Status of three-nucleon force study by nucleon-deuteron system

Status of three-nucleon force study by nucleon-deuteron system

August 22, 2006FB18, Santos, Brazil

1. Introduction

2. dp elastic measurements by NUCLOTRON at DUBNA

3. How far we understand 3NF effects?

4. How data are reliable ?

5. Facilities

6. Summary

H. Sakai

Department of Physics

The University of Tokyo

1. Introduction

How 3NF are established

by experiments?

How to study 3NF?

2BS

3BS

2NF

3NF

3NF is much smaller than 2NF.

　　→ 3NF effects are easily masked by 2NF effects.

1 Equations of motion for 3BS must be solved exactly. →Faddeev eq.

2 Realistic modern 2NF must be established. x2 1 for 4,000 data points.

CD Bonn AV18

Nijmegen I/II Main differences are off-shell properties.3 2πexchange 3NF (Fujita-Miyazawa)

TM99 Urbana IX (U9)

New development in theory

1 PT

2 Relativistic effects

3 Coulomb effects

Why Nd measurements at intermediate energies?

•H.Witała et al., 　 PRL 81(1998) 1183.

　　　→ Go to higher energies for Nd elastic scatt.

and look at X-sec. minimum region.

Typical mom. transfer: 1.5--3 fm-1 for Nd scatt. at intermediate energies.

D-state of deuteron mainly contributes in the reaction.

At intermediate energy, this may correspond to x-sec. min.

internal mom. dist. of deuteron

Reactions for Nd system

Observables (Nd-sys.)

d/d

AP (Ay, iT11, T20, T21, T22) VLS, (VLS)2, VT, D-state

PT (Kij, Kij

k) V (spin-spin int.)

SC (Ci,j, Ci,jk, Cij,k) V 　

　　 q(fm-1)@135 MeV1 elastic scattering 0--2.4--3.4 (0º--90º--180º)

2 breakup (FSI, QFS, Space star) 　　 0--3

3 capture 2.5--3.5 (0º--180º), MEC

Cross section/AP meas.

pd

nd np n

d

p

d

p/d p

difficulties of measurements

p/dp

d

L

RPT

characteristic

Cross section : absolute quantity 　　　　　　　 systematic errors

Pol. Obs. : relative quantity

normalize to pp scatt.

normalize to np scatt.

tiny yield (difficult exp.)

Pol. transfer meas.

polarimeter calibration

small yield (difficult exp.)

Present achievement of experiments @ intermediate energies

Recent tendency of experiments @ intermediate energies

1 higher bombarding energies R3-17 Tamii et al. pd-392 MeV

2 nd data become available R3-16 Maeda et al. nd-250 MeV

3 breakup 2πcoverage, PT R2- Kystrin et al. dp-130 MeV (cancelled)

R3-15 Mardanpour et al. dp-190 MeV 2πcoverage R3-25 Sekiguchi et al. dp-270 MeV PT

4 radiative capture R3-18 Messchendorp et al. dp-190 MeV -coinc.

R3-24 Tameshige et al. dp-137 MeV

5 four-nucleon system R3-20 Miki et al. dd-270 MeV DFSI

Please come to “Experimental Few-Body session”, Room 3, Friday (Aug. 25)

RIKEN exp.

DUBNA exp.

2 dp elastic measurements

by

NUCLOTRON at DUBNA

Nuclotron at JINR, Dubna

superconducting synchrotron (E/A < 6 GeV)

• Nuclear structure• Medium effects on particle production• Modification of nuclear matter• Hypernuclei and nuclei• Nucleon structure

d-p elastic scattering measurement at NUCLOTRON

Internal Target Station

30-pairs plastic scintillation counterstarget:CH2(10 m)

Measurements at 270 MeV, 880 MeV and 2 GeVby Uesaka/Ladygin et al.

Ay ~ 0.3 ; moderately large

Ayy ; large only at cm 0 deg

insufficient statistics due to small beam intensity

→ strong beam with new ion source CIPIOS

d-p Analyzing powers at 880 MeV

Beam Intensity < 2-3 x107 /spillPolarizations (pZ, pZZ)=(+1/3,+1),(+1/3,-1), (0,0)

measured values: (preliminary) pZ pZZ

mode 1 -0.207 ± 0.044 0.879 ± 0.116 mode 2 -0.176 ± 0.035 -0.421 ± 0.093

Results

Suda et al.

R3-17 Tamii pd-392 MeV

3 How far we understand 3NF effects?

Success and failure

Success & failure

1 d/d, vector AP(Ay), PT(Kijk) (Tp135 MeV)

very successful

2 tensor AP, PT, SC

some successful, some not.

confusing, chaotic!

3 d/d (Tp>200 MeV)

large discrepancy in backward angles

(nucleon-exchange process)

due to 3NF? / relativity? / ?

Success 1 d/d, vector AP(Ay) , PT(Kij

k) (Tp135 MeV)

very successful

Sekiguchi et al.

NN only

NN+3NF(TM99)

AV18+3NF(U9)

CDBonn+△

Coulomb

Failure?2 iT11, Tij, PT some successful, some not.

confusing, chaotic!

Sekiguchi et al.

NN only

NN+3NF(TM99)

AV18+3NF(U9)

CDBonn+△

Failure? 3 d/d ? (Tp>200 MeV)

R3-17 Maeda nd elastic scattering measurements at En=250MeV

Calc. even including 3NF still underestimate the data by 50% !

nucleon-exchange process ?

Relativistic calc. by Witala improve the fit only at θcm > 160 deg. but not enough.

Doleschall approx. by Kamada

Screened Coulomb by Deltuva

Coulomb effects ? (too large !)

4 How data are reliable ?

Inconsistency between data sets

Consistency between data sets

1 d/d(Tp=135 MeV) pd-elastic scatt.

RIKEN vs. KVI

2 Axx ,Ayy (Td=200 MeV) dp-radiative capture

RCNP vs. KVI

Different group data-sets are consistent?

3NF effects are at most 30% effect.

Consistency among data sets

1 d/d(Tp=135 MeV) pd-elastic scatt. RIKEN vs. KVI

○ N. Sakamoto, PL B367 (1996)60.

● H. Sakai, PRL 84(2000)5288.

● K. Sekiguchi, PR C65(2002)34003.

▲ K. Ermisch, PR C68(2003)51001.

○ K. Sekiguchi, PRL 95(2005)162301.

How do you judge?

NN only

NN+3NF(TM99)

AV18+3NF(U9)

CDBonn+△

Consistency among data sets

2 Axx , Ayy (Td=200 MeV) dp-radiative capture

RCNP vs. KVI

d+pd+p33He+He+ @ 200 MeV/A @ 200 MeV/A

No anomaly observed In KVI data!!

Sagara, Preliminary

— Hanover (virt. ) Deltuva, PRC67, 034001(03)

— Bochum/Cracow (MEC) Skibinski, PRC67, 054001(03)

— Bochum/Cracow (Sieg.) Skibinski, PRC67, 054001(03)

KVI, PL B Mehmandoost/van Garderen

Ayy Axx

Ayy Axx

d+pd+p33He+He+ @ @ 270270 MeV/A at RIKEN MeV/A at RIKENOne of the last experiment at SMART.

by Suzuki et al. by Sekiguchi et al.

Another confusion !

270 MeV

200 MeV

5 Facilities

Facilities

1. Phase out from nuclear physics experiment

• IUCF (2002) pol-p, d

• TSL (2005) n-fac.

• RIKEN (2005) pol-d

• KVI (2007) pol-p,d (soon)

2. Active

• RCNP pol-p(<400 MeV), pol-d(<200 MeV), n-fac.

• LANL n-fac.

• NUCLOTRON pol-d(<6 GeV)

• COSY pol-p, pol-d

• iThemba(NAC) p,d

3. Coming

• RIKEN RIBF pol-d(400-880 MeV)

Beam Line Polarimeter

dp elastic/breakup Measurement

Polarized Ion Sourcevector & tensor pol. d

RIKEN RIBF

Polarized d (400-880 MeV) available

in 2008(?)

SMART

Pol. d (140-270 MeV) Contact person: Dr. K. Sekiguchi

SMART spectrometer

Most of the 3NF studies were performed

by using the magnetic spectrometer SMART!

Facilities1. Phase out for nuclear physics experiment

• IUCF (1998) pol-p, d• TSL (2005) n-fac.• RIKEN (2005) pol-d • KVI (2007) pol-p,d (soon)

2. Active• RCNP pol-p(<400 MeV), pol-d(<200 MeV), n-fac.• NUCLOTRON pol-d(<6 GeV)• COSY pol-p(<1GeV), pol-d(?)• iThemba(NAC) p(<200 MeV), d(<80 MeV)• LANL n-fac.(<800 MeV)

3. Coming• RIKEN RIBF pol-d(400-880 MeV)

Theory

Without exact calc., nothing can be conclusive!

Key to the few-body study!

6 Summary

Summary

─ Tendency of 3NF study.

1. Higher energies DUBNA exp.

2. nd measurement

3. Breakup

4. Readiative capture

─ 3NF are successful? (comparison to theories)

1. d/d, Ay Tp135 MeV good fits

2. Tp>200 MeV fail, 50% off. small rel. effects.

(nd)/(pd) Coulomb ?

3. Tensor AP, PT confusing, chaotic!

dp-breakup measurement at 270 MeV at RIKEN

R3-25 Sekiguchi

another confusion ! ?

vector AP tensor AP tensor-to-vector PT

1=27°-35°, 2=31°, 12 ＝ 180°

Summary─ Tendency of 3NF study.

1. Higher energies DUBNA exp.

2. nd measurement

3. Breakup

4. Readiative capture

─ How present 3NF are successful. (comparison to theories)

1. d/d, Ay Tp135 MeV good fits

2. Tp>200 MeV fail, 50% off. small rel. effects.

(nd)/(pd) Coulomb ?

3. Tensor AP, PT confusing, chaotic!

─ Consistencies between data sets

1. d/d at Tp=135 MeV

2. Radiative capture

─ Facilities

How far we understand 3NF, that is the question.

Collaborators

•Jagiellonian Univ.H. Witala, J. Golak

• KITH. Kamada

• BochumW. Glockle

• Honnove P.U. Sauerr• Lisbon A. Deltuva

• University of Tokyo

• RCNP

• RIKEN

• Kyushu University

• TITech

• Saitama University

This talk is helped by

K. Sekiguchi (RIKEN)

Y. Meda (U. Tokyo)

K. Suda (U. Tokyo)

J. Messchendorp (KVI)

Experiments Theory

Announcements.

The 23rd International Nuclear Physics Conferencewith a special session in commemoration of the centenn

ial of the birth of Prof. Hideki Yukawa

June 3(Sun)-8(Fri), 2007Tokyo International Forum, Tokyo

hosted byKEK, RIKEN, RCNP, JAEA, JWE and Yukawa Memorial Foundation

sponsored byIUPAP, The Science Council of Japan, The Physical Society of Japan

The Organizing Committee chaired by Shoji Nagamiya (KEK)

homepage: http://www.inpc2007.jpfor pre-registration email: inpc07reg@convention.co.jp

Organizers: Organizers: H. Sakai (UT) (chair)H. Sakai (UT) (chair) K. Hatanaka (RCNP)K. Hatanaka (RCNP) H. Okamura (RCNP)H. Okamura (RCNP) K. Sagara (Kyushu)K. Sagara (Kyushu) Y. Suzuki(Nigata)Y. Suzuki(Nigata) Y. Akaishi (Nihon/RIKEN)Y. Akaishi (Nihon/RIKEN) T. Motobayashi(RIKEN)T. Motobayashi(RIKEN) K. Sekiguchi (RIKEN) (secretary)K. Sekiguchi (RIKEN) (secretary)Topics to be covered :Topics to be covered :

- Few Nucleon Systems and Three Nucleon Force- Few Nucleon Systems and Three Nucleon Force - Chiral Effective Field Theory- Chiral Effective Field Theory - Three Nucleon Force Effects in Nuclear Structure- Three Nucleon Force Effects in Nuclear Structure - Three Nucleon Forces in Hyper Nuclei- Three Nucleon Forces in Hyper Nuclei

International Symposium onInternational Symposium on

New Facet of Three Nucleon ForceNew Facet of Three Nucleon Force～ ～ 50 years of Fujita-Miyazawa Three Nucleon Force50 years of Fujita-Miyazawa Three Nucleon Force ～～

October 29(Mon.) - 31(Wed.), 2007October 29(Mon.) - 31(Wed.), 2007Koshiba Hall, University of TokyoKoshiba Hall, University of Tokyo

End

Thank you for your attention.

Four nucleon system is interesting.

2BS

3BS

2NF

3NF

4BS 4NF

2NF 3NF 4NF

1

3 1

6 4 1

─ 4BS is a good tool to study 3NF effects.

─ stressed by Fonseca.

─ solve Faddeev-Yakubovsky eq. exactly.

─ 4NF effects?

─ First of all, establish 3NF.

─ But look for where?

VNN 20 MeV/pair

V3NF 1 MeV/triplet

V4NF 0.1 MeV/quartet

by J.L. Friar, FBS 22(1997)161.

Results(1) Differential Cross Sections

Faddeev calc (by Prof. H. Kamada)　　　 : NN only

(CD-Bonn, AV18, Nijmegen-I,II,93)　　　 : NN with TM-3NF　　　 : AV18+UrbanaIX-3NF　　　 : CD-Bonn+TM’-3NF

Calculations even including 3NF still underestimate the data at cm = 110 – 180 deg.

CC calc (by Honnover group)　　　 : CD-Bonn　　　 : CD-Bonn+-3NF

Relativistic effects

Hamiltonian of 3N system (total momentum = 0) Relativistic energy

Relativistic NN potential ( in CM system of particle i, j)

Lorentz boosted NN potential into CM system of 3N (Fully relativistic)

Approximations of Vij

• pij <<1• Dependence of k and k’

ji

ijVHH2

10

i

i mmH ])p[( 2/1220

2

2

2

2

41)

21(

)q(

1

,)q'(

1)q'q,(

)q(

1)'kk,(

m

q

m

q

h

hv

hv NR

ijij

22

2/1222/122

2)k(

,]p)k([p])k([

mk

vV

ij

ijijijijijij

ijij

ijij vm

vV2

2

8

p

2222

2

k'

1

k

1

8

p

mv

mvV ij

ijijij

Relativistic prediction

Relativistic kinematical correction

(calc. by Prof. H. Witala) relativistic energy relativistic NN potential

(green line; not fully relativistic) Lorentz boost to 3N c.m. syst

em

(red & pink line) Fully relativistic calculations im

prove the fit to the data only at cm > 160 deg but improvements are not enough. Relativistic 3NF Dirac eq.

Non-Rel.

Rel. NN potential

Lorentz boosted potential

Approx. １ Approx. ２

There still remains 50% discrepancy!.

X-sec. ratios at 250 MeV & 95 MeV

σ(p+d) /σ(n+d)σ(p+d) /σ(n+d) at at 250250 MeV MeV σ(d+p)/σ(n+d)σ(d+p)/σ(n+d)

at at 9595 MeV / nucleon MeV / nucleon

Coulomb effects ? (too large !)

<4% level by Sauer & Deltuva.

o IUCF, PRC35, 37(87) Sagara, Preliminary

— Hanover (virt. ) Deltuva, PRC67, 034001(03)

— Bochum/Cracow (MEC) Skibinski, PRC67, 054001(03)

— Bochum/Cracow (Sieg.) Skibinski, PRC67, 054001(03)

p+dp+d33He+He+ @ 9 @ 90 MeV/A0 MeV/A

No anomaly observed inpreliminary KVI data!!

KVI, Preliminary Mehmandoost/van Garderen

dd

Ay(d) Ay(N)

Ayy Axx

Axx

present dataAV18AV18+URBIX

●- - -

―

Ayy

present dataAV18AV18+URBIX

●- - -

―

Axx

present dataKVI dataAV18AV18+URBIX

●●

- - -―

Ayy

present dataKVI dataAV18AV18+URBIX

●●

- - -―

Axx 　 ~ 　 Ayy in pd capture

KVI

RCNP

Aｘｘ

Aｙｙ

AｙｙAxx

Ayy & Axx measured

Only Ayy measured