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

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**FB18, Santos, Brazil**August 22, 2006 Status of three-nucleon force study by nucleon-deuteron system H. Sakai Department of Physics The University of Tokyo • Introduction • dp elastic measurements by NUCLOTRON at DUBNA • How far we understand 3NF effects? • How data are reliable ? • Facilities • Summary**1. Introduction**How 3NF are established by experiments?**2NF**2BS 3BS 3NF • How to study 3NF? 1 Equations of motion for 3BS must be solved exactly. →Faddeev eq. 2Realistic modern2NF must be established. x2 1for 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) • 3NF is much smaller than 2NF. • →3NF effects are easily masked by 2NF effects. • 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. internal mom. dist. of deuteron 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.**Reactions for Nd system**q(fm-1)@135 MeV 1 elastic scattering 0--2.4--3.4 (0º--90º--180º) 2breakup (FSI, QFS, Space star) 0--3 3 capture 2.5--3.5(0º--180º), MEC • Observables (Nd-sys.) d/d AP (Ay, iT11, T20, T21, T22) VLS, (VLS)2, VT, D-state PT (Kij, Kijk) V (spin-spin int.) SC (Ci,j, Ci,jk, Cij,k) V**L**p p/d p p/d R d d n p n d p • difficulties of measurements • characteristic Cross section : absolute quantity systematic errors Pol. Obs. : relative quantity • Cross section/AP meas. pd normalize to pp scatt. normalize to np scatt. tiny yield (difficult exp.) nd • Pol. transfer meas. polarimeter calibration small yield (difficult exp.) PT**Recent tendency of experiments @ intermediate energies**DUBNA exp. 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 MeVPT 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 MeVDFSI RIKEN exp. Please come to “Experimental Few-Body session”, Room 3, Friday (Aug. 25)**2 dp elastic measurements**by NUCLOTRON at DUBNA**d-p elastic scattering measurement at NUCLOTRON**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 • Measurements at 270 MeV, 880 MeV and 2 GeV by Uesaka/Ladygin et al. Internal Target Station target:CH2(10 m) 30-pairs plastic scintillation counters**d-p Analyzing powers at 880 MeV**Beam Intensity < 2-3 x107 /spill Polarizations (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 Ay ~ -0.3 ; moderately large Ayy ; large only at qcm< 60 deg insufficient statistics due to small beam intensity → strong beam with new ion source CIPIOS Suda et al. Results 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? / ?**Coulomb**NN only NN+3NF(TM99) AV18+3NF(U9) CDBonn+△ • Success 1 d/d, vector AP(Ay) , PT(Kijk) (Tp135 MeV) very successful Sekiguchi et al.**NN only**NN+3NF(TM99) AV18+3NF(U9) CDBonn+△ • Failure? 2 iT11, Tij, PT some successful, some not. confusing, chaotic! Sekiguchi et al.**Failure?**3 d/d ? (Tp>200 MeV) R3-17 Maeda nd elastic scattering measurements at En=250MeV Doleschall approx. by Kamada Screened Coulomb by Deltuva Calc. even including 3NF still underestimate the data by 50% ! Relativistic calc. by Witala improve the fit only at θcm > 160 deg. but not enough. Coulomb effects ? (too large !) nucleon-exchange process ?**4 How data are reliable ?**Inconsistency between data sets**Consistency between data sets**Different group data-sets are consistent? 3NF effects are at most 30% effect. 1 d/d(Tp=135 MeV) pd-elastic scatt. RIKEN vs. KVI 2 Axx ,Ayy (Td=200 MeV) dp-radiative capture RCNP vs. KVI**NN only**NN+3NF(TM99) AV18+3NF(U9) CDBonn+△ • 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?**Bochum/Cracow (MEC)**Skibinski, PRC67, 054001(03) • Bochum/Cracow (Sieg.) Skibinski, PRC67, 054001(03) • Consistency among data sets 2 Axx , Ayy (Td=200 MeV) dp-radiative capture RCNP vs. KVI d+p3He+g @ 200 MeV/A Ayy Axx • Sagara, Preliminary • KVI, PL B Mehmandoost/van Garderen • Hanover (virt. D) Deltuva, PRC67, 034001(03) No anomaly observed In KVI data!!**d+p3He+g @ 270 MeV/A at RIKEN**One of the last experiment at SMART. by Suzuki et al. by Sekiguchi et al. 270 MeV Ayy Axx 200 MeV Another confusion !**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) 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 Coming RIKEN RIBF pol-d(400-880 MeV) • Facilities**Contact person: Dr. K. Sekiguchi**SMART spectrometer • RIKEN RIBF • Polarized d (400-880 MeV) available • in 2008(?) Most of the 3NF studies were performed by using the magnetic spectrometer SMART! Polarized Ion Source vector & tensor pol. d Beam Line Polarimeter dp elastic/breakup Measurement SMART • Pol. d (140-270 MeV)**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) 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) Coming RIKEN RIBF pol-d(400-880 MeV) • Facilities • Theory Without exact calc., nothing can be conclusive! Key to the few-body study!**Summary**• Tendency of 3NF study. • Higher energies DUBNA exp. • nd measurement • Breakup • 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!**vector AP**tensor AP tensor-to-vector PT R3-25 Sekiguchi q1=27°-35°, q2=31°, f12＝180° dp-breakup measurement at 270 MeV at RIKEN another confusion ! ?**Summary**• Tendency of 3NF study. • Higher energies DUBNA exp. • nd measurement • Breakup • 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**Theory Experiments • University of Tokyo • RCNP • RIKEN • Kyushu University • TITech • Saitama University • Jagiellonian Univ. • H. Witala, J. Golak • KIT • H. Kamada • Bochum • W. Glockle • Honnove • P.U. Sauerr • Lisbon • A. Deltuva This talk is helped by K. Sekiguchi (RIKEN) Y. Meda (U. Tokyo) K. Suda (U. Tokyo) J. Messchendorp (KVI)**The 23rd International Nuclear Physics Conference**with a special session in commemoration of the centennial of the birth of Prof. Hideki Yukawa June 3(Sun)-8(Fri), 2007 Tokyo International Forum, Tokyo hosted by KEK, RIKEN, RCNP, JAEA, JWE and Yukawa Memorial Foundation sponsored by IUPAP, The Science Council of Japan, The Physical Society of Japan The Organizing Committee chaired by Shoji Nagamiya (KEK) homepage: http://www.inpc2007.jp for pre-registration email: inpc07reg@convention.co.jp**International Symposium onNew Facet of Three Nucleon**Force～ 50 years of Fujita-Miyazawa Three Nucleon Force～ Organizers: H. Sakai (UT) (chair) K. Hatanaka (RCNP) H. Okamura (RCNP) K. Sagara (Kyushu) Y. Suzuki(Nigata) Y. Akaishi (Nihon/RIKEN) T. Motobayashi(RIKEN) K. Sekiguchi (RIKEN) (secretary) October 29(Mon.) - 31(Wed.), 2007Koshiba Hall, University of Tokyo Topics to be covered : - Few Nucleon Systems and Three Nucleon Force - Chiral Effective Field Theory - Three Nucleon Force Effects in Nuclear Structure - Three Nucleon Forces in Hyper Nuclei**End**Thank you for your attention.**Four nucleon system is interesting.**2NF 3NF 4NF 1 3 1 6 4 1 2BS 2NF 3BS 3NF 4BS 4NF • 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. • 4BS is a good tool to study 3NF effects. • stressed by Fonseca. • solve Faddeev-Yakubovsky eq. exactly.**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 CC calc (by Honnover group) : CD-Bonn : CD-Bonn+-3NF • Calculations even including 3NF still underestimate the data at qcm = 110 – 180 deg.**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’**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. system (red & pink line) • Fully relativistic calculations improve the fit to the data only at qcm> 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 at250MeV &95 MeV**σ(p+d) /σ(n+d) at 250 MeV σ(d+p)/σ(n+d) at 95 MeV / nucleon Coulomb effects ? (too large !) <4% level by Sauer & Deltuva.**ds/dW**• IUCF, PRC35, 37(87) • Sagara, Preliminary • Hanover (virt. D) Deltuva, PRC67, 034001(03) Ay(d) Ay(N) • Bochum/Cracow (MEC) Skibinski, PRC67, 054001(03) • Bochum/Cracow (Sieg.) Skibinski, PRC67, 054001(03) Ayy Axx p+d3He+g @ 90 MeV/A No anomaly observed in preliminary KVI data!! • KVI, Preliminary Mehmandoost/van Garderen**present data**AV18 AV18+URBIX ● - - - ― Axx**present data**AV18 AV18+URBIX ● - - - ― Ayy**Axx**present data KVI data AV18 AV18+URBIX ● ● - - - ―**Ayy**present data KVI data AV18 AV18+URBIX ● ● - - - ―**Axx~Ayy in pd capture**Only Ayy measured KVI Ayy & Axx measured Aｘｘ Aｙｙ RCNP Aｙｙ Axx