木曜の輪講

11/25/2010T.Gogami

Paper

The experiment was performed in 1997 - 1998

Abstract

12C

2𝑝32

1 𝑓72

1𝑑32

2𝑠12

1𝑑52

1𝑝12

1𝑝32

1𝑠12

1 𝑓52

2

8

20

28

2𝑝12 40

1𝑔92

p = 6 n = 6

FULL FULL

FULLFULL

51V

2𝑝32

1 𝑓72

1𝑑32

2𝑠12

1𝑑52

1𝑝12

1𝑝32

1𝑠12

1 𝑓52

2

8

20

28

2𝑝12 40

1𝑔92

p = 23 n = 28

FULL

FULLFULL

FULL

FULLFULL

FULL

FULLFULL

FULL

FULLFULL

FULL

89Y

2𝑝32

1 𝑓72

1𝑑32

2𝑠12

1𝑑52

1𝑝12

1𝑝32

1𝑠12

1 𝑓52

2

8

20

28

2𝑝12 40

1𝑔92 FULL

p = 39 n = 50

FULL

FULLFULL

FULL

FULLFULL

FULL

FULL

FULLFULL

FULL

FULLFULL

FULL

FULLFULL FULL

FULLFULL

Flow chart

1. Introduction2. Experimental apparatus3. Data analysis4. Experimental results5. discussion

Introduction 1Λ hypernuclei investigation– Deep inside nucleus– Y-N interaction– Narrow intrinsic width

• Medium Λ hypernuclei– Behavior in nuclear medium• Effective mass• Potential depth

– Spin-orbit splitting

Introduction 2

• (K-,π-)– Light hypernuclei

• (π+,K+)– Heavy hypernuclei(Thiessen , Dover et al.)

• At BNL51

ΛV , 89ΛY

≈3 [MeV] (FWHM)

• At KEK (KEK-ps E140a) 92 - 9310

ΛB , 12ΛC , 28

ΛSi , 89ΛY , 139

ΛLa , 208

ΛPb≈2 [MeV] (FWHM)

(π+,K+) experiments

ud

ddu

us

sdu

– –π+

Λn

π+ + n ➝ K+ + Λ

us

ddu

ud

sdu

–K-

Λn

–π-

K- + n ➝ π- + Λ

K+

Introduction 3

High statistics and resolution exp. have been long awaited !

KEK-ps E140a208Pb(π+,K+)208

ΛPbPπ+=1060 MeV/c

Phys. Rev C , Vol.53 – 3, 1996 , T.Hasegawa(Fig.10)

Phys. Rev C , Vol.38 – 3 , 1988 , T.Motoba(Fig.2)

Introduction 4

• In this paper– KEK-PS E369– 12

ΛC , 51ΛV , 89

ΛY via (π+,K+)– Best energy resolution ( < 2 [MeV] FWHM )– High statics ( E140a × 8 )

(π+,K+) experiment

𝑀𝐻𝑌=√ (𝐸 𝜋+𝑀𝐴−𝐸𝐾 ) 2−(𝑝 𝜋 2+𝑝𝐾 2−2𝑝𝜋 𝑝𝐾 𝑐𝑜𝑠 𝜃)π+

np

Λ

K+

θ

𝑀𝐻𝑌𝑀 𝐴

Measure:

-BΛ = MHY – MCore - MΛ

Experimental setup

K+

0.72 [GeV/c]

π+

1.05 [GeV/c]

Δp/p ≈ 10-4

Δp/p ≈ 10-3

BEAM ≡ BH1×BH2×eGCPIK ≡ BEAM× TOF × AC ×LC

Lucite Cherenkov

Aerogel Cherenkov

Rate:180 / (1.5e+6 / spill)

Beta:• βP =0.61• βK+ =0.82• βπ+ =0.98

Analysis

Momentum measured by SKS

TOF measurement

Kaon PID in offline analysis

target

BH2

K+

π+

Angular cut

≥2 [deg]

Energy calibration

During 89Y(π+,K+)89ΛY

12ΛC : 10.76±0.19 [MeV/c] by emulsion

(Nucl. Phys. A547 (1992)369c-378c , D.H.Davis)

Systematic Error:Fitting + Linearity + E• 12

ΛC : 0.17• 89

ΛY,51ΛV : 0.23

Cross section

• Systematic error– Beam , ≈ ±7%– Effective solid angle ≈ ±1%– Target thickness

– Total• 12

ΛC , 89ΛY : ±9%

• 51ΛV : ±10%

Table.1

Results

89Y(π+,K+)89ΛY 51V(π+,K+)51

ΛV 12C(π+,K+)12ΛC

1.45 [MeV] (FWHM)KEK-PS E36989Y(π+,K+)89

ΛYKEK-PS E36951V(π+,K+)51

ΛV KEK-PS E36912C(π+,K+)12

ΛC

89Y(π+,K+)89ΛY

Energy separations are getting wider as increase ! Spin-orbit splitting

Fitting resultKEK-PS E36989Y(π+,K+)89

ΛY

Parameters :

89Y(π+,K+)89ΛY

KEK-PS E36989Y(π+,K+)89

ΛY

Λ single particle potential (Woods-Saxon)

Distorted Wave Impulse approximation (DWIA)( Phys. Rev C , Vol.38 – 3 , 1988 , T.Motoba )

Global bump OKIntensity ratio NO

Effective mass in the nuclear medium

Y.YamamotoAssuming Λ l-s splitting to reproduce the double peak.• NHC-F

• NSC97f

M.M.Nagels , Phys. Rev. D , 20 , 1633 (1979)T.A.Rijken , Phys. Rev. C , 59 , 21 (1990)

KEK-PS E36989Y(π+,K+)89

ΛY

Conclusion

• 12ΛC , 51

ΛV , 89ΛY

• 1.65 [MeV] (FWHM) BEST !• 51

ΛV , 89ΛY

– s , p , d , f bump !– Λ l-s splitting ?

(e,e’K+) reaction

uud

ussud

e e

–pK+

Λ

γ*

ud

ddu

us

sdu

– –π+

Λn

us

ddu

ud

sdu

–K-

Λn

–π-

e + p ➝ e + K+ + Λ π+ + n ➝ K+ + Λ

K+

K- + n ➝ π- + Λ

(π+ , K+) (K- , π-)(e,e’K+)

Momentum transfer(pbeam = 1.5 [GeV/c] )

~300 [MeV/c] ~300 [MeV/c] ~90 [MeV/c]

Λ’s Spin

Λ’s from proton neutron neutron

flip ≈ non-flip non-flip non-flip

Beam primary secondary secondary

Target Thin (~100 mg/cm2)(Isotopically enriched)

Thick(> a few [g/cm2] ) Thick(> a few [g/cm2] )

Reaction

Λ can be bounded in deeper orbit

Spin dependent structure

Mirror lambda hypernuclei

High quality , high intensity

Fine structureEnergy resolution

(FWHM)≤ 500 [keV] 1 – 3 [MeV] 1 – 3 [MeV]

Spectroscopic experiment via (e,e’K+) reaction

p

n

γ*

ΛK+

e-

e + p ➝ e’ + K+ + Λe e

M2HY = (Ee + MT - EK+ - Ee’)2 - ( pe - pK+ - pe’)2

measuretarget nucleus

Feynman diagram

uud

ussud

–pK+

Λ

γ*

Missing mass :

•Binding energy•Cross section

Strangeness 2010 at KEK

JLab E05-115 experimental setup

2×10-4

7 [msr]3 – 12 [deg] 2×10-4

11 [msr]2 – 12 [deg]

e + p → e’ + Λ + K+

7Li , 9Be , 10B , 12C , 52Cr

Jlab E05-115

In the future

51V(π+,K+)51ΛV

KEK-PS E369 Gogami D論

52Cr(e,e’K+)52ΛV

Coun

t [/2

50[k

eV/c

2 ]]

∆𝐸𝐸

=500[keV ]

End