Structure and production of medium-mass hypernuclei

Transcription

1 Structure and production of medium-mass hypernuclei HYP2012, Barcelona, Oct. 1-5, 2012 (Osaka E-C) Toshio MOTOBA 1

2 Talk is based mostly on T. Motoba, P. Bydzovsky, M. Sotona, and K. Itonaga, Prog.Theor. Phys. S.185 (2010) 224. P. Bydzovsky, M. Sotona, T. Motoba, K. Itonaga, K. Ogawa, and O. Hashimoto, Nucl. Phys. A 881 (2012)

3 CONTENTS 1. Introduction/ Basic motivations for spectroscopy of medium-heavy hypernuclei 2. A brief review of theoretical framework for hypernuclear production reaction 3. Electro/Photo-production of sd-shell hypernuclei: Theoretical results with typical targets: ( 19 F ; 28 Si, 40 Ca, 52 Cr ) 4. Propose to use odd-z targets available in medium-mass region 5. Summay 3

4 1. Introduction Why medium-mass hypernuclei? Basic motivation (1) : The great success of JLab Hall A and Hall C experiments : -- sub-mev resolution ( Γ= 0.5 MeV) -- p-shell theor. predictions: confirmed These facts encourage extension of high-resolution reaction spectroscopy to heavier hypernuclei: 4

5 (K -,π - ) (π +,K + ) played a great role of exciting high-spin series Γ = 1.5 MeV (best) (e,e K + ), (γ, K + ) Motoba. Sotona, Itonaga, Prog.Theor.Phys.S.117(1994) T.M. Mesons & Light Nuclei (2000) updated w/nsc97f JLab Exp t : Γ = 0.5 MeV 5

6 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.----à Hall C (up) T. Miyoshi et al. P.R.L.90 (2003) Γ=0.75 MeV Hall A (bottom), J.J. LeRose et al. N.P. A804 (2008) 116. Γ=0.67 MeV 6

7 Why medium-mass hypernuclei? Basic motivation (2) Unique characteristics of the (e,e K + ), (γ, K + ) process are based on the basic properties of elementary amplitudes for γ p ΛK + : --- sizable momentum transfer to excite high-spin states, like (π +,K + ) --- spin-flip dominance of the operator, leading to unnatural parity states 7

8 2. A brief review of theoretical treatments for hypernuclear production cross sections (π+,κ+) (γ, Κ+) (Κ-,Κ+) Three factors: 1. PW vs. DW ( DW effects ) 2. Microscopic treatment with elem. amplitudes, 3. Nuclear core excitation effects 8

9 (A) FACTORIZED VS. (B) MICROSCOPIC (A) Factorized DWIA treatment by Huefner-Lee-Weidenmuleler, NPA234, 429 (1974) α= kinematical factor for A-body to 2-body transformation, Neff= Effective neutron number : 9

10 (A-1) Meson waves by the Eikonal approximation Applicable to forward scattering, 10-20% error of K-G DW ( Auerbach et al (1983). (A-2) Meson DW with the Klein-Gordon solutions 10

11 PW vs. DW (1) DW effect In a typical (π+,k+): Neff = (PW) (DW) (2) XS to low-j states are much more reduced, resulting in the sharper peaks (3) Low-L partial waves are reduced by distortion 11

12 (B) Microscopic treatment based on the elementary transition amplitudes (π,k) case Elementary amplitude N à Y f = spin-nonflip, g= spin-flip, σ= baryon spin 12

13 M. Sotona and J. Zofka described the πnà ΛΚ cross sections and polarization data in terms of f and g elementary amplitudes so as to be easily applied to hypernuclear production. J. Zofka stayed at INS where O. Hashimoto was preparing the (p+,k+) experiment. 13

14 R(i,f ;M) is expressed with three kinds of the reduced effective numbers (microscopic) Magnetic subspace population P(i,f : M) is defined by Polarization of Hypernuclear state Jf > is calculated by 14

15 H. Bando, T. Motoba, M. Sotona, J.Zofka, Phys. Rev. C30 (1989) 584, K. Itonaga, T. Motoba, O. Richter, M. Sotona, Nucl. Phys. A 547 (1992) 57. K. Itonaga, T. Motoba, M. Sotona, Prog. Theor. Phys. Suppl.117 (1994)

16 3. Electro/photo-production of sd-shell hypernuclei - Microscopic cal. based on elem. ampl. - DW: solution of the Klein-Gordon eq. - Emphasize the importance of taking account of nuclear core excitation effects 16

17 Hyperon recoil momentum and the transition operator determine the reaction characteristics q Λ = MeV/c at Eγ=1.3 GeV

18 Lab dσ/dω for photoproduction (2Lab) Spin-flip interaction are dominant 18

19 These characteristic merits of the γp Λ K + process(ability to excite high-spin unnatural-parity states) should be realized better in heavier systems involving large j p and large j Λ (e,e K + ) d 3 σ/de e dω e dω K = Γ x dσ/dω K Γ : virtual photon flux (kinematics) Hereafter we discuss dσ/dω K for A Z (γ,k+) ΛA Z 19

20 3-1. The simplest sd-shell target Choose the 19 F(1/2 + ) target ( 16 O+p+2n ) for demonstration of the hypernuclear photoproduction (asking the feasibility as a practical target ) 20

21 Choose 19 F(1/2 + ) target for demonstration 0d 3/2 1s 1/2 0d 5/2 0p 1/2 0 外側の軌道 0d 3/2 1s 1/2 0d 5/2 0p 1/2 0p 3/2 0 1s 1/2 0d 5/2 0p 1/2 0p 3/2 0s 1/2 E 0d 3/2 1s 1/2 0d 3/2 1s 1/2 0d 8M 5/2 0 1s ev 1/2 0d 5/2 0p 1/2 0 0d 5/2 0p 1/2 0p 3/2 0s 1/2 16 0pO 1/2 0p 3/2 0s 1/2 閉殻 0p 3/2 0s 1/2 Shell-model 中性 子の軌道 configuration 陽 子の軌道 neutron proton 0d 5/2 0p 1/2 0p 3/2 0 0p 1/2 0p 3/2 0s -2.5M 1/2 ev 0p 3/2 0s 1/2-13M ev Λ 粒粒 子の 生成軌道 (DDHF)

22 Partial contributions Conversion of 1s 1/2 -proton(nb/sr) 1s1/2 軌道からの生成断面積 60 cf. A trial calculation: If the last odd proton were in 0d 5/2, then s p ハイパー核励起エネルギー MeV d 生成断 面積 μ b/sr 生成断面積 μb/sr s1/2 軌道から 0d5/2 軌道から エネルギー M ev

23 Partial contributions from core-excitation Conversion of 0p 1/2 à Λ (s,p,d) 0p1/2 軌道からの生成断面積 p s d 生成断面積 μb/sr Conversion 0p3/2 軌道からの生成断面積 from 1p 3/2 d p s 生成断面積 μb/sr ハイパー核励起エネルギー MeV (use arbitrary widths for proton p1/2 and p3/2.) ハイパー核励起エネルギー MeV 0

24 SUM γ of 線によるハイパー核 the partial Λ19O の生成断面積 contributions 合計 1s1/2 0p1/2 0p3/2 19 F(γ,K + ) Λ 19 O 生成断面積 μb/sr ハイパー核励起エネルギー MeV 0 As a closed core ( 18 O) + Λ, cf. SO-splitting(0p)= kev(c13)

25 Exp. C 2 S for p-pickup from 16 O core 25

26 Lightest sd-shell target: 19 F A s: p1/2-hole series, B s: p3/2-hole series 26

27 Umeya s Calculation 27

28 Umeya s Calculation 28

29 3-2. Single-j model for the 28 Si target to show the selectivity A typical example of medium-heavy target: 28 Si: assuming (d 5/2 ) 6 closure. to show characteristics of the (γ,k + ) reaction with DDHF w.f. ( Spin-orbit splitting: consistent with Λ7 Li, 9 Be, 13 C, 89 Y ) 29

30 Theor. x-section for (d 5/2 ) 6 (γ,k + ) [ j h -j Λ ]J 30

31 3-3. Realistic prediction for 28 Si (γ,k + ) Λ 28 Al compared with exp. 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 à Comparison with the 28 Si (e,e K + ) exp. 31

32 proton-state fragmentations should be taken into account to be realistic 32

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

34 Peaks can be classified by the characters 34

35 Exp. data: O. Hashimoto et al, Nucl. Phys. A 835 (2010) (waiting for the finalization of analysis)

36 Peak energies: 28 Λ Si vs. 28 Λ Al H.Hotchi et al, PRC 64(2001) vs. O.Hashimoto et al, NP A804(2008) j 28 Si(p +,K + ) 28 Λ Si 28 Si(e,e K + ) 28 Λ Al Λ E Λ =-B Λ (Ex ) (as read on the Sendai08 poster) (γ,k + ) CAL s (GS) ?? (GS) (GS) -15.7? -13.0? -10.8? (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) 36 36

37 3-4. Extend to heavier nuclear targets 52 Cr: (f 7/2 ) 4 assumed 40 Ca: (sd-shell LS-closed) 37

38 52 Cr ( j > dominant target case) typical unnatural-parity high-spin states 38

39 Well-separated series of peaks due to large q and spin-flip dominance: j > =l+1/2, j < =l-1/2 39

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

41 4. Propose to use odd-proton targets in sd- and fp-shell regions: Λ energies within sub-mev resolution Λ hyperon on the 0+ core Λ coupled with core-excited configuration 41

42 Single-particle energies of Λ G-matrix results vs. experiments (Y. Yamamoto et al.: Prog. Ther. Phys. S.185 (2010) 72. ) Sd- and fp-shell data are quite Important to extract the Λ behavior in nuclear matter. 42

43 Available odd-z targets ( feasibility to be checked by experimentalists ) 43

44 SUMMARY and PROSPECTS 1) Based on the elementary amplitudes, the microscopic theoretical framework for hypernuclear production XS were discussed. 2) Several photo-production spectra have been calculated by taking account of major coreexcitation effects. The prediction for 28 ΛAl is well compared with the recent experiments. 3) Predictions are made also for heavier typical targets, 40 Ca and 52 Cr, showing fruitful aspects. 44

45 4) Medium-mass hypernuclear production. by (e,e K+) provide us with good opportunities in understanding the details of the hyperon motion in nuclear matter. (Λ-s.p.e. to establish textbook, Rotation/Vib.-Λ coupling, Auger effect, µ Λ, e eff (Λ), etc ) Remark: The present frameworks apply also to Ξ-hypernuclear production with sd-shell targets which might be fruitful at J-PARC. 45