Electroproduction of medium-heavy  -hypernuclei Toshio MOTOBA （ Osaka E-C) major part done in collaboration with P. Bydzovsky ( Prague) M. Sotona ( Prague) K. Itonaga ( Gifu ) K. Ogawa ( Chiba ) O. Hashimoto ( Tohoku ) JSPS Core-to-Core Seminar EU SPHERE Network Meeting September 4-6, 2010, Villa Lanna, Prague 1

CONTENTS 1. Basic motivation ｓ for medium-heavy systems 2. Go to sd-shell: “Simplest” target ( 19 F) and the (d 5/2 ) 6 model to demonstrate the present theoretical treatments. 3. Realistic predictions for photo-production reaction with a typical target 28 Si( , K + )  28 Al 4. Extension of the approach to produce heavier hypernuclei around A= Outlook 2

3 1. Basic motivation: Why medium-heavy hypernuclei ? (1) The great success of Hall A and Hall C experiments at Jlab: -- sub-MeV (  approx. 0.5 MeV) -- predictions for p-shell confirmed encourages extension of high-resolution reaction spectroscopy to heavier hypernuclei: cf. (e,e’K + ), ( , K + ) vs. (K -,  - ) and (  ＋,K + )

(K -,  - ) (  ＋,K + ) played a great role of exciting high-spin series  = 1.5 MeV (best) (e,e’K + ), ( , K + ) Motoba. Sotona, Itonaga, Prog.Theor.Phys.S.117(1994) T.M. Mesons & Light Nuclei (2000) updated w/NSC97f JLab Exp’t :  = 0.5 MeV 4

Theor. prediction vs. (e,e’K + ) experiments Theory Motoba. Sotona, Itonaga, Prog.Theor.Phys.Sup.117 (1994) T.M. Mesons & Light Nuclei (2000) updated w/NSC97f Sotona’s Calc.----  Hall C (up) T. Miyoshi et al. P.R.L.90 (2003)  =0.75 MeV Hall A (bottom), J.J. LeRose et al. N.P. A804 (2008) 116.  =0.67 MeV 5

6 Why medium-heavy hypernuclei ? motivation (2) Unique characteristics of the (e,e’K + ), ( , K + ) process are based on the basic Properties of elementary amplitudes for  p →  K + : --- sizable momentum transfer to excite high-spin states, like (  ＋,K + ) --- spin-flip dominance of the operator, leading to unnatural parity states

Comparison of the recoil momentum q  = MeV/c at E  =1.3 GeV 7

Elementary amplitudes (2CM):  p   K + 8

Lab d  /d  for photoproduction (2Lab) 9

These characteristic merits of the  p →  K + process(ability to excite high-spin unnatural-parity states ) should be realized better in heavier systems involving large j p and large j  (e,e’K + ) d 3  /dE e d  e d  K =  x d  /d  K  : virtual photon flux (kinematics) Hereafter we discuss d  /d  K for A Z ( ,K+)  A Z’ 10

2. Go to sd-shell : 2-1. Simplest sd-shell target Choose 19 F (1/2 + ) target for demonstration of the hypernuclear photoproduction (asking the feasibility as a practical target ) 11

Choose 19 F (1/2 + ) target for demonstration neutronproton  DDHF 

Conversion of 1s 1/2 -proton(nb/sr) Cf. a trial calculation: If the last odd proton were in 0d 5/2, then Partial contributions

Conversion from 0p 1/2 Conversion from 1p 3/2 Partial contributions

19 F( ,K + )  19 O SUM of the partial contributions As a “closed core ( 18 O)”+  cf. SO-splitting(0p)= keV(C13)

2-1. Single-j model for the 28 Si target A typical example of medium-heavy target : 28 Si: (d 5/2 ) 6 to show characteristics of the ( ,K + ) reaction with DDHF w.f. ( Spin-orbit splitting: consistent with  7 Li, 9 Be, 13 C, 89 Y ) 16

Theor. x-section for (d 5/2 ) 6 ( ,K + ) [ ｊ h - ｊ  ]J 17

18 XS(J) DWIA (65%) vs. PWIA

d  /d  (  K ): angular dependence 19

[ j   20

3. Realistic prediction for 28 Si ( ,K + )  28 Al 21 By fully taking account of -- full p(sd) 6.n(sd) 6 configurations, -- fragmentations when a proton is converted, Al core nuclear excitation -- K + wave distortion effects  Comparison with the 28 Si (e,e’K + ) exp.

proton-state fragmentations should be taken into account to be realistic 22

23 Proton pickup from 28 Si(0 + ):(sd) 6 =(d 5/2 ) 4.1 ( 1 s 1/2 ) 0.9 (d 3/2 ) 1.0

24 Peaks can be classified by the characters

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26 Peak energies: 28  Si vs. 28  Al H.Hotchi et al, PRC 64(2001) vs. O.Hashimoto et al, NP A804(2008) j  28 Si(p +,K + ) 28  Si E  =-B  (Ex ) 28 Si(e,e’K + ) 28  Al (as read on the Sendai08 poster) ( ,K + ) CAL s (GS) ?? (GS)-16.6 (GS) ? ? ? (E x =4.7) p (E x =9.6) ?? (E x =11) -8.1 ( E x =8.5) (E x =12.4) -5.6, -4.0 d E x =17.6) /- (E x =19.2)+0.9 (E x =17.5)

4. Extend to heavier nuclear Targets 52 Cr: (f 7/2 ) 4 assumed 40 Ca: (sd-shell LS-closed) 27

Well-separated series of peaks due to large q and spin-flip dominance: j > =l+1/2, j < =l-1/2 28

52 Cr ( j > dominant target case) typical unnatural-parity high-spin states 29

40 Ca ( LS-closed shell case): high-spin states with natural-parity (2 +,3 -,4 + ) 30

6. SUMMARY 31

. ３ ) Realistic prediction for the 28 Si target was made. The calculation is in good agreement with the recent JLab exp. The predictions are made also for 40 Ca and 52 Cr. 4) Almost all predictions for the p-shell targets have been confirmed by the recent Jlab exp.(Hall A, C). 5) Medium-mass hypernuclear production by (e,e’K+) provide us with good opportunities in understanding the details of the hyperon motion in nuclear matter.(  -s.p.e. to establish “textbook”, Rotation/Vib.-  coupling, Auger effect,  , e eff (  ), etc ) 32

Single-particle energies of  33

SO splitting in 89 Y vs. Nijmegen models 34

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Additional part: Demonstration of p-Shell Targets : (Full shell model cal.) 7 Li, 9 Be, 10 B, 12 C, 14 N, 16 O 36

16 O target: Prediction Motoba-Sotona- Itonaga, P.T.P. Suppl.117 (1994) Hall A Exp: J.J.LeRose et al., Nucl.Phys. A804, 116 (2008) 37

10 B target: Prediction Motoba-Sotona- Itonaga, P.T.P. Suppl.117 (1994) compared with other theoretical calculations for (K-,  -) (  +,K + ) x 38

9 Be target: Prediction Motoba-Sotona- Itonaga, P.T.P. Suppl.117 (1994) Hall A Exp: J.J.LeRose et al., Nucl.Phys. A804, 116 (2008) c 39

40

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Comparison with new exp. data JLab Hall C Hashimoto et al., Nucl. Phys. A804 (2008) 42 Major peaks: as redicted Satellite peaks ? Wait for the final report.

Left ： Hotchi et al., PRC 64 (2001) Λ 51 V, Λ 89 Y, R:Hasegawa et al., PRC 53 (1996) Λ 139 La, Λ 208 Pb 43

.. 44

All the existing exp.data can be explained. Genuine hypernucear states confirmed !

For further example, Brief look at the results of the detailed analysis for 89 Y(  +,K+) 89  Y 46

1. Introduction / Motivation 47

 spin-orbit splitting in heavy hypernuclei as deduced from DWIA analyses of the 89 Y(  +,K + )  89 Y reaction T. Motoba (Osaka E-C U.) D.E. Lanskoy (Moscow State U.) D.J. Millener (Brookhaven Nat. Lab.) Y. Yamamoto (Tsuru U.) Nucl. Phys. A804 (2008) 48

All the 2p-1h configurations adopted 49

CONCLUSION (1)Reproduce cross section ratios among a series of pronounced peaks and sub-peaks. 50

Λ s.p.e. vs. DDHF Mfcal based on realistic interactions 51

52 Peak energies: 28  Si vs. 28  Al H.Hotchi et al, PRC 64(2001) vs. O.Hashimoto et al, NP A804(2008) j  28 Si(p +,K + ) 28  Si E  =-B  (Ex ) 28 Si(e,e’K + ) 28  Al ( ,K + ) CAL s (gs) ?? (gs) (4.7)-15.7, -14.1,-12.3 p (9.6) ?? (11) (12.4)-5.6, -4.0 d (17.6)+0.9

Kinematics for electroproduction process e(p e ) + p(p p )  e’(p e’ )+K + (p K ) +  (p  ) A(p A ) HN(p H ) 53

Express the amplitudes in {S 2 } frame spin- nonflip term (f ) and 3 spin-flip terms (g ‘s) 54

Typical 4 amplitudes (among 16 sets) AW2: Adelseck-Wright, P.R. C 38 (1988) AS1: Adelseck-Shagai, P. R. C 40 (1990) C4: William-JI-Cotanch, P.R. C 46 (1992) SL-A: Mizutani et al. P.R. C 58 (1998) 55

Polarizations much different from each other. need more exp. data 56

Basic Properties of Elementary Amplitudes for  + p →  K + (Physical contents: discussed by Bydzovsky) (e,e’K + ) d 3  /dE e d  e d  K =  x d  /d  K  : virtual photon flux (kinematics) Hereafter we discuss d  /d  K for A ( ,K+)  A 57

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