Satoshi N NakamuraTohoku UniversityHUGS 2010 Lecture14 -17 June 2010 @ Jefferson Lab

Day 2 : #3 and #4

Good reference for Lambda hypernuclei spectroscopy :O.Hashimoto & H.Tamura, Prog. Part. Nucll.Phys. 57 (2006) 564.

LL NeffvHH t Nucleus) (Core

Neff

VN vv L

LN interaction model such as Nimegen and Julich Interaction

NN interaction models with SU(3)F

symmetry, fit to scattering data

Effective Interaction in Nucleus

G-Matrix Calculation

Two-body scattering matrix in medium

1) LN interaction is weaker than NN2) LN spin-spin is weak -> spin-vector pN-hN excitation suppressed3) L isospin=0, only iso-scalor pN-hN excitation for core4) No exchange term

Hypernucleus is long lived baryonic system(10-10s).

12C target

Magic Momentum for (K,p)

Endoergic

Exoergic

1.05GeV/c

L = r x pp, K : s = 0g : s = 1

ΔL = 0

Spin non-flip,

1.05GeV/c

No magic momentum for beam

Recoil momentum is large : Various states populated

Angular mom. stretch, natural parity states[(j>=lN+1/2)-1]N(J<=lL-1/2)L : Jmax lN+lL[(j<=lN-1/2)-1]N(J>=lL+1/2)L : Jmax lN+lL

L production

xL trapped in nucleus

L hypernucleus

Excitation Energy (MeV)

L QF

Substituten [p-1 ] x L[p]

n [p-1 ] x L[p]

n [p-1 ] x L[s]X1/

100

ZA

LC12

L

A : Number of BaryonsL, S : HyperonZ : Charge of nucleus

(p x 6 + n x 5) + L

He4

S

(p x 2 + n ) + S0

(p + n x2 ) + S

He6

LL

(p x 2 + n x 2 ) + Lx2

Updated from: O. Hashimoto and H. Tamura, Prog. Part. Nucl. Phys. 57 (2006) 564.

(2009)

52LV

KEK 12GeV PS K6 beamline Beam 1.4sec/4.0 spill6M / 1012 protons

Central p 1.06 GeV/cMomentum bite +-3%Momentum resolution 0.1%

Pt f6x60 mm2

Superconducting Kaon Spectrometer (SKS)

Beam 1.4sec/4.0 spill6M / 1012 protons

Central p 1.06 GeV/cMomentum bite +-3%Momentum resolution 0.1%

Pt f6x60 mm2 1.06 GeV/c p

0.72 GeV/c KCentral p 0.72 GeV/cMomentum accept. +-10%Angle Accept +- 15 deg.Momentum resolution 0.1%Solid Angle 100msrBending Angle 100 degFlight path ~5m

Max B 3TStored E 10.6MJPole Gap 0.4975mNiTi/Cu conductorHeal leak @ 4K 5WLiq. He Vol. 156 lDispersion 3.2cm/%

Nucleus

n

L

K

p

(Ep, Pp)

(MA, 0) (EK, PK)

)(

)()( 22

LL

mMMB

EMEM

CoreHYP

KKAHYP pppp

Core

Nucleus

L

Binding energyL separation ene.

12C(p, K) 12LC

BNL-AGSEnergy Resolution = 3MeV (FWHM)

KEK-SKSEnergy Resolution = 1.5 MeV (FWHM)

(P.H.Pile et al., PRL 66 (1991) 2585)

(H.Hotch et al., PRC 64(2001) 044302)

sL : n [p-1 ] x L[s]

pL : n [p-1 ] x L[p]

10.76MeV Assumed :BL (12

LCg.s.) = 10.76 MeV

No absolute missing mass calibration

Reference for all (p, K) BL data:BL (12

LCg.s.) = 10.76 +-0.19MeVStatistical error only

11C (3/2-) : Ex = 4.8MeV

KEK E336 1.86 g/cm2 C targetResolution ~ 2MeV (FWHM)

Core configuration shell model + DWIA

)(

.).(

12

x

CMM

sgMME

A

HYP

-BL (MeV)

x.).(

)(

EsgB

mMMB coreHYP

L

LL

Ex : Relative energy to g.s.BL /Mhyp : Absolute energy

L

sL L in L = 0

11C

L

pL L in L = 1

Lcouples weakly to core nucleus.#3 may be

L

L pmixing) config. (Core s)2

3C(4.8MeV;

-

11

11C

Lcouples weakly to core nucleus.#3 may be

L

L pmixing) config. (Core s)2

3C(4.8MeV;

-

11

7LLi is the first L hypernucleus

thoroughly studied by g-ray spectroscopy

Ex(#2) = 2.05Ex(#3) = 3.88

Well known by g-ray spectroscopy .

To be discussed later.

LLLL

fdpsg ,,,0

1

2/9

s

p

d

f

First direct proof of discrete single baryon orbitsin deep inside of nucleus.

(2.82 g/cm2)

ls splitting?Core configuration mixing?

fm1.1:)1(

}/)exp{(1

1)(

0

3/1

0

L

RARR

aRrrf

lsdr

rdf

rcmVrfVU LS

)(1)(

2

0

LL

L

p

Woods-Saxon

MeV2

fm6.0

MeV300

L

L

L

LSV

a

V

One parameters set

“Text book” example of single-particle shell structure.

Many theories :Density dependent non-local L potential

J. Millener, C.B.Dover, A.Gal, Phys. Rev. C38 (1988) 2700.

LNN threebody force and L effective mass in Skyrme-Hartree-FockY.Yamamoto, H.Bando, J.Zofka, Prog.Theo.Phys. 80 (1988) 757.D.E.Lanskoy and Y.Yamamoto, PRC 55 (1997) 2330.

Density dependent relativistic hadron field (DDRH)C.M.Keil, F.Hofmann, H.Lenske, PRC 61 (2000) 064309

Quark-Meson coupling model (QMC)K.Tsushima, K.Saito, J.Haidenbauer, A.W.Thomas, NPA 630(1998) 806

L is still keeping its identity as the first approximation in deep inside of nucleus.

Pauli-blocking effect in a clusterized 3n-quark systemS.Takeuchi and K.Shimizu, Phys.Lett. 179 (1986) 197.

Dover : Distinguishability of L as a hyperon in a nucleus : Int. Symp. On Medium Energy Physics (Beijing) 1987

D.E.Lanskoy and Y.Yamamoto, PRC 55 (1997) 2330.

(PRC-Lanskoy-Yamamoto)

D.E.Lanskoy and Y.Yamamoto, PRC 55 (1997) 2330.

Normal nucleir ~ 1.12 A1/3

r(A=16)~2.8 fmr(A=208)~6.6fm

dR : Core deformation

Pauli-blocking effect in a clusterized 3n-quark systemS.Takeuchi and K.Shimizu, Phys.Lett. 179 (1986) 197.

x : cluster parameterlimit shellQuark : 1

limitBaryon : 0

x

x

Pauli-blocking effect in a clusterized 3n-quark systemS.Takeuchi and K.Shimizu, Phys.Lett. 179 (1986) 197.

x : cluster parameterlimit shellQuark : 1

limitBaryon : 0

x

x

AZp A

L(Z-1)

(p,K) reaction established hypernuclear reaction spectroscopy(e,e’K) has similar features with better resolution

Electromagnetic production Photo/electron strangeness production

Proton goes to Lambda

Both spin flip and non-spin flip amplitudes

High quality primary beam High energy resolution (< 1MeV) Thin enriched target

Real photon (g,K) HY spectroscopy is practically impossible.

Eg. JLab-CLAS Bremsstrahlung tagged photon ~ 5o MHz, 10-3 E0 = 2 MeV for 2 GeV

E91-016 @ JLab-HallC , PRL 93(2004)242501

3He(e,e’K+)3LH

4He(e,e’K+)4LH

12C(g,K+)12LB

ES132 @INS-TAGX, PRC 52 (1995) 1157.

NEXT STEP: Spectroscopy withmass resolution of sub-MeV

R.A.Schmacher for CLAS

Eg ~ 1.5 GeV

for elementary process Max. at Eg ~ 1.5 GeV

Lower Eg : Close unnecessary reaction channel

Higher Eg : Smaller K decay loss, Larger L trapping rate

Eg ~ 2.2 GeV

12C target

Endoergic

Exoergic

1.5GeV/c

)cos()1(2)2cos(

''

3

K

K

LTLK

K

TT

K

LL

K

T

Kee d

d

d

d

d

d

d

d

dddE

df

eef

e

e

ep

a g

1

1'

2 22 Q

E

E

E1

2

2

2

)2/(tan2

1

e

Qe

qe

we

2

2QL

E01-011 : Q2 ~ 0.01 (GeV/c)2 , e~6.5 deg.e ~ 0.04, eL~1.7x10-4

KKee d

d

dddE

d

~

''

3

Virtual but almost real photon

1.2 GeV/c, K+

1.8 GeV, e0.3 GeV/c, e’

pL1.5 GeV, g*

Both of e’ & K+ are forward.

Large e’ Background due to Bremsstrahlungand Mfller scattering

Signal/Noise, Detector

Less Hypernuclear Cross Section

Coincidence Measurement (e’, K+)

Limited Statistics, DC beam is necessary

Continuous beam for coincidence exp.

Electron beam E > 1.5 GeV

High current beam > 30A

Beam stability

Momentum p/p < 1 x 10-4

Good emittance : x < 100m, x’ <1mrad

So far, only JLab CEBAF had been providing such a beam.

E89-009 (HNSS; HyperNuclear Spectrometer System)

SPL + SOS +HMS

Demonstrated that

the (e,e’K) hypernuclearspectroscopy is possible!

12C(e,e’K+) 12LB

PRL 90 (2003) 232502, PRC 73 (2006) 044607

Good energy resolution <900 keV (FWHM)

Best hypernuclear energy resolution achieved by the reaction spectroscopy at that time

sLpL

Energy resolution as well as acceptance are limited by the kaon spectrometer (SOS)

Severe background from electrons associated with Bremsstrahlung (200 MHz for e’ arm)

Tilt Method

New Spectrometer

High resolution Kaon Spectrometer (HKS)

The 2nd Generation Experiment was approved by Jlab PAC19

E01-011 (Spokesmen: Hashimoto, Tang, Reinhold, Nakamura)

Zero degree tagging method to maximize virtual photon flux

ct (K+) ~4m

2005 E01-011 (Hall C)

First step to midium heavy hypernuclei (28Si, 12C, 7Li)

Beam: 30 μA , 1.8GeV

HKS: Δp/p=2 x 10 -4 [FWHM]

Solid angle 16msr(w/ splitter)

ENGE

HKS

Splitter

Electron beam

To beam dump

Target

Two Major Improvements

New HKS

Tilt Method

configuration Split-pole

Momentum

acceptance0.316 GeV/c± 30 %

Momentum

resolution4×10-4 (FWHM)

Configuration QQD

Momentum acceptance 1.2 GeV/c± 12.5 %

Momentum resolution 2×10-4 (FWHM)

Angular acceptance 1°~ 13°

Solid angle 16 msr (w/ splitter)

e’ 0.3 GeV/c

K+ 1.2 GeV/c

e 1.8 GeV

HKS (newly designed)

c.f. E89-009, 183 hours(8.8 mg/cm2, 0.5 or 1.0 uA)

T. Miyoshi et al., Phy. Rev. Lett. 90, 232502(2003)

Better resolution and statistics

~ 3.5 MeV (FWHM)

L1.9 MeV(FWHM)

S2.3 MeV (FWHM)

E01-011~70 hours(450 mg/cm2, 1.5 uA)L

S0

Absolute mass scale calibration

Septum + HRS + HRS

Ee = 4GeV,Pe’= 1.8 GeV/c = 2.2 GeVPK=2.0 GeV/ce, K~ 6 degQ2 = 0.079 (GeV/c) 2

E94-107

~ 640 keV(FWHM)

12LB

12LB : Reference Spectrum w/ best resolution

28LAl : First beyond-p shell HY. by (e,e’K)

7LHe : First reliable data, CSB effect

To be published soon.

#1 #2

Binding energies are consistent with The other (e,e’K) data.

#1 #2#3

First sd-shell hypernuclearspectroscopy by (e,e’K+)

#1 #2#3

#1

First reliable observation of 7LHe w/ good statistics

M.Juric et al. NP B52 (1973) 1

L n

p p

L n

n p

MeV 04.004.2)H,0( 4

LLB

0

1MeV 06.000.1)H,1( 4

LLB

MeV 03.039.2)He,0( 4

LLB

MeV 06.024.1)He,1( 4

LLB

0.35 MeV

0.24 MeV

Coulomb effect is very small.A.R.Bodmer&Q.N.Usmani, PRC 31(1985)1400.

A=4, T=1/2 SystemBL(4

LHe) BL(4LH)0.35MeV (0+)

0.24MeV (1+)

CSB effect by cluster modelE.Hiyama et al.PRC80,054321(2009) Four-body cluster model

Phenomenological potential

A=7, T=1 iso-triplet

L n

p p

L n

n p

L

nn

a L aL

n

a

p p p

CSB effect by cluster modelE.Hiyama et al. PRC80,054321(2009)A=7, T=1 iso-triplet

-6.71±0.03±0.2

CSB effect by cluster modelFour-body cluster model

A=7, T=1 iso-triplet

L n

p p

L n

n p

L

nn

a L

n

ap

L ap p

L

n

a L apa a

A=4, T=1/2 System

A=10, T=1/2 system

4LH, 4LHe

7LHe, 7LLi, 7LBe

10LBe, 10

LB

3LH 4

LH 5LHe

MeV 05.013.0 LB

MeV 04.004.2 LB

MeV 02.012.3 LB

R.H.Dalitz et al. NPB47 (1972) 109.

Dalitz BL(5LHe) = 5.46MeV

5LHe Overbound

Akaishi D2 BL(5LHe) = 3.01MeV

Akaishi D2 BL(4LH) = 0.69MeV

4LH Underbound

K.S.Myint, Y.Akaishi et al. NPA684(2001)592.

L n

p p

S n

n p

S0 n

p p

0+ (g.s.) Lp – SN couple enhance1+ [Lp – SN] –[Ln – SN]cancel

Usually hyperon appears

r ~ 23 r0

Coherent LN-SN coupling maymake L appearance at lower density in asymmetric nuclear matter (Z!=N).

Outer Crust (0.5km) ion, e-

Inner Crust (2km) I n+ e-

Outer Core (9km) I n+ p +e- +

Inner Core (0.3km) I Hyperon?p, K ?Quark?

Study of Pulsers

M < 1.5 Msun

R ~ 10-12km

05.0~ r

02~5.0 r

015~2 r

PRC 64 (2001) 025804

r~2r0: hyperon threshold (S, L), r5r0: hyperon dominates

Hyperon in Neutron Star = Hyperon Star

H.Lenske : GCOE seminar @ Tohoku U.

p

nnn

nep

SLL

L

-Equilibrium

1

Neutron Star Mass-Radius Relation

PRC 64 (2001) 025804

H.Lenske : GCOE seminar @ Tohoku U.

EOS is harder than DDRH(Assuming S interaction is repulsive)

H.Lenske et al.Proc. of HYP2006,p325

JLab E01-011

Medium - Heavy hypernuclei

Light Hypernuclei (s,p shell)

A 1 20 50 200 1057

Elementary Process

Strangeness electro-production

Fine structureBaryon-baryon interaction in SU(3)LS coupling in large isospin hypernucleiCluster structure

HyperonizationSoftening of EOS ?

Superfluidity

Single-particle potentialDistinguishability of a L hyperon

U0(r), mL*(r), VLNN, ...

E01-0117Li 12C 28Si

Neutron/Hyperon star,Strangeness matter

E89-00912C

Medium - Heavy hypernuclei

Light Hypernuclei (s,p shell)

A 1 20 50 200 1057

Elementary Process

Strangeness electro-production

Fine structureBaryon-baryon interaction in SU(3)LS coupling in large isospin hypernucleiCluster structure

HyperonizationSoftening of EOS ?

Superfluidity

Single-particle potentialDistinguishability of a L hyperon

U0(r), mL*(r), VLNN, ...

Neutron/Hyperon star,Strangeness matter

E05-1156,7Li 10,11B 12C 51V 52Cr 89Y

3rd Generation Experiment

E01-0117Li 12C 28Si

E89-00912C

2009 E05-115 (Hall C)

Wide mass range hypernuclear spectroscopy (52LV, 12

LB ,10LBe, 9LLi, 7

LHe )

Major Improvements(10 times more VP tagging )

New HESbest match to HKS

New CalibrationsH2O cell target

Beam energy scan

Target Number of Quasi-Free L(observed)

Quasi-Free L

Cross Section (assumed)

Hypernuclei (g.s)Cross Section(assumed)

Expected number of g.s

7Li 6.4 x104 1.0 b/sr 21 nb/sr 1300

9Be 4.5 x104 1.2 b/sr 4 nb/sr 150

10B 4.8 x104 1.3 b/sr 21 nb/sr 780

12C 3.4 x104 1.5 b/sr 112 nb/sr 2500

52Cr 1.4 x104 4.7 b/sr 69 nb/sr 210

• Cross section of QF L is assumed as 0.2*A0.8 [b/sr]

• # of g.s is calculated as (# of L)*(g.s cross section)/(QF L cross section)• Cross Section of 9Be is derived by Progress of Theoretical Physics Supplement No.117 (1994) pp. 151-175 (M. Sotona and S. Frullani) and other cross sections are summarized in E05-115 experiment proposal (JLab PAC 28 and 33).

FINUDA@DAFNE

0.51 GeV e+, e- colliderF(1020) factory

F KK(EK~16 MeV)

L

pZZK AAstop

~ 0.55 MeV (1.3 MeV FWHM)200mg/cm2 targetLarge SA ~ 3140 msr

12LC

Phys. Lett. B 622 (2005) 35