Magnetic Moment of a in a Nucleus H. Tamura Tohoku University 1. Introduction 2. -ray spectroscopy of hypernuclei and spin-flip B(M1) 3. Experiments.

Magnetic Moment of a in a Nucleus

H. TamuraTohoku University

1. Introduction

2. -ray spectroscopy of hypernuclei and spin-flip B(M1)

3. Experiments at J-PARC

4. Summary

1.1. IntroductionIntroduction

Motivation for in nucleusNuclear medium effect is not well studied for baryons.

Detection of the effect is not easy.

Magnetic moment of in a hypernucleus

Hyperons are free from Pauli effect

long lifetime (~0.2 ns), stays in 0s orbit

( and short lifetime in medium by N->N, N->)

Partial restoration of chiral symmetry

-> Reduction of mass ? Partial deconfinement?

　　　　 -> N changes? No theoretical calculations

-- Clue to understand the origin of baryon magnetic moment

Constituent quark: B looks OK with q=eh

2mqcmq: constituent quark mass

Nucleon spin = quark spin (~0.2) + gluon spin + L

how to understand B ?

Other effects for in nucleus

Pauli effect between quarks (“quark exchange current”) Changes B in nucleus Sensitive to baryon size (b)

Meson exchange current Rather small for (OPE forbidden)　

mixing Large for large T hypernuclei

Quark Cluster Model Takeuchi et al., N.P. A481(1988) 639

/ : 4He(1+) -1% ~ -2%, larger by mixing

4+Li(1+) -40% ~ -100%

b = 0.6 fm -> 0.8 fm, becomes twice large.

Saito et al.,

N.P. A625 (1997) 95

Spin-flip B(M1) and g in nucleus

How to measure in nucleus?

Direct measurement of : extremely difficult. “Dream Experiment” -- Planned at GSI using relativistic HI beams

B(M1) of -spin-flip M1 transition -> g

Established for “hypernuclear shrinkage” in 7

Li from B(E2) : PRL 86 (’01)1982

core nucleus

Jc

Jc +1/2

Jc -1/2

M1

in s-orbit

"hypernuclear fine structure"

g

hypernucleus

ψ↑ψc

ψ↓ψc

Doppler Shift Attenuation Method~100%

Assume “Weak coupling” between a and core

2. 2. -ray spectroscopy-ray spectroscopy

of of hypernuclei hypernuclei

and spin-flip B(M1)and spin-flip B(M1)

Hypernuclear -ray data since 1998

“Table of Hyper-Isotopes”

=> Information onN spin-dependentinteractions

Two-body N effective interaction Dalitz and Gal, Ann. Phys. 116 (1978) 167Millener et al., Phys. Rev. C31 (1985) 499

= 0.4 S = -0.01 SN = -0.4 T = 0.03 MeV

Setup for AZ (+,K+) AZ at KEK

SKS @KEK-PS

Hyperball2 (2005~)

-ray spectrum of 7Li

(KEK E419)

H. Tamura et al., PRL 84 (2000) 5963

E ~ 2 MeV (FWHM)

E ~ 3 keV (FWHM)

Tanida et al., PRL 86 (2001) 1982

Lifetime measurement by Doppler shift attenuation method (DSAM)

Hypernucleusin excited state

γray emissionbefore stop B ｒ = 93.8 -0.8 %

+3.6

1/2+

3/2+

5/2+

Weak decay

Lifetime

γray emissionafter stop

tstop ~ 12 psSame order

B(E2) = 3.6 ±0.5 +0.5 e2fm4 -0.4

“Shrinkage by ” was confirmed. K. Tanida et al., PRL 86 (2001) 1982

7Listudy from 10B(K-,-) at BNL(E930)

10B (K-,- ) 10B*(3+) -> 7

Li* +3He

471 keV coincidence

coin

First coincidence for hypernuclei

All the bound states determined Ukai et al., PRC 73 (2006) 012501

10B*(3+) -> 7

Li*(3/2+) + 3He10B (K-, -) 10B*,

simulation

First data of g in nucleusg = -1.1 N

+0.6- 0.4

preliminary (statistical error only)

g(free) = - 1.226 N

Spin-flip B(M1) in 7Li (BNL E930)

indirect population

Indirect population => more background, ambiguities in production

Prelim

inary

11B rays from 12C(+,K+)12

C

highly excited states region

1481.7±0.7 keV

p states region

261.6±0.2 keV

Unfortunately, E is too low -> 1/ ∝E3 , then >> tstop

-> No broadening. DSAM unusable.

Another attempt:using low density target (CH2:polyethylene) for DSAM

1.036+ 2.453 S + 0.039 SN - 3.330 T

~ 450 keV by Millener

spin-spin int.

3. Experiments at J-PARC3. Experiments at J-PARC

J-PARC (Japan Proton Accelerator Research Complex)

J-PARC (Japan Proton Accelerator Research Complex)

Tokai, JapanTokai, Japan

World-highest beam intensity : ~1 MW x10 of BNL-AGS, x100 of KEK-PS

Material and Biological Science Facility

50 GeV Synchrotron (15 A)

400 MeV Linac (350m)

3 GeV Synchrotron (333 A)

Neutrino Facility

Hadron Hall60m x 56m

Under commissioning

K1.8 will run from the summer, 2009

J-PARC 50 GeV facilityTokai, Japan

Handron Hall

Beam Dump

T1 target

K1.8

K1.8BR

K1.1S-type

KL

K0.8C-type

30GeV primary beam (phase 1)

Hyperball-J

productiontarget (T1)

SKS

Hyperball2 (2005~) -> Hyperball-JSKS @KEK-PS

Proposed B(M1) measurement (E13)

To avoid ambiguities, we will use the best-known hypernucleus, 7Li.

Energies of all the bound states and B(E2) were measured. -ray background level was measured. Cross sections are reliably calculated. = 0.5ps, tstop = 2-3 ps for 1.5 GeV/c (K-,-) and Li2O target

Calc. by Motoba(K-,-) at 1.5 GeV/c

PRL 84 (2000) 5963PRC 73 (2006) 012501

Weak coupling assumption is OK?

B(M1) [N2 ] method

0.322 5He+p+n cluster model (Hiyama et al.)

0.309 shell model (Motoba et al.)

0.352 +d+cluster model (Motoba, old)

0.364 shell model (Gal, old)

0.326 shell model (Gal, old)

The variation gives a rough magnitude of nuclear effect.

Theoretical predictions without exotic effects

7Li (3/2+->1/2+)

Expected yield and sensitivity Yield estimateNK = 0.5 x 106 /spill

Target (7Li in Li2O) = 20cm x 2.0g/cm3 x 14/30 x 0.934 / 7 x 6.02x1023

∫d/d(1/2;1) x BR(1/2+;1->3/2+) = 0.84 b x 0.5

(Ge) x (tracking) = 0.7 x 0.6

=>

Yield (3/2+->1/2+) = 7.3 /hr(1000 spill)

= 3600 / 500 hrs Background estimated from E419 7

Li spectrum

Fitting result: 0.478±0.027 ps Syst. error < 5%

mainly from stopping time

Stat. error /5.4%|g-gc|

|g-gc|~ 3%=>

Future possibility

If a large shift of B(M1) is observed,

and T dependence should be studied from various hypernuclei

Meson-exchange current, mixing => T dependence Restration of chiral symmetry => dependence

(M1) ~ tstop (condition for DSAM) cannot be often satisfied. Heavier hypernuclei -> smaller doublet spacing -> longer (M1) ~ (weak decay)

Another method for longer (M1) is necessary.

Proposed method:B(M1) measurement

by -weak coincidence

900 hours, 9x106 K-/spillat K1.1 (50 GeV full beam) -> 5% stat. error of B(M1)

12C case

How to measure lifetimesfor hypernuclear transitions

1 W.u.

1 W.u.

7Li

4H

11B

12C

Spin-flip M1

7Li

9Be

E2

4. Summary

Magnetic moment of a in hypernuclei provides an opportunity to study nuclear medium effect of baryons.

Theoretical predictions are welcome.

g can be studied from B(M1) of -spin-flip M1 transition.

B(M1) measurement is one of the most important subjects in our

spectroscopy project.

Using Doppler shift attenuation method, the first B(M1) result was obtained for 7

Li with a large error.

The new J-PARC experiment will provide us with B(M1) of 7Li with

accuracy of ~5%. Preparation is going on.

For slow M1 transitions, B(M1) measurement with “-weak coincidence method” is proposed.

Predicted by Motoba, Bando, Ikeda　　　 Prog.Theor.Phys. 70 (1983) 189.

　　 4He + d + model 　～ 20% shrinkage

B(E2) |<f| e r∝ 2 Y2 |i>|2

∝R4 or (<r2>)2

R <r2>

Hiyama et al. PRC 59 (1999) 2351, NPA684(2001)227 　　

　　　 5He + p + n, 4He + p + n +

Shrink between 5He – pn distance

22% shrinkage

Confirmation of shrinking effect by