H YN,YNN,YY,YYN - PowerPoint PPT Presentation

第７回 J-PARC ハドロンサロン ＫＥＫ東海、２０１３年３月１日 中性子過剰核 6 Λ H, 5 ΛΛ H における YN,YNN,YY,YYN 有効相互作用 赤石 義紀 理研、日大理工

Hyper-heavy hydrogen 6 Λ H in collaboration with Theingi & Khin Swe Myint arXiv:1211.5719 [nucl-th] 最近話題になっている 6 Λ Η の束縛のメカニズムを追究することによって、中性子過剰核特有の３ 体力効果を明らかにする。この効果は、 Λ と Σ が相互に転移する平均場を用いて記述できる。こ の新しい型の平均場は、中性子過剰のハイパー核に通常のハイパー核にはない際立った特質を もたらす。 6 Λ Η で当面する課題について議論する。

Γ = 1.9 MeV 1 6 2 5 H ( He, He, He He ) H Superheavy hydrogen 1.7 (MeV) A.A. Korsheninnikov et al, Phys. Rev. Lett. 87 (2001) 092501 3 H + n 2 + Λ 3 H + 2n 0.0 -4.4 MeV -2.04 4 H 2n 2n + Λ -1.4 MeV force Λ NN = Coherent Λ - Σ coupling which solves the 5 Λ He overbinding problem. -4.1 6 H 6 Li ( π - , K + ) Λ “Hyperheavy hydrogen” Khin Swe Myint & Y. Akaishi, Prog. Theor. Phys. Suppl. 146 (2002) 599

Pions from stopped K - on 6 Li M. Agnello et al., Nucl. Phys. A 881 (2012) 269 = 203 ± 1 . 3 MeV

Evidence for heavy hyperhydrogen 6 Λ H M. Agnello et al., Phys. Rev. Lett. 108 (2012) 042501 − → + Λ p π Weak decay ; 2.6E-10 s − + + 6 → 6 + − 6 → 6 + K Li H π H He π stop Λ Λ

Candidates of 6 Λ H 4 Λ H+2n threshold: 5801.71 MeV Dalitz Akaishi

Evidence for 6 Λ H Bressani et al. Unbound nn +1.7 MeV 0 Bound nn 5 H + Λ -0.35 MeV 2.4 MeV from 3 H- Λ Λ H + 2n 4 Modified Dalitz 1.8 MeV from nn- Λ -4.1 MeV Akaishi -4.55 MeV Dalitz (1963)

⎧ ⎫ 2 ⎧ 2 ⎫ ⎛ ⎞ ⎪ ⎪ ⎛ ⎞ r ⎪ ⎪ r = − − ⎜ ⎟ 10 . 5 exp ⎨ ⎬ = − − ⎜ ⎟ v ⎜ ⎟ 13 . 3 exp ⎨ ⎬ v t(nn) MeV ⎜ ⎟ t(nn) MeV 2 . 2 ⎝ ⎠ ⎪ ⎪ 2 . 2 ⎝ ⎠ fm ⎪ ⎪ ⎩ ⎭ ⎩ fm ⎭ E =0 ⎧ 2 ⎫ E =-0.35 MeV Evidence for 6 Λ H ⎧ ⎫ 2 ⎛ ⎞ ⎪ ⎪ ⎛ ⎞ r ⎪ ⎪ r = − − ⎜ ⎟ 43 . 8 exp ⎨ ⎬ ⎜ ⎟ v = − − 45 . 4 exp ⎜ ⎟ ⎨ ⎬ v t Λ MeV ⎜ ⎟ t Λ MeV 1 . 53 ⎝ ⎠ ⎪ ⎪ 1 . 53 ⎝ ⎠ ⎪ ⎪ ⎩ fm ⎭ fm ⎩ ⎭ E =-2.04 MeV ⎧ ⎫ E =-2.4 MeV Bressani et al. 2 ⎧ ⎫ 2 ⎛ ⎞ ⎪ ⎪ ⎛ ⎞ r ⎪ ⎪ r ⎜ ⎟ = − − 11 . 5 exp ⎨ ⎬ = − − ⎜ ⎟ v ⎜ ⎟ 11 . 5 exp ⎨ ⎬ Λ v (nn) MeV ⎜ ⎟ Λ (nn) MeV 1 . 8 ⎝ ⎠ ⎪ ⎪ 1 . 8 ⎝ ⎠ ⎩ fm ⎭ ⎪ ⎪ ⎩ fm ⎭ E t(nn) Λ = -3.26 MeV E t(nn) Λ = -4.54 MeV Unbound nn +1.7 MeV 0 Bound nn 5 H + Λ -0.35 MeV *) Unstable 2.4 MeV from 3 H- Λ 3BF Λ H + 2n 4 Modified Dalitz -3.26 MeV 1.8 MeV from nn- Λ -4.1 MeV Akaishi -4.55 MeV Dalitz (1963) * ) This state comes above the threshold and cannot survive till weak decay. Thus, the coherent Λ - Σ coupling is necessitated. at best only a rough estimate

3 candidate events of 6 Λ H Production 3 H + Λ + 2n "Event-selection line" M1 Λ H(1 + ) + 2n 4 Weak decay ~ 2.6 x10 -10 s Modified Λ H(0 + ) + 2n 4 Dalitz Akaishi 6 Λ H

Λ separation energy (unit in MeV) α +n+n+ Λ 0.98 6 Λ H 6 Λ He 7 Λ He 3 Λ H 4 Λ H 4 Λ He 5 Λ He 0 -0.13 (-0.89) 1 + -0.99 -1.24 α +n+ Λ (-1.7) t+n+n+ Λ 0 + -2.04 -2.39 -3.12 DAFNE -4.0 Phenomenological model -4.2 -4.18 -4.28 Dalitz =-2.04-2.24 -5.36 n n n n -5.8 ) 4 2 -2.24 +1.7 Akaishi . 2 -0.98 - ( α t Λ Λ -2.04 -3.12 6 Λ H 7 Λ He

Λ separation energy (unit in MeV) α +n+n+ Λ 0.98 6 Λ H 6 Λ He 7 Λ He 3 Λ H 4 Λ H 4 Λ He 5 Λ He 0 -0.13 (-0.89) 1 + -0.99 -1.24 α +n+ Λ (-1.7) t+n+n+ Λ 0 + -2.04 -2.39 -3.12 DAFNE -4.0 Phenomenological model -4.2 -4.18 Dalitz -4.28 =-2.04-2.24 -5.36 -5.8 Dynamical model Akaishi Overbinding problem Dynamical model with coherent Λ - Σ coupling

Coherent Λ - Σ coupling Λ T =0 1116 MeV/c 2 Σ T =1 1193 MeV/c 2

YN interaction weights from s -shell nucleons 4 Σ H(0 + ) 4 Σ H(1 + ) 5 Σ He 4 4 = = 3 2 3 2 1 3 T T g g Σ N Σ N 3 3 3 1 7 1 3 1 3 1 + + g g g g Σ N Σ N Σ N Σ N 2 6 6 2 3 1 1 1 3 1 3 1 − + g g g g Σ N , Λ N Σ N , Λ N Σ N , Λ N Σ N , Λ N 2 2 2 2 3 3 5 1 3 1 + 3 1 3 1 3 + + g g g g g g Λ N Λ N Λ N Λ N Λ N Λ N 2 2 2 2 4 Λ H(0 + ) 4 Λ H(1 + ) 5 Λ He

4 He He Λ (MeV) 30 D2 interaction + U ( 0 ) − ΣΛ 20 1 + -1.03 -1.04 1 + -1.24 0 + -1.04 10 ( + U 1 ) − ΣΛ 0 U Λ 0 ( + ) -2.27 0 + -2.39 MeV -10 Exp U Λ 1 ( + ) -20 0 1 2 3 4 r (fm) Y. Akaishi, T. Harada, S. Shinmura and Khin Swe Myint, Phys. Rev. Lett. 84 (2000) 3539

Stochastic variational calculation of 5 Λ He H. Nemura, Y. Akaishi & Y. Suzuki, Phys. Rev. Lett. 89 (2002) 142504 J.A. Carlson, The first successful ab initio 5-body calculation AIP Conf. Proc. 224 (1991) 198 SC89: unbound including Σ degrees of freedom 3 4 5 H H He He Λ Λ Λ -0.10 [0.15%] -0.13 SC97e(S) -0.92 [0.98%] NN:G3RS -0.99 -2.04 p Σ -2.06 [1.49%] -2.75 [1.55%] -3.12 (MeV)

Theory: T. Harada, Phys. Rev. Lett. 81 (1998) 5287 T. Harada 4 Λ He 4 Σ He

Y- (NNN) T =1/2 : interactions from D2 40 30 + U ( 0 ) − Coherent Λ - Σ coupling ΛΣ 20 U Σ 1 ( + ) 10 U ( + 1 ) − ΛΣ 0 2 1 3 4 5 r (fm) U Λ 0 ( + ) -10 U Λ 1 ( + ) -20 -30 U ( 0 + ) 4 Σ H formation Parametrized by T 1 / 2 Σ = (MeV) Sander Myint Oo

Coupling scheme Coherent Λ - Σ coupling Σ - n Σ H formation 4 α formation n Λ -n Σ 0 -p Σ - coupling h Σ 0 Σ - n p Σ 0 Σ - n p t t Λ n Λ n Spectator Participant α t 6 Λ H - n 7 Λ He - n

YN interaction weights in 6 Λ H(0 + ) g for p -shell N is the sum of even & odd state effective interactions. 4 2 2 = = = 1 3 2 3 3 2 1 3 2 T T + T g g g Σ N Σ N Σ N 3 3 9 3 1 1 1 3 1 3 1 + + g g g g Σ N Σ N Σ N Σ N 2 6 12 36 3 1 1 1 3 1 3 1 − + g g g g Σ N , Λ N Σ N , Λ N Σ N, Λ N Σ N, Λ N 2 2 4 12 3 1 3 3 3 1 3 1 + + g g g g Λ N Λ N Λ N Λ N 4 4 2 2 from s -shell nucleons from p -shell neutrons Program code swe3/LH6.f

NSC97f is used.

Dependence of coherent Λ - Σ coupling on 6 Λ H size 2 1 h ω = h b ho [fm] 2 M b ho 0.6 0.8 1.0 1.2 1.4 1.6 0 Coherent Λ - Σ coupling effects from s -shell nnp g -matrix HF from p -shell nn 40 -5 30 -10 E Λ [%] [MeV] 20 -15 10 P coh. Σ -20 -25 0 0.6 0.8 1.0 1.2 1.4 1.6 b ho [fm]

10 10 Li Li Λ H + α = 6 Λ -12.09 1 - 2 - -12.11 -12.17 2 - Λ NN force γ 0.21 MeV 1 - -12.28 ( P coh Σ =0.31%) D2 int. (MeV) ( s ) U 30 BHF cal. Σ 20 Y. Akaishi & Khin Swe Myint ( p ) U , Λ Σ 10 0 3 1 2 r (fm) ( p ) U -10 Λ ( s ) U Λ -20 ( p ) U Σ -30

10 B ( π - ,K + ) 10 Λ Li spectrum P.K. Saha et al. (T. Fukuda), Phys. Rev. Lett. 94 (2005) 052502 9 Li+ Λ 9 Li+ Λ 9 Li+ Σ 0

Incoherent + Λ Σ − Λ Σ − n p n p T N for for T T = z = T 1 2 + Coherent + Λ Σ 0 Λ Σ 0 Λ coh = Λ / Σ 0 n p n p n p

+ Coherently enhanced 3BF

Relativistic mean field model Baryons: n, p, Λ , Σ Mesons: σ , ρ , ω X X Coherent Λ - Σ mixing X “Normal state of infinite matter” Baryons in the medium carry the same quantum numbers in vacuum. N.K. Glendenning, Astrophys. J. 293 (1985) 470.

Effective ΛΛ interaction in neutron-rich hypernuclei in collaboration with Aye Aye Min & Khin Swe Myint 二重ハイパー核 5 ΛΛ Η を取り上げる。ここでのテーマは「 ΛΛ 有効相互作用は、 中性子物質中と Ν=Ζ 核物質中で同じか？」である。中性子星中での YY 相互 作用を知るために、 5 ΛΛ Η の実験データが欠かせないことを示す。

Thermal evolution of hyperon-mixed neutron stars S. Tsuruta, J. Sadino, A. Kobelski, M.A. Teter, A.C. Liebmann, T. Takatsuka, K. Nomoto & H. Umeda, Astrophys. J. 691 (2009) 621 1.47 Hyperon cooling 1.52 1.53 1.6 Is hyperon superfluidity not too weak?

A. Gal, Invited Lecture at J-PARC, Tokai, on Feb. 9, 2012, ( neglecting K.S. Myint et al., Eur. Phys. J. A 16 ) Simple physics! Δ B ΛΛ Δ B ΛΛ Λ Λ Λ Λ -2.04 -3.12 NAGARA α t 0.67+-0.17 MeV

Khin Swe Myint, S. Shinmura & Y. Akaishi, Eur. Phys. J. A 16 (2003) 21 Only in the right diagram T =1/2 is conserved in intermediate state. ( ) - 0 1 = = − + 0 Ξ p Ξ n T 2

Δ 5 Δ 6 ( H) vs. ( He) B B ΛΛ ΛΛ ΛΛ ΛΛ Filikin-Gal

T =0 T =1 ΛΛ - p Ξ - - n Ξ 0 - ΛΣ 0 - Σ + Σ - - Σ 0 Σ 0 couplings