Harada, Toru Osaka - PowerPoint PPT Presentation

特定領域研究「ストレンジネスで探るクォーク多体系」理論班主催 「ストレンジクォークを含むクォーク多体系分野の理論的将来を考える」研究会 2009年2月27-28日, 熱海市 ハイパー核反応の今後 原田 融 Harada, Toru 大阪電気通信大学 Osaka Electro-Communication University Neyagawa 572-8530, Osaka, Japan harada@isc.osakac.ac.jp

-これまでにどういう新しい物理を明らか にしてきたか？ ・生成のメカニズムとDWIA計算の改良 ・  nucleus potential の性質  原子 v.s.(      反応 ・中性子過剰ハイパー核生成 シグマ混合率 - 今後、どういう新しい展開が期待できる のか？ ・２重荷電交換反応によるハイパー核生成！ - J-PAＲCに対して、どういう実験を提 案していくのか？

Momentum transfer to  -hyperons 1.20 GeV/c   n →    spin-stretched states   n →    q  MeV/c Stopped p F 0.6 GeV/c ～ 270 MeV/c   N →  q  MeV/c   n →    q  MeV/c substitutional states

Hypernuclear Production Reactions (K  ,   ) ・反応の特徴を生かす ・  状態を選択的に励起 720 MeV/c q  ～ 60MeV/c “Substitutional” (   ,K  ) reactions    0  +  + (   ,K  ) 1040 MeV/c q  ～ 350MeV/c 1f “Spin-Stretched’’ f 7/2 2s 3/2 n  1 [(  ) (  ) ] n j n j  N J 1d d  [ 1 ] j j    max N J J 1p 1s (K  ,   )  Stooped K- Lambda q  ～ 300MeV/c by R.Hausmann and W.Weise neutron H.Bando, T.Motoba, J.Zofka, Int.J.Mod.Phys. A5(1990)4021

Distorted wave impulse approximation （ DWIA)   核内核子  （陽子・中性子） 観測 / 測定 （  + , K + )    p n K 放出粒子 p    入射粒子 素過程 π + + “n” → K + +  p 標的核 Y Double-Differential Cross Sections Strength function   2   d d     ( , ) q       ( )*  ( )  2     S ( , ) q | | | | ( )   S f U i E E          K K dE d d       n K f Elementary cross sections (Fermi-averaging) Meson distorted-wave functions (Eikonal approximation )           ( )* ( ) ( ) ˆ ( ) r ( ) r 4 (2 1) ( ) ( ) r L L i j r Y    K LM LM L   '  l l L 2 1  l ˆ           ( ) ( ) ( ) * ( ) ( ) 4 (2 ' 1) ( ; ) ( ; ) ( 0 ' | )( 0 '0| 0) (k ) 2 j r l j k r j k r l l M LM l l L Y   ' ' LM 2 1 l l K l M K L ' ll

Optimal Fermi-averaging for the  + +n → K + +  t-matrix in  -hypernuclear production from (  + , K + ) reactions T.H and Y.Hirabayashi, NPA744(2004)323

 Quasi-free production spectrum Fermi gas model (K  ,   ) q  ～ 60MeV/c R.H.Dalitz, A.Gal, PL64B(1976)154 720 MeV/c  =206 MeV elem     d d     ( , )   R     d dE d L L peak position － 28 MeV － 58 MeV 270 MeV /c 14 MeV 2 2 k q        ( )(1 ) ( ) F M M U U   N 4 N 2 M M M   30 MeV N 174 MeV (   ,K  ) q  ～ 300MeV/c (K-,  ): 2 MeV 1225 MeV/c width (  ,K+,): 56 MeV  =245 MeV k q k q        F F (K-,  ): 14 MeV M M (  ,K+,): 73 MeV   73 MeV C.B. Dover et al., PRC22 (1980) 2073.

 spectrum by      reaction at 1.20, 1.05GeV/c 12 C (  + ,K + )反応による  -QF生成 P.K.Saha et al., KEK-E438, E521   q ～ 400 MeV/c peak width q ～ 380 MeV/c 1.20GeV/c (MeV) (MeV) ～  ～  1.20GeV/c 1.20GeV/c ～  ～  1.05GeV/c 1.05GeV/c 1.05GeV/c

Elementary cross sections of  →      ‐ reactions 1050 T.O.Binford, et al. PR183(1969)1134 800 N(1650)S11 N(1675)D15  0    d N(1710)P11 (  b/sr)   N(1720)P13    d 600 LAB 1200 K +  400   p →    K +   1200 K +   200   p →     K +   0 1000 1200 1400 1600 1800  momentum (MeV/c)

Optimal Fermi-averaging for an elementary t-matrix T. Harada and Y.Hirabayashi, NPA744 (2004) 323. “Optimal” cross section   + opt     N d k E 2 ˆ ( p   opt ; , ) q K K  + t p   K p    2   (2 )  d v       p K   p  Optimal Fermi-averaged t-Matrix On-shell T-matrix      ˆ    2 sin ( ; , ) ( ) d p dp t E p p p   ˆ N N N N N  opt ( ; , ) q 0 0 Lab t p         2 sin ( ) d p dp p N N N 0 0 *  p p N N given         * 2 * 2 ( p q ) p “On-energy-shell’’ equation E E m m  f i N N N given    * p p p p S,A.Gurvitz, PRC33(1986)422: Optimal factorization   N K

Optimal cross section of the  + +n → K + +  reaction in nuclei opt     + +n → K + +  Cross Section d k E 2 ˆ   opt ( , ) K K t E     2   (2 ) d v       1.05 p K 1.20  1.05GeV/c M(  + n) 1.20GeV/c

 spectrum by      reaction at 1.2GeV/c 28 Si KEK-E438      / d d 1d(5/2)h d  p  1p(3/2)h 1p(1/2)h S  1s(1/2)h The contribution of deep hole-states is important !

 C      Reactions • The calculated spectra in QF region can 1.20 GeV/c explain the experimental data at 1.20 and 1.05GeV/c. • The  energy-dependence originates from the nature of the “optimal Fermi-averaging” 1.05 GeV/c t-matrix. make the width look narrow opt   2   d d    ( , ) q S      dE d d       n K Strength function “Optimal Fermi-averaging” ˆ (   q opt t-matrix ; , ) well-known well-known t p  -nucleus potential Need careful consideration for energy-dependent of the elementary cross section.

Is the  -nucleus potential for   atoms consistent with the (   , K + ) data? 28 Si T.H and Y.Hirabayashi, NPA759(2005)143 Isospin dependence of  -nucleus potentials for N > Z 209 Bi T.H and Y.Hirabayashi, NPA767(2006)206

Observation of n=3   atomic X-ray n=4 RMF n=9 n=10 G. Backenstoss, et al., Z. Phys. A273(1975)137 n=5 C.J. Batty, et al.,Phys.Lett.B 74 (1978) 27 R.J. Powers, et al.,PRC47(1993)1263 n=6  →  u Shifts C   →  u Mg  →  u  →   u Al Widths  →   u Si n=3  →   u S n=4  →  u Ca n=9  →  u Ti  →  u Ba n=5 n=10  →   u W Pb  →   u n=6 Only 23 measurements !!

 ‐ -nucleus optical potentials in 27 Al+  ‐ Imag. LDA-NF LDA-NF DD DD-A’ LDA-S3 LDA-S3 Real WS-sh WS-sh RMF RMF t eff ρ teff RMF RMF LDA-NF LDA-S3 LDA-NF DD-A’ LDA-S3 DD teff WS-sh t eff ρ WS-sh Real part Imag. part Real part Imag. part repulsive strong ( 30-40MeV ) (weak) attractive weak ( < 10MeV ) Type I Type II

 ‐ -nucleus potentials fitted to the  ‐ -atomic data DD-A’ Density-dependent (DD) potential C.J.Batty et al., Phys.Rep.287(1997)385                       ( ) ( ) r r               2 4 1 ( ) ( )         U b B r b B r  0 0 1 1      (0) (0)        m                   ( ) ( ) ( ) ( ) ( ) ( ) r r r r r r p n n p Relativistic mean-field (RMF) potential J. Mares et al., NPA594(1995)311 RMF    Local density approximation (LDA) with YNG-NF LDA-NF    D. Halderson, Phys. Rev. C40(1989)2173 Repulsive T.Yamada and Y.Yamamoto, PTP. Suppl. 117(1994)241 J. Dabrowski, Acta Phys. Pol. B31(2001)2179 Local density approximation (LDA) with SAP3 (simulates ND) LDA-S3 T.Harada, in: Proceedings of the 23nd INS Symp. 1995, p.211 Attractive Shallow Woods-Saxon potential : (V 0 ,W 0 )=( － 10, － 9) MeV WS-sh R.S.Hayano, NPA478(1988)113c t eff ρ –type potential ( B 0 = B 1 =0): a 0 =0.36+i0.20 fm t eff ρ    C.J.Batty, E.Friedman, A.Gal, PTP. Suppl. 117(1994)227

Strong-shifts and widths on  ‐ atoms  ‐ 28 Si 28 Si