0.6cm Solid angle: 26% 9(T)+9(B)+8(S)% n p polarization axis 7

The g.s. peak is clearly seen in all spectra with coincident decay particles. inclusive w/ proton w/ pi± w/neutron w/ gamma previous experiment at BNL Excitation spectra w/ coincident decay particles for 5  He S. Kameoka et al. Nucl. Phys. A754 (2005) 173c S. Okada et al. Nucl. Phys. A754 (2005) 178c Excitation spectra w/ coincident decay particles for 12  C ８

n p n p n  N→nN n n n p p p p p n n n p  NN→nNN FSI re-scattering n n n p p p p p n n n p counts Q/2 Energy spectra (image) Energy distribute low energy region up to Q/2 broad peak around Q/2 continuous distribution Expected Spectrum ９

Single proton/neutron spectra from 5 Λ He and 12 Λ C S.Okada et al., PLB 597 (2004) 249 N n ～ 2N p Calculation by Garbarino et al. 10

np- & nn- angular distribution ( 5 Λ He)  n  p  nn /  np = 0.45±0.11±0.03 systematic error is mainly come from efficiency for neutron (6%) + acceptance(3%) Back-to-back 11

Coincidence Measurement (A=12) cos n + p n + n p + p E n + E p E n + E n E p + E p MeV  NN Counts 12 Λ C  n  p  nn /  np = 0.51±0.13±0.05 Analysis detail on Kim’s Poster 12

 n /  p 0.93±0.55 (Szymanski et al.) for 5  He Exp. Λ N NN W S π One Pion Exchange (OPE) Theo. N N N Λ Direct Quark mechanism Meson Exchange mechanism Λ N NN π,K,η,ρ,ω…  n /  p ratio Previous exp. (at BNL) N nn / N np ( 5  He)= 0.45±0.11±  He (E462) Kang et al. PRL 96 (2006) Γ n / Γ p ( 12  C)= 0.51±0.13±  C (E508) Kim et al. PLB641 (2006) 28 13

Asymmetry measurement of decay proton N(  ) = N 0 (1 + Acos  )  Asymmetry Asymmetry : Volume of the asymmetric emission from NMWD A = (R - 1) (R + 1) R = N(-)N(-) N(+)N(+), Asymmetry parameter = N 0 (1 +  Pcos  ) Difference of acceptance & efficiency → canceled out !! R = N(  + (-  ))×N(  - (+  )) N(  + (+  ))×N(  - (-  )) 1/2  K >0 ++ K+K+  /p KK    K <0 ++ K+K+ /p/p KK   P P 14

Initial state Final state Amplitude Isospin Parity 1S01S0 1S01S0 a1No 3P03P0 b1Yes 3S13S1 3S13S1 c0No 3D13D1 d0 1P11P1 e0Yes 3P13P1 f1 If assuming initial S state We can know the interference between states with different Isospin and Parity. (Applying  =1/2 rule) Importance of α nm measurement 15

 NM for 5 Λ He NMWD A=PA=P A  :Asymmetry of Pion    Asymmetry Parameter of Pion (= － 0.642±0.013) P   Polarization of Lambda  :Attenuation factor ・ Polarization of  ・ Asymmetry Parameter of Proton A p =  NM P   p Estimated from mesonic decay We can calculate  NM without theoretical help ! p 16

Theory: ～ Asymmetry parameter of 5 Λ He  NM =0.08± p statistical  contami Nucl.Phys.A754 (2005) 168c nucl-ex/

Asymmetry parameter of 12 C, 11 B   NM = － 0.14± p statistical  contami E160 : － 0.9±0.3 18

Comparison with previous experiment PID function Energy spectrum p  Precious Experiment E508 w/proton w/pion range&E tot dE/dx&E tot TOF&E tot 19

Comparison with recent calculations OPE  +K  +K+DQ OME  +K,OME can reproduce  n /  p ratio but predict large negative  NM  +K+   +K+  +DQ  n /  p and  NM can be reproduced by  +K+  +DQ model Sasaki et al. PRC71 (2005) (1) Large b( 1 S 0 → 3 P 0 ) and f( 3 S 0 → 3 P 1 ) amplitude (2) Violation of ΔI=1/2 rule considered T. Maruta ; parallel A2  a  Calculation by Itonaga 20

Decay Widths → Okada’s poster 21

Summary   N→NN was directly observed for the first time !! 5 Λ He: Γ n / Γ p ratio ～ N nn / N np = 0.45±0.11±0.03 Kang et al. PRL 96 (2006) Λ C: Γ n / Γ p ratio = 0.50±0.13±0.05 Kim et al. PLB641 (2006) 28 ◆ Asymmetry parameter measured with improved accuracy !! 5 Λ He : 11 Λ B and 12 Λ C : Maruta et al. nucl-ex/ ; thesis ◆ Total & partial decay rates are measured very accurately  NM =0.08± p [1] Importance of shorter-range mechanism OPE ⇒ Heavy meson & DQ exchange [2] Suggesting significant contribution from ΛN initial spin-singlet initial state σ-meson exch. / ΔI=1/2 violation? ⇒ 4 Λ H &  NM = － 0.14± p

Spare OHPs

Neutron energy resoltion →  7MeV(FWHM) at 75MeV Neutral PID Constant background very small 1 /  spectra Neutral particles from 12  C Good  n separation Charged particles from 5  He PID function Charged PID Good  p d separation Decay particle identification 8

Coincidence Measurement(E462/E508) Pair numbers/NMWD Estimated contamination from Energy sum distribution n + p n + n

experimentaldata theoreticalcalc. Comparison with theoretical calc. for angular correlation Garbarino’s calc. assuming Gn/Gp = 0.46 (for 5  He ), 0.34 (for 12  C ) considered 2N-induced( ～ 20%), FSI 5  He (E462) 12  C (E508) n+p coincidence n+n coincidence n+p n+n cos  n+p coincidence n+n coincidence n+p n+n p+p Pair number /NMWD /NMWD Pair number /NMWD /NMWD n+p coincidence n+n coincidence p+p coincidence n+p coincidence n+n coincidence p+p coincidence Phys. Rev. Lett. 91 (2003)

Neutron Efficiency Correction

N n / N p Ratio Γ n Γ n (Λ+“ ｎ ”→ ｎ + ｎ ) Γ p Γ p (Λ+“ ｐ ”→ ｎ + ｐ ) If Γ n / Γ p = 1 → N n / N p = 3 If Γ n / Γ p = 0.5→ N n / N p = 2 If Γ n / Γ p = 0→ N n / N p = 1 Naive estimation (without considering FSI and ΛNN→NNN) To avoid suffering from FSI effect & ΛNN→NNN, High energy threshold Γ n :Γ p N n N p 1 : 1 … 3 : 1 1 : 2 … 2 : 1 0 : 1 … 1 : 1 N n / N p = 2×  n /  p + 1

Mass number dependence of neutron energy spectra ( A=5,12,89 ) ( previous experiment ) As the mass number become lager, the number of neutron become lager in the low energy part, and smaller in the high energy part. Q / 2 = 76 MeV No peaking at Q / 2 (76MeV) even 5 Λ He suggested larger contribution of ΛNN→NNN or FSI than theoretical prediction. Theoretical calc. 5 Λ He w/ FSI Q/2

Spare OHPs for asymmetry

E160 E508 Statistical comparison with E C event  246 event 11 B event  393 event 2779 event 2122 event ×11 ×5×5 Total 639 event 4901 event ×8×8 P-coin spectrum

Comparison with E160 PID functionEnergy spectrum

Polarization (P), asymmetry parameter(a) Asymmetry parameter S.Ajimura et al., PLB282, 293 (1992) W(  ) = 1 + A 1 P 1 (cos  ) A 1 = ka 1 P 

KEK-PS E278 experiment Experimental target: 6 Li Observable: Mesonic decay branching ratios Polarization E278 Decay counter  / p separation by dE/dx and E tot

Polarization of 5  He 6 Li(  +, K + ) spectrum S. Ajimura et al., PRL80, 3471 (1998) Consistent with experimental data

Proton asymmetry parameter of 5  He 6 Li(  +, K + ) spectrum S. Ajimura et al., Submitted to PRL Inconsistent with meson exchange model

Polarization of  ー : E462 ー : E278 : Motoba et al. NPA577 (1994) 293c NOTE: Calculation by Motoba et al. considers excited state at E=4.5 MeV

E462   - /   of   He  - branching ratio  0 branching ratio Lifetime Other results  - decay width for 5  He Errors were much improved !!  0 decay width for 5  He and 12  C HYP2003 proceedings Nucl. Phys. A754 (2005)

Null asymmetry test ( ,pX) reaction : Only Strong Interaction Asymmetry = 0 expected Instrumental Asymmetry < 0.3% p or 

np coincidence analysis n p n p  n n p n p Coincidence NMWD np back-to-back event  NM =0.31±0.22 p

One and only(?) solution  + K +  + DQ Sasaki et al. PRC71 (2005)  N NN W S ,K,,K,  b( 1 S 0 → 3 P 0 ) と f( 3 S 0 → 3 P 1 ) amplitude に影響を与える   I = 3/2 が大きく寄与する  今回  n /  p ratio と  NM を高精度で測定したことにより、 こういう反応機構の必要性が認識された。 p

Mijung の OHP から

Before subtraction After subtraction Uniform components subtraction

FSI consideration using pp-pairs r n,p r n,p fraction ratio of the neutron and proton induced channels. f n,p f n,p is reduction factor due to FSI. g n,p g n,p is cross over influx of neutron(proton) from proton(neutron) due to FSI. p,q,q’ p,q,q’ are angular acceptance factor.,,, N np (bb) N nn (bb) N pp (bb) Before FSI correction 4%

Systematic error calculation 1)Intentionally add 2 pp events in -0.8<cos  <-0.7 2) 3)Uniform b.g. level for different angular regions:6.6%

6 Li Hypernuclear mass spectra 6 Li +  + →  6 Li + K +  6 Li →  5 He + p 5  He 6  Li 5 Li 0MeV 8.3MeV 18.3MeV ( P n -1,S  ) ( P n -1,P  ) ( S n -1,S  ) p decay  decay inclusive  coin p coin 5.2×10 4 events 3.2×10 3 events 1.6×10 3 events 

Instrumental Asymmetry ( ,pC) reaction : Only Strong Interaction Asymmetry = 0 expected Instrumental Asymmetry < 0.3%

Spin / isospin dependence p p n Λ n n p Λ p p n n Λ Non-mesonic weak decay of 4  He and 4  H 4 He (K -,  - ) 4  He or 4 He (  +,K + ) 4  He  n+n back-to-back 4 He (K -,  0 ) 4  H  p+n back-to-back (  0 spectrometer ) see S.Ajimura : J-PARC LOI 21 To J-PARC R NS … N :  n  nn,  p  np S : spin = 0 or 1  nm ( 4  H) = ( 3R n1 + R n0 + 2R p0 ) ×  4 / 6  nm ( 4  He) = ( 2R n0 + 3R p1 + R p0 ) ×  4 / 6  nm ( 5  He) = ( 3R n1 + R n0 + 3R p1 + R p0 ) ×  5 / 8  Need one-order higher statistics.  J-PARC

π+π+ K+K+ decay counter K6/SKS setup

Identification of hypernuclear formation K+K+  T1 target Z-vertex Mass Z

Non-mesonic weak decay strong tenser coupling (  L=2,  S=2) → dominant term 3 S 1 → 3 D 1 (amplitude “d”)  + N→ N + N  + p → n + p :  p = a 2 +b 2 +c 2 +d 2 +e 2 +f 2  + n → n + n :  n = a 2 +b 2 +f 2 OPE :  n /  p ～ 0.1 Λ N NN W S π One Pion Exchange (OPE) model  n /  p ratio : The most important observable to study the isospin structure of the NMWD. Exp. :  n /  p ～ 1  n /  p ratio puzzle Simple theoretical model with large error

 -nucleus overlap for 5  He   0 /   = 0.201±0.011 (   He)   nm /   = 0.395±0.016 (   He) Γtotal ( 56 Λ Fe) ～ Γnm(A→∞) ～ 1.2Γ Λ （ E307 ） Γnm ( 5 Λ He) = 0.4Γ Λ （ Present) 1/3 of Λ is inside α Both results are consistent, preferred larger overlap than YNG prediction. 5 Λ He (ORG) ～ 40% 5 Λ He (YNG) ～ 20% 1/3 of Λ is inside α     0 /   locates in between ORG and YNG.

ちょっと前の講演のから..

Mesonic Weak Decay Decay mechanism is known fairly well “How to use it” Mass number 4～54～5 ～ ～ 100 q ～ 400MeV/c ΛN→NN Spin/isospin dep. ΔI=1/2 rule test Mass number dependence Λ→Nπ Λ-nucleus potential Spin/parity assignment Pion distortion effect in nuclei q ～ 100MeV/c Non-Mesonic Weak Decay (NMWD) Decay mechanism is unknown “What is it ?” Fermi momentum ～ 270MeV/c > > 4

History of hypernuclear weak decay experiments… Year ～ ～ ～ Γ π _ Γ π _ (  → ｐ + π － ) Γ π 0 Γ π 0 (  → ｎ + π ０ ) Γ p Γ p (  +“ ｐ ”→ ｎ + ｐ ) Γ n Γ n (  +“ ｎ ”→ ｎ + ｎ ) 1/  HY =Γ tot ΓmΓm Γ nm New era started! → / J-PARC Merit/ Demerit ＊ Clean decay identification → ground state spin assignment ＊ Low energy threshold for p ＊ Hypernuclear formation is not identified ＊ Blind for neutral particles ＊ No timing information ＊ Hypernuclear formation tagged → branching ratio ! ＊ Direct lifetime meas. w/TOF counter ＊ Still hard to see neutral particles ＊ High energy threshold for p (Ep>30 ～ 40MeV) Emulsion and Bubble chamber Method Counter experiment w/ (K,π) SKS experiments w/ (π,K) reaction n+p/n+n coincidence ＊ Heavy Λ hypernuclear production ＊ Neutral particle detection ＊ Asymmetry of p from NMWD ＊ Improved statistics → n+p/n+n double coincidence 7

Hyperon-nucleus potential Λnucleus YN interaction attraction ～ repulsion Repusive core is the common feature of Y-nucleus potential 18

Σ-nucleus potential I=1/2 I=3/2 ＊ Bound state only in I=1/2 ＊ Due to the existence of repulsive core, Σ is pushed outside of the nucleus and ΣN→ΛN conversion is supressed 4 Σ He (I=1/2, S=0) 19

Spin/isospin dependence       8/RR3 R R3 = He 6/RR3 R2 = 6/R2 R R3 = H 50p1p0nn1 5 nm 40p1pn0 4 nm 40p0nn1 4 nm       Test of =1/2 rule p p n Λ n n p Λ p p n n Λ NMWD of 4 Λ He and 4 Λ H × 35

Theoretical approach N N N Λ Direct Quark (DQ) mechanism q ～ 400MeV/c (← large!) → short-distance interaction One Meson Exchange (OME) mechanism Λ N NN π,K,η,ρ,ω,K * → large  n /  p ( ～ ) Kaon exchange model (OME)  dominant term 3 S 1 → 1 P 1 (amplitude “f”) (  range ～ 0.5 fm) 36

only proton Most of the experiments measured only proton energy specra   n /  p = (  nm –  p ) /  p difficulty in detecting neutrons) (because of the difficulty in detecting neutrons) n n n p p p p p n n n p rescattering  NN→NNN (2N-induced process) Λ N N N W π N N Final state interaction (FSI) effect Experimental difficulty Proton energy loss inside a target and detectors Final state interaction (FSI) effect (  not well established theoretically) to distinguish between the FSI and 2N-induced process (  NN  nNN) (One of the theoretical model) 37

Hypernuclear mass spectra on C, Si and Fe target nat C(  +,K + ) nat Si(  +,K + ) nat Fe(  +,K + ) 45

KEK-E307 COSY-13 ? Lifetime of very-heavy hypernuclei ? (J-PARC) (π,K) K1.1BR 49

By-products of E307 exp. 1. Mesonic decay widths of midium-heavy Λ hypernuclei 2. Proron energy spectra → Γn/Γp ratio “puzzle” 50

Enhancement of π-mesonic decay widths Momentum transfer q ～ 100MeV/c << 270MeV/c → “Forbidden” process in nuclear matter 1. Fermi motion of Λ 2. Smaller local Fermi momentum at the surface region 3. Pion distortion effect 1) Pion feels attraction in nuclear medium due to the P-wave part of the optical potential 2) Inside the nucleus, pion can carry smaller energy for fixed momentum q 3) Due to the energy conservation, final nucleon has more chance to come out above the Fermi surface 51

Effects of nuclear shell structure and  -nucleus potential T. Motoba et al. Prog. Theo. Phys. Suppl. No.117, 477 (1994) H. Noumi et al. PRC52, 2936 (1995) J. J. Szymanski et al. PRC43, 849 (1991) A.Sakaguchi et al. PRC43, 73 (1991) T. Motoba et al., PTP Suppl. No.117, 477 (1994) Potential dependence of decay rate  mesonic decay rates for p-shell  hypernuclei 52

Hypernuclear mass spectra on C, Si and Fe target nat C(  +,K + ) nat Si(  +,K + ) nat Fe(  +,K + ) 53

Results of  - Mesonic decay width Branching ratio  - Mesonic decay width Motoba Y.Sato et al. Recently re-submitted to PRC 54

Gross behavior of hypernuclear  -mesonic decay rate E.Oset et al. Prog. Theo. Phys. Suppl. No.117,461 (1994)T. Motoba et al. Nucl. Phys. A547, 115c (1992) 55

Measurement of π0 mesonic decay 33

Only one old experiment…. (stopped K-,π-) Sakaguchi et al. Phys. Rev. C43 (1991 ) Λ C ～ 1000 π 0 branching ratio of 12 Λ C ＝ 0.174±0.057± γcoincidence 2γcoincidence Still large error!! → NMWD branch ?

one gamma ray from “  0  2  ” process was detected. For observing  0 particle, Constant background level is very low. Gated ground state of hypernuclei ( 5  He, 12  C) 1 /  ( TOF ) spectrum Neutral particle identification Layer multiplicity  2 ADC sum  20MeVee Good separation (between  and neutron) 34

Large plastic scintillator arrays were used as  detector. Start timing counter Charged VETO 30cm  detection system  0 identification Background (low energy):  from nuclear decay process 00   EM shower (~70MeV) K+K+ ++  0 emit energetic gamma. (~70MeV)  set threshold of ADC sum. The gamma  cascade in many layers.  select high multiplicity event. To reject the nuclear decay  In these cut conditions, It is hard to estimate gamma detection efficiency.  So we simulated with same conditions using GEANT code. 5  He 35

Mul   2 Mul   3 Mul   4 Mul   5 Mul   6 Layer multiplicity ADC sum distribution Mul   1  efficiency estimation using GEANT simulation * Blue histogram : GEANT simulation * Plot (with error bar) : Experimental data Nuclear  is shown only Mul  1. To remove it completely, we apply Mul  2 and ADCsum  20MeVee. Well agree with Geant simulation. assuming  0 momentum in GEANT simulation as 5  He : MeV (mono) 12  C : Motoba’s calculation PTP117(1994)  from  0 20MeV nuclear  36

 0 branching ratio of 5  He Free  b   / b  0 = 1.78±  He  b   / b  0 = 1.70±0.08 MeV Mass spectra for 6 Li(  +,K + ) 5  He g.s. quasi free w/ gamma Mul   2  20 MeVee inclusive efficiency = 9.59% N (inc) = N (w/  ) = b  0 = N (w/  ) / N (inc) × eff = 0.212±0.008 ADC sum w/ Geant sim 5  He  + p +    + n +  0 Same Q-value as that of free  37

 0 branching ratio of 12  C b  0 = N (w/  ) / N (inc) × eff = 0.133±0.005±0.003 MeV Mass spectra for 12 C(  +,K + ) quasi free w/ gamma 12  C g.s. inclusive Mul   2  20 MeVee efficiency = 9.53% N (inc) = N (w/  ) = ADC sum w/ GEANT sim

Results of   0   He   0 /   = 0.201±0.011   C   0 /   = 0.165±0.008 Lifetime : ps (E462) -10 Lifetime : ps (E508) -6 Much improved accuracy Okada et al., HYP03 nucl-ex/

Fuse-Kumagai’s recent calculation JPS meeting (2004 Spring) 39

0.336 ± 0.016ΓΛ

SG: excluded → Existence of repulsive core!! 40

  He  nm /   = 0.406±0.020   C  nm /   = 0.953±0.032  tot = 0.947±0.038 Γ Λ bπ 0 = bπ 0 = 0.212±0.008 bπ - = bπ - = 0.359±0.009 bπ - = bπ - = 0.099±0.011 bπ 0 = bπ 0 = 0.133±0.005  tot = 1.242±0.042 Γ Λ 0.41± ±0.09 Non-mesonic deca rate 5  He and 12 Λ C Γtotal ( 56 Λ Fe) ～ Γnm(A→∞) ～ 1.2Γ Λ （ E307 ） Γnm ( 5 Λ He) = 0.4Γ Λ （ Present) Γnm calculation must use the Λ w.f. which can well reproduce Γπ 41

Mass number dependence of Γ NM 42