1. ORNL- 7/14/05 Puzzling Over Intricacies of the Few Nucleon Force Thomas B. Clegg University of North Carolina and Triangle Universities Nuclear Laboratory

2. ORNL- 7/14/05 Outline of Talk Introduction NN potential models Experimental techniques and polarization measurements in few-body nuclear systems Low-energy scattering measurements at TUNL –The A y puzzle in 3N and 4N systems –Tensor force in few-nucleon scattering

3. ORNL- 7/14/05 Outline of Talk Introduction NN scattering and potential models Experimental techniques and polarization measurements in few-body nuclear systems Low-energy scattering measurements at TUNL –The A y puzzle in 3N and 4N systems –Tensor force in few-nucleon scattering

4. ORNL- 7/14/05 A Simple Example p + 3 He elastic scattering Differential cross section measured below 11.5 MeV Data described with a 3-parameter phase shift analysis Cross Section (mb/sr) Center-of-mass scattering angle T B Clegg, et al., Nucl. Phys 50 (1964) 621

5. ORNL- 7/14/05 Parameterization of Data Cross Section (mb/sr) Center-of-mass scattering angle Major structure in the differential cross section is well described by a simple calculation Small difficulties remain with fits in forward and mid-angle ranges E p = 7.51 MeV

6. ORNL- 7/14/05 Partial Wave Analysis Phase shift Coulomb scattering termNuclear scattering term L=0, s-wave L=1, p-wave L=2, d-wave Data are parameterized by phase shifts for individual partial waves. E p (MeV)

7. ORNL- 7/14/05 Conclusion? Nuclear scattering from 3 He is basically pretty simple. Right?

8. ORNL- 7/14/05 Conclusion? Nuclear scattering from 3 He is basically pretty simple. Right? Not quite! What about spin?

9. ORNL- 7/14/05 What About Spin? Real nuclei can also carry spin angular momentum Full phase shift analysis includes a separate partial wave and phase shift for each angular momentum state J Notation Multiplicity Total Angular Momentum Singlet States Triplet States …

10. ORNL- 7/14/05 Full Phase Shift Analysis Real nuclei can also carry spin angular momentum Full phase shift analysis includes a separate partial wave and phase shift for each angular momentum state J Notation Multiplicity Total Angular Momentum Singlet States Triplet States … 11 Mixing Parameter

11. ORNL- 7/14/05 Mixing Parameter Presence of a tensor component mixes states with and The scattering matrix then has the form

12. ORNL- 7/14/05 Full Phase Shift Analysis Real nuclei can also carry spin angular momentum Full phase shift analysis includes a separate partial wave and phase shift for each angular momentum state J Notation Multiplicity Total Angular Momentum Doublet States Quartet States …

13. ORNL- 7/14/05 Outline of Talk Introduction NN scattering and potential models Experimental techniques and polarization measurements in few-body nuclear systems Low-energy scattering measurements at TUNL –The A y puzzle in 3N and 4N systems –Tensor force in few-nucleon scattering

14. ORNL- 7/14/05 N-N Scattering - 1959 p-p scattering cross sections measured with absolute accuracy ~ 0.2% E = 3.037 MeV

15. ORNL- 7/14/05 N-N Scattering Today Over 10,000 data points between 0 and 3 GeV are parameterized by phase shifts Difference indicates spin-spin interaction Differences indicate spin-orbit interaction Presence indicates tensor interaction

16. ORNL- 7/14/05 The predominant long-range component is attributed to one-pion exchange Additional terms are included in modern potentials, e.g. –Iso-tensor dependent –Weak interaction –Two pion and other meson exchange –Three-body force Potentials are used to fit the NN phase shifts, with ~40 parameters with overall χ 2 = 1. NN Interactions From J. Carlson and R. Schiavilla, Rev. Mod. Phys. 70 (1998) 743

17. ORNL- 7/14/05 Comparison of Phase Shifts From J. Carlson and R. Schiavilla, Rev. Mod. Phys. 70 (1998) 743

18. ORNL- 7/14/05 Deuteron Properties Experimental bound-state properties of the deuteron are well predicted by all models. A s = Asymtotic S-state wave function normalization η = Asymtotic D-to-S state ratio r d = Radius μ d = Magnetic moment Q d = Quadrupole moment P d = D-state probability From J. Carlson and R. Schiavilla, Rev. Mod. Phys. 70 (1998) 743

19. ORNL- 7/14/05 Need for a 3-N Force Under-predictions of binding energy of 3H and 3He (find good reference) – Tjon line? Improved fits to the p + d cross section –See Kievsky et al PRC63 024005 (2001)

20. ORNL- 7/14/05 Energy Levels of Light Nuclei AV18 – Deletes 3-N force terms AV8’- Deletes electromagnetic terms AV6’ - Deletes spin orbit terms NN potential with 3-parameter, 3N force adjusted to fit 27 states in light nuclei with rms deviation of only 600 keV. R.B. Wiringa and S.C. Pieper, Phys. Rev. Lett, 89 (2002) 182501

21. ORNL- 7/14/05 Outline of Talk Introduction NN scattering and potential models Experimental techniques and polarization measurements in few-body nuclear systems Low-energy scattering measurements at TUNL –The A y puzzle in 3N and 4N systems –Tensor force in few-nucleon scattering

22. ORNL- 7/14/05 What Does Polarization Mean? For protons, neutrons, or 3 He with, one defines +1/2 -1/2 P z = +0.602 Intensity B z (mTesla) B z ( ) Intensity +1/2 -1/2 P z =-0.689 P z =+ 0.602P z =-0.689 +1/2 -1/2

23. ORNL- 7/14/05 What Does Polarization Mean? For deuterons with, one defines -1 P z = 0.518 P zz =-0.034 - +1 0 Intensity B z (mTesla) P z = -0.073 P zz =-1.352 0 -1 +1 Intensity B z (mTesla)

24. ORNL- 7/14/05 Sourcery - 1964 First production of polarized H or D negative ions I beam = 300 pA

25. ORNL- 7/14/05 Polarized Sourcery -1965 First acceleration of polarized ions in tandem accelerator I beam  5-20 pA P beam  0.45 Polarization preserved with foil stripper

26. ORNL- 7/14/05 What Does One Measure? Incident polarized ions experience an force. More particles are scattered to one side than the other, producing a left-right scattering asymmetry, Modified from H.H. Barschall, Am J. of Phys 35 (1967) 119 Spin up, L down Spin up, L up Incident Beam Scattered Beam

27. ORNL- 7/14/05 Simplest measureable is the vector analyzing power. New measurements for p-p scattering showed that global phase-shifts were not correct at low energy. Types of Data J.D. Hutton, et al., Phys. Rev. Lett. 35 (1975) 429 p + p scattering – 10.0 MeV

28. ORNL- 7/14/05 Using a polarized beam and target, one can study the tensor interaction Tensor force depends both on B-field and on location. Nuclear tensor force mixes states with similar J having ΔL= 2, i.e. S and D states. In nuclear systems, there is evidence for tensor forces in both of the spin (σ) and the isospin (τ) sectors. What Does One Measure?

29. ORNL- 7/14/05 Types of Data - 1968 First spin correlation measurement with polarized beam & target P target  0.1 I beam  0.5 nA Two points in 48 hours! A xz θ cm

30. ORNL- 7/14/05 Outline of Talk Introduction NN scattering and potential models Experimental techniques and polarization measurements in few-body nuclear systems Low-energy scattering measurements at TUNL –The A y puzzle in 3N and 4N systems –Tensor force in few-nucleon scattering

31. ORNL- 7/14/05 Atomic Beam Polarized Source Atomic Beam Systems Ionizer Systems Acceleration & Spin Precession Systems

32. ORNL- 7/14/05 Triangle Universities Nuclear Lab Polarized H ± and D ± beams –beam energies between 20 keV & 20 MeV. [Clegg, et al., NIM A357 (1995)200] –Rapid Lamb-shift polarimetry at ion source [Mendez et al. RSI 67 (1996) 3073] Proton spin state populations +1/2 - 1/2 Deuteron spin state populations +1 0

33. ORNL- 7/14/05 Low Energy Target Area – E=20-680 keV

34. ORNL- 7/14/05 Low-Energy Target Facilities Low-Energy Target Facility –Beam energies: 20 to 680 keV –Full range of p and d polarizations Two essential components –Mini-tandem accelerator with terminal voltages up to 200 keV –Charged particle scattering chamber at voltages up to 200 keV

35. ORNL- 7/14/05 p + d Elastic Scattering Cross section measured at E cm = 431 keV. Calculations based on NN with no additional free parameters. AV18 and AV18+URIX to describe the NN force. Data fit well only by calculations based on AV18+URIX which includes 3-body interaction. Plot of σ (θ) Expt / σ (θ) Theory No 3N Force With 3N Force

36. ORNL- 7/14/05 p + d Elastic Scattering Brune et al., Phys Rev C63 (2001) 44013 Measured vector and tensor analyzing powers Compare to calculations with and w/o 3N force. AyAy iT 11 T 21 T 20 A yy

37. ORNL- 7/14/05 What Must Be Changed? Need to adjust splitting among the 4P phases, i.e. the spin-orbit interaction is wrong Need to adjust coupling between 2P 3/2 states, i.e. the spin-spin interaction strength is also wrong. Notation Multiplicity Total Angular Momentum Doublet States Quartet States … M. Wood, et al., Phys Rev 65 (2002) 34002  3/2

38. ORNL- 7/14/05 Supersonic Gas Jet Target Originally fabricated at Erlangen –G. Bittner, et al. NIM 161(1978)1 –http://www.tunl.duke.edu/~unc/gasjet / High target density –5 x 10 17 atoms/cm 2 obtained –10 18 atoms/cm 2 possible Very low backgrounds in spectra Used for 3 He + p scattering –B. Fisher, TUNL Ph.D. thesis, 2003 Nozzle Catcher

39. ORNL- 7/14/05 p + 3 He Elastic Scattering New, low-energy cross section data taken with high accuracy, ~1% Cross-normalized to pp scattering Data are fit extremely well by calculations which include a 3N force B Fisher, Ph.D Thesis, UNC-CH, 2003

40. ORNL- 7/14/05 p + 3 He Vector Analyzing Power Differences between experiment and theory with 3NF persist for several targets and over a significant energy range B Fisher, Ph. D Thesis, UNC-CH, 2003

41. ORNL- 7/14/05 The A y Puzzle – Status Spin-dependent effects in these systems are not small. Larger A y values 2- and 3-body systems make it easy to study these in great detail. Theoretical explanations based on NN interaction fail. Barker et al., PRL 48 (1982) 918. p+p Brune, et al., PR C63, 044013 (2001) p+d 667 keV p+ 3 He 1.20 MeV 1.69 MeV Viviani et al, PRL 86 (2001) 3739

42. ORNL- 7/14/05 Chiral Pertubation Theory Use QCD knowledge to develop underlying amplitudes Form basis states which maintain necessary symmetries, and link NN with 3-body and 4-body systems Set parameters to fit NN phase shifts Calculate the 3-and 4-body observables. Long-range goal is to link few-body forces to underlying quark dynamics

43. ORNL- 7/14/05 The Nuclear Tensor Force One measures the tensor force by manipulating spins of both beam and target and observing the effect on the total scattering cross section. One actually measures the asymmetry

44. ORNL- 7/14/05 Polarized H Target Brute force polarization of target by cooling sample to ~10 mKelvin in a 7 Tesla B-field B W Raichle, et al., Phys Rev Lett 83 (1999) 2711

45. ORNL- 7/14/05 P.W. Lisowski et al., Nucl. Phys A232 (1975) 298 Polarized Neutron Beam  d + d  3 He + n n p n p n p p n + + In a d stripping reaction, yield is strongly peaked at 0 . Outgoing neutron largely maintains the polarization it had in the incident polarized deuteron. Roughly constant neutron polarizations are obtained between ~7 and 22 MeV.

46. ORNL- 7/14/05 Experimental Setup Measure neutron transmission changes when spins are flipped Provides most direct indication of tensor force coupling Polarized Target Incident Polarized Neutron Beam Neutron Detector

47. ORNL- 7/14/05 n-p Tensor Force The 3 S 1 - 3 D 1 coupling parameter ε 1 measures strength of the tensor force. Modern n-p potentials underpredict ε 1 ; spin-spin data require a larger tensor force. A stronger tensor force implies a weaker ρ - meson exchange contribution in present N-N one-pion- exchange models. Raichle, et al., PRL 83 (1999) 2711 New data

48. ORNL- 7/14/05 Possible Explanation The 3 S 1 - 3 D 1 coupling parameter ε 1 is a measure of the tensor force in n-p scattering. Modern n-p potentials underpredict ε 1 ; spin-spin data require a larger tensor force. A stronger tensor force implies a weaker ρ - meson exchange contribution in present N-N OPE models. Raichle, et al., PRL 83 (1999) 2711 n+p p+p Tornow, Nucl. Phys A684 (2001) 193

49. ORNL- 7/14/05 Alley and Knutson Refining Spin Dependence in p + 3 He p + 3 He Phase-Shift Calculation: Curves show effect on A oy at E p = 5 MeV when optimum p-wave phase shifts are changed by ±10 %.  cm

50. ORNL- 7/14/05 Spin Correlation A yy p + 3 He Phase-Shift Calculation: Curves show effect on Ayy at E p = 5 MeV when optimum p- wave phase shifts are changed by ±10 %. Alley and Knutson No change  cm

51. ORNL- 7/14/05 Essential needs for 3 He target –The target cell must be in vacuum. –Target volume must be isolated from external B-fields. –Beam must enter and exit through thin foils. –Scattered particles must emerge through thin windows. Concern: Foils and glue for windows may cause 3 He depolarization and limit target cell pressure –Target system should be compact enough to fit in an existing TUNL scattering chamber. Requirements for Low Energy Experiments

52. ORNL- 7/14/05 New Polarized 3 He Target New spin-exchange optically- pumped, 3 He polarizer –Pyrex target cell with Kapton windows placed inside sine-theta coil –Polarized 3 He Pressure ~1ATM – 3 He polarization ~ 25 to 30% monitored on-line with NMR First use – 3 He(p,p) 3 He Goal: Measure strength of the tensor force coupling Katabuchi et al., Rev Sci Instrum 76 033503 (2005).

53. ORNL- 7/14/05 3 He Spin-Exchange Polarizer Polarize 3 He by spin-exchange with optically pumped Rb vapor Diaphragm pump 3 He Storage cells Laser beam Optical Pumping Cell

54. ORNL- 7/14/05 Details of Target

55. ORNL- 7/14/05 Sine-Theta Coil – B-Field Calculation Poisson/Superfish: LANL code used to calculate magnetic field from currents and magnetic properties Geometry: Shielded infinite cylinder Results: A 5 cm diam central region has 7.5 cm 24 current rods (3 mm diam ) mu-metal (1 mm thick) 5 cm

56. ORNL- 7/14/05 Sine-Theta Coil – Design Details 24 Copper rods placed on Delrin cylinder. Twelve separate currents regulated to 10 -3. Coil is covered with a mu-metal shield with windows for emerging scattered particles.

57. ORNL- 7/14/05 Sine-Theta Coil – Realization Assembled coil with rods and current carrying wires. Delrin cut horizontally for easy access to target cell. Horizontal slot provided for scattered particles.

58. ORNL- 7/14/05 Beam Polarimetry – 1971 First absolute calibration method for spin-1/2 particle polarization AyAy Proton Lab Energy p + 4 He A y = 1 points

59. ORNL- 7/14/05 Calibration for NMR System Using 3 He + 4 He scattering at a known A y =1 point, the NMR coil sensitivity to 3 He polarization was calibrated

60. ORNL- 7/14/05 p + 3 He Data Taken Energy (MeV) ObservablesLab Angles (deg) 5.52Axx 30-150 5.50Ayo,Aoy,Ayy30-150 4.04Ayo,Aoy,Ayy30-150 3.18Axx 30-150 2.74Ayo,Aoy,Ayy70-150 2.74Axx 30-130 2.68Ayo,Aoy,Ayy30-130 2.29Axx 30-90

61. ORNL- 7/14/05 Triangle Universities Nuclear Lab 4 He polarimeter in position to measure n beam polarization for n-d A y measurement Polarized Neutron Source: D(d pol,n pol ) 3 He –Neutron polarization ~70% and constant versus energy 4 He polarimeter –100 bar pressure 95% He; 5% Xe –Utilizes 4 He(n,n) 4 He –Effective A y ~ 85%