Structure and production of medium-mass

hypernuclei

HYP2012, Barcelona, Oct. 1-5, 2012

（Osaka E-C) Toshio MOTOBA

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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) 199.

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CONTENTS1. 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: (19F ; 28Si, 40Ca, 52Cr )

4. Propose to use odd-Z targets available in medium-mass region

5. Summay 3

1. Introduction

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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: cf. (e,e’K+), (γ, K+) vs. (K-,π-) and (π＋,K+)

(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

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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) 232502. Γ=0.75 MeV Hall A (bottom), J.J. LeRose et al. N.P. A804 (2008) 116. Γ=0.67 MeV 6

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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

2. A brief review of theoretical treatments for hypernuclear production cross sections

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(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

(A) FACTORIZED VS. (B) MICROSCOPIC

(A) Factorized DWIA treatment by Huefner-Lee-Weidenmuleler, NPA234, 429 (1974)

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　α= kinematical factor for A-body to 2-body transformation, Neff= Effective neutron number :

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(A-1) Meson waves by the Eikonal approximation

(A-2) Meson DW with the Klein-Gordon solutions

Applicable to forward scattering, 10-20% error of K-G DW ( Auerbach et al (1983).

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PW vs. DW (1) DW effect In a typical (π+,K+): Neff = 0.184 (PW) 0.030 (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

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(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

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M. Sotona and J. Zofka described the πnàΛΚ 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.

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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

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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) 17.

3. Electro/photo-production of sd-shell hypernuclei

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- Microscopic cal. based on elem. ampl. - DW: solution of the Klein-Gordon eq. - Emphasize the importance of taking account of nuclear core excitation effects

Hyperon recoil momentum and the transition operator determine the

reaction characteristics

qΛ=350-420 MeV/c at Eγ=1.3 GeV

Lab dσ/dΩ for photoproduction (2Lab)

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Spin-flip interaction are dominant

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 jp and large jΛ

(e,e’K+) d3σ/dEe dΩe dΩK = Γ x dσ/dΩK Γ　: virtual photon flux (kinematics)

Hereafter we discuss dσ/dΩK for AZ (γ,K+)ΛAZ’ 19

3-1. The simplest sd-shell target

Choose the 19F(1/2+) target (16O+p+2n ) for demonstration of the hypernuclear

photoproduction

(asking the feasibility as a practical target )

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外側の軌道

19F(η ,K+) η19O 16O 閉殻

陽⼦子の軌道中性⼦子の軌道

0d3/2 1s1/2 0d5/2 0p1/2 0p3/2 0s1/2

0d3/2 1s1/2 0d5/2 0p1/2 0p3/2 0s1/20d3/2 1s1/2 0d5/2 0p1/2 0p3/2 0s1/2

0d3/2 1s1/2 0d5/2 0p1/2 0p3/2 0s1/2

0d3/2 1s1/2 0d5/2 0p1/2 0p3/2 0s1/2

0d3/2 1s1/2 0d5/2 0p1/2 0p3/2 0s1/2

Λ 粒粒⼦子の⽣生成軌道

8M eV

-2.5M eV

-13M eV

E

0d3/2 1s1/2 0d5/2 0p1/2 0p3/2 0s1/2

0d3/2 1s1/2 0d5/2 0p1/2 0p3/2 0s1/20d3/2 1s1/2 0d5/2 0p1/2 0p3/2 0s1/2

0d3/2 1s1/2 0d5/2 0p1/2 0p3/2 0s1/20d3/2 1s1/2 0d5/2 0p1/2 0p3/2 0s1/2

0d3/2 1s1/2 0d5/2 0p1/2 0p3/2 0s1/2

Choose 19F(1/2+) target for demonstration

neutron proton

Λ (DDHF)Shell-model configuration

0

5

10

15

20

25

30

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-13 -2.5 -2.3 8.3 8.4 8.5エネルギー　〔M eV〕

生成断面積〔μb／ｓｒ〕

1s1/2 軌道から

0d5/2 軌道から

Conversion of 1s1/2-proton(nb/sr) cf. A trial calculation: If the last odd proton were in 0d5/2, then

Partial contributions　

　1s1/2軌道からの生成断面積

0

10

20

30

40

50

60

-20 -15 -10 -5 0 5 10 15 20

ハイパー核励起エネルギー〔ＭｅＶ〕

⽣生成断⾯面積〔μb/sr〕

s p

d

0p1/2軌道からの生成断面積

0

5

10

15

20

25

30

35

-20 -15 -10 -5 0 5 10 15 20

ハイパー核励起エネルギー〔ＭｅＶ〕

生成断面積〔μb/sr〕

s

p

d

0p3/2軌道からの生成断面積

0

5

10

15

20

25

30

35

40

-20 -15 -10 -5 0 5 10 15 20

ハイパー核励起エネルギー〔ＭｅＶ〕

生成断面積〔μb/sr〕

s

d

p

Partial contributions from core-excitation　

(use arbitrary widths for proton p1/2 and p3/2.)

Conversion of 0p1/2 à Λ (s,p,d) Conversion from 1p3/2

γ線によるハイパー核Λ19Oの生成断面積

0

10

20

30

40

50

60

-20 -15 -10 -5 0 5 10 15 20

ハイパー核励起エネルギー〔ＭｅＶ〕

生成断面積〔μb/sr〕

合計

1s1/2

0p1/2

0p3/2

19F(γ,K+) Λ19O SUM of the partial contributions　

As a “closed core (18O)”+ Λ , cf. SO-splitting(0p)=152+-54 keV(C13)

Exp. C2S for p-pickup from 16O core

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

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Umeya’s Calculation

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Umeya’s Calculation

A typical example of medium-heavy target:28Si: assuming (d5/2)6 closure.

to show characteristics of the (γ,K+) reaction with DDHF w.f.

( Spin-orbit splitting:

consistent with Λ7Li, 9Be,13C, 89Y ) 29

3-2. Single-j model for the 28Si target to show the selectivity

Theor. x-section for (d5/2)6 (γ,K+) [ ｊh-ｊΛ]J

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3-3. Realistic prediction for 28Si (γ,K+) Λ28Al compared with exp.

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By fully taking account of -- full p(sd)6.n(sd)6 configurations, -- fragmentations when a proton is converted, -- 27Al core nuclear excitation -- K+ wave distortion effects à Comparison with the 28Si (e,e’K+) exp.

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

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33 33

Proton pickup from 28Si(0+):(sd)6 =(d5/2)4.1(1s1/2)0.9(d3/2)1.0

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Peaks can be classified by the characters

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Exp. data: O. Hashimoto et al, Nucl. Phys. A 835 (2010) 121 (waiting for the finalization of analysis)

36 3636

Peak energies: 28ΛSi vs. 28ΛAl H.Hotchi et al, PRC 64(2001) vs. O.Hashimoto et al, NP A804(2008)

j Λ

28Si(p+,K+)28ΛSi EΛ=-BΛ (Ex )

28Si(e,e’K+)28ΛAl (as read on the Sendai08 poster)

(γ,K+) CAL

s -16.6+-0.2 (GS) -17.85 ?? (GS) -16.6 (GS)

-15.7 ? -13.0 ? -10.8 ?

-11.9+-0.4 (Ex=4.7)

p -7.0+-0.2 (Ex=9.6) - 6.88 +- ?? (Ex=11) -8.1 ( Ex=8.5)

-4.3+-0.2 (Ex=12.4) -5.6, -4.0

d +1.0+-0.8 Ex=17.6) + 1.35 +/- (Ex=19.2) +0.9 (Ex=17.5)

52Cr: (f7/2)4 assumed 40Ca: (sd-shell LS-closed)

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3-4. Extend to heavier nuclear targets

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

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

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

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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

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Single-particle energies of　Λ G-matrix results vs. experiments

(Y. Yamamoto et al.: Prog. Ther. Phys. S.185 (2010) 72. )

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Sd- and fp-shell data are quite Important to extract the Λ behavior in nuclear matter.

Available odd-Z targets

43 ( feasibility to be checked by experimentalists )

SUMMARY and PROSPECTS

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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 core-excitation effects. The prediction for 28ΛAl is well compared with the recent experiments.

3) Predictions are made also for heavier typical targets, 40Ca and 52Cr, showing fruitful aspects.

.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, µΛ , eeff (Λ), etc )

Remark: The present frameworks apply also to   Ξ-hypernuclear production with sd-shell   targets which might be fruitful at J-PARC.

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