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First Study of Three-body 3 Photodisintegration of He with Double Polarizations at HIgS Ph.D. Dissertation Defense Xing Zong Committee members: Prof. Haiyan Gao (Advisor) Prof. Thomas Mehen Prof. John Thomas Prof. Henry Weller Prof. Ying Wu Feb 19th, 2010 Outline • Introduction and Physics Motivation • The Experiment – Overview – HIGS working principle – Polarized 3He Target – Neutron Detection • Data Analysis • Result and Discussion • Summary & Outlook Introduction • Understanding Nuclear force has been a fundamental goal in nuclear physics: Hideki Yukawa: exchange of pion accounted for the force between two nucleons • Two nucleon (NN) system can be described by realistic NN potentials: – long range one-pion exchange, intermediate attraction, short-range repulsion – Modern NN potentials include: AV18[1] and CD Bonn[2]. [1] R.B.Wiringa et al. PRC 51, 38 (1995) [2] R.Machleidt et al. PRC 53, R1483 – NN potentials reproduce NN scattering (1996) database up to 350 MeV with high precision. – They underbind triton Three-nucleon system • Excellent testing ground of theory – simplest non-trivial nuclear system – sufficient complex to test the details of theory – small enough to allow exact calculations – Hamiltonian is written as Pi 2 H Vij Vijk . i 2m i j i j k • Three-nucleon Force (3NF) △ (a) Fujita and Miyazawa first introduced 3NF in 1957[1]; △ isobar yields an effective 3NF (b) Urbana IX is one of the most widely used 3NFs[2] [1] J. Fujita and H. Miyazawa, Prog. Theor. Phys. 17, 360 (1957) [2] J. Carlson, et al. Nucl. Phys. A 401, 59 (1983) Three-nucleon system: 3He ~90% ~2% ~8% Polarized 3He is an effective neutron target Movitation I: Test 3-body calculations g He p p n 3 Deltuva Golak Calculation AGS Faddeev framework NN CD Bonn AV18 Potential 3 NF △ isobar Urbana IX Nuclear Siegert Expliticit MEC: EM current theorem for single nucleon 1body electric current+ two (p current, explict r) body current MEC for magnetic multipoles and h.o. terms E Include Yes Only in bound Coulomb? states Relativistic Yes No 2005 Nagai data @10.2 and 16 MeV (green) treatment? Motivation II: Test GDH sum rule d 2p 2 2 Fundamental Interpretation: any particle N N P A N with a nonzero anomalous magnetic thr MN 2 moment has internal structure 496b 3He GDH Sum Rule thr GDH 3 He 217 39b ??? HIgS @ DUKE p thr GDH 3 He Extrapolated from low Q2 3He GDH (E94-010) measurement @ JLab, (E97-110 much lower Q2) 2 3GeV 247 38b p GDH 3 He 31.9 9.6b 2 3GeV GDH 3 He 23GeV GDH 3 He Pn 2 3GeV GDHn 2 Pp 23GeV GDH p 0.87 35 2 (0.027) (26) [1] M. Amarian, PRL 89, 242301(2002) [2] J. L. Friar et al. PRC 42, 2310 (1990) [3] N. Bianchi, et al. PLB 450, 439 (1999) Few-body calculations of GDH integral up to p Compare to our simple estimation: 217 39b ??? It is crucial to carry out 3-body measurement to provide stringent test of the theories! Deltuva et al. PRC 72, 054004 (2005): Green (with △ isobar) and Blue (without △ isobar) Golak et al. PRC 67, 054002 (2003) (Black curve) Outline • Introduction and Physics Motivation • The Experiment – Overview – HIGS working principle – Polarized 3He Target – Neutron Detection • Data Analysis • Result and Discussion • Summary & Outlook Experimental Overview 1. Beam: HIgS provides circularly polarized gray @ 11.4 MeV 2. Polarized 3He target: flip target spin to form helicity-dependent measurement 3. ONLY neutrons are detected! 7 detectors from 50 to 160 degs. High Intensity g-ray source Progress in Particle and Nuclear Physics 62 (2009) 257, Henry R. Weller, et al. Experimental Setup Polarization preserving mirror Liquid D2O 22mm target collimator Optics table Experiment Setup@ Duke FEL Spin Exchange Optical Pumping (SEOP) • Rb vapor in a weak B field is optically pumped N2 buffer gas • Spin exchange of hybrid alkali Rb only: Rb 3He Rb 3He Hybrid: Rb K Rb K K 3He K 3He Largest 3He cell ever made! NMR Polarimetry • A magnetic moment when placed in an external B-field dM |lab g M B g gyromagnetic ratio dt • Transform into a rotating frame rotates around the B field at frequency w dM dM |lab |rot w M dt dt • The motion of M in the rotating frame dM w |rot gM B0 dt g • Apply oscillating RF field B coswt x B1 sin wt y B x 2 B1 coswt x 1 B1 coswt x B1 sin wt y • Effective field in the rotating frame at frequency wz w Beff ( B0 ) z B1 x ˆ ˆ g NMR - Adiabatic Fast Passage (AFP) • Ramp the holding field B0 z from below the ˆ resonance w / r to above it w Beff ( B0 ) z B1 x ˆ ˆ g • AFP line shape B1 B0 0 B 1 2 B0 w / g 2 1/ 2 Amplitude of voltage at resonance, proportional to the sample polarization. Water calibration to extract 3He Polarization • The ratio of 3He signal to water signal 0h wPn nV h w rf frequency R p 0 wPn nV p Pn nuclear polarization n number density • The definition of polarization V volume of the cell n n pn magnetic moment n n • The polarization of proton in water is given by Pnp tanh pw p / kTpg p p w p / kTp g p • The polarization of 3He is Pnh Vw 2 2 p n pTh R p h pressure of 3 He cell Vw h g pT p p h T h temperature of 3 He cell W.Lorenzon et al. Phys. Rev. A, 47, 468 (1993) K.Kramer et al. Nucl. Inst. Method A, 582, 318 (2007) Spin up/down curves The typical spin up/down curves: measurement every 3 hrs. 17 mV corresponds to ~40% polarization. During the run, the average polarization was 42%, and quite stable. Neutron Detection Important info from the signal: ADC: Pulse-height (energy) TAC: Pulse-shape discrimination (particle separation) TDC: Time of flight (time) g n 1D TAC: Proportional to the length of the The traditional PSD working principle trailing edge of the detector signal, therefore measure the particle type. Outline • Introduction and Physics Motivation • The Experiment – Overview – HIGS working principle – Polarized 3He Target – Neutron Detection • Data Analysis • Result and Discussion • Summary & Outlook 11.4 MeV Run summary Run Summary: Data Analysis Overview: D2 run: used as a 1. Calibration: relate ADC and calibration of main experiment TDC to PH (energy) and 3He run: took spin P and A alternatively TOF (timing) information. to form asymmetry and to reduce 2. Cuts: separate gammas and systematic uncertainties. neutrons Al run: determine gamma peak position 3. Integrated flux determination to obtain timing information 4. GEANT4 simulation to N2 run: background subtraction determine the acceptance Calibration I: ADC Determine Pedestal (offset Compare Cs source runs with simulation resulting from electronics bias) to find tune gains (energy per channel) Calibration II: TDC Determine Gamma peak TDC Compare D2 run and simulation to position determine C (TDC Calibration constant) How to select neutrons? Gammas Neutron Cuts Values Candidates PSD 6 PH 0.2 MeVee TOF 1.1 MeV Note: 1. roughly corresponds to 30 TAC channels, 2. ee means electron equivalent Cut effects En=1.1 MeV Monte Carlo Simulation • Geant4 Simulation helps to determine – the ADC, TDC calibration constant – The back detector efficiency (for flux determination) – Main detector acceptance • The acceptance is the convoluted effect of all the factors: the extended target effect and detecting efficiency of the detectors. • G4 simulation was ran twice under the same conditions first with a point target (Run 1), then with 40cm long target (Run 2). Then divide the number of detected neutrons from Run 2, by the number of neutrons into the detectors from Run 1. Integrated flux determination Principle: g D pn 1257 36b d A sin 2 d Note: 1. We use back detectors to monitor the gamma flux. 2. The info was used to extract DXS. 3. The D2 calibration run is based on the same principle. Normalization Issue Normalized Yields by back detectors: 1. Spin P (black), spin A (red) 2. A downward trend is observed, which gives rise to false asymmetry Gamma peak normalization Gamma peak method: 1. Only provide a relative (not absolute) photon measurement 2. Cell-dependent. We use it to get relative integrated flux between spin P and A. Compare run-to- run stabilities between back detectors and gamma peak Systematic uncertainty study • Uncertainty from analysis cuts PSD cut: vary from 5 to 7 PH cut: vary from 0.19 MeVee to 0.21 MeVee (5% change) TOF cut: vary the trailing edge by from 1.0 MeV to 1.2 MeV (+/- 3 ns). • Uncertainty from HIgS beam Integrated Photon Flux: different methods for asymmetry and DXS Beam polarization: we assume 5% relative uncertainty • Uncertainty from target Target polarization: 4% (NMR/EPR measurement) Target Thickness: 2%(uncertainty in the density measurement, temperature change) Outline • Introduction • The Experiment – Overview – HIGS principle – Polarized 3He Target – Neutron Detector • Data Analysis • Result and Discussion • Summary & Outlook D2 differential cross section Goal of this run is consistency check: • calibration • data selection (cuts) • simulation • normalization B*sin2()+C A*sin2() The two fits give us very similar results. Using the Bsin2()+C fit result, we obtained total cross section :1247+/-45 b in agreement with world data: 0 = (1257+/-36 b) I. Asymmetry Results Expression: Systematic study includes PSD, PH, TOF cuts variations, beam and target polarization, and integrated photon flux. Top two curves are from Deltuva (CD Bonn), bottom two from Golak (AV18). En starts from 1.1 MeV. The fitted average asymmetry agrees with theory within 2. II. Unpolarized differential cross section Expression: AV18 AV18+UIX CD Bonn CD Bonn+ △ is the detector acceptance which includes both detector efficiency and the extended target effect. Data is from En=1.1 MeV, corrected by simulation (model-dependent) from 0. Statistical uncertainty: III: Total Cross Section Two methods: 1. Fit the data with a constant times the AV-18 curve (725b), the constant is about 1.053 2. Expand the DXS: d a P cos d l l l Fit results: a 61 .7 2.9 b 0 Total cross section result: 776±18(stat.) ±32(sys.)±11(mod)b Compared with 05 Nagai data at 10.2 MeV, our datum agrees with theory much better! Outline • Introduction & Physics Motivation • The Experiment – Overview – HIGS working principle – Polarized 3He Target – Neutron Detection • Data Analysis • Result and Discussion • Summary & Outlook Summary • We carried out a first study of three-body photodisintegration of 3He at HIgS with 11.4 MeV circularly polarized photons. • We have extracted three sets of results: asymmetry, unpol DXS and TXS. • Results are compared to two sets of state-of-the-art three-body calculations from Deltuva and Golak using CD Bonn and AV18 potentials. • Fitted average asymmetry is within 2 of the theoretical value, unpolarized DXS agrees reasonably with theory. • Total cross section is obtained by two methods. The final result agrees with theoretical calculation much better than 2005 Nagai data. Outlook • A new proposal was approved by HIGS physics advisory committee (PAC) in July 2009. • PAC granted us 180 hrs to run measurements at three photon energies. • Beam time could be as early as fall 2010. 3He Three-body Photodisintegration Collaboration @ Duke HIgS M. Ahmed, C. Arnold, M. Blackston, W. Chen, T. Clegg, D. Dutta, H. Gao (Spokesperson/ Contact Person), J. Kelley, K. Kramer, J. Li, R. Lu, B. Perdue, X. Qian, S. Stave, C. Sun, H. Weller (Co-Spokesperson), Y. Wu, Q.Ye, W. Zheng, X. Zhu, X. Zong Duke University, Durham, NC Acknowledgement • U.S. DOE contract number DE-FG02- 03ER41231 • Duke University School of Arts and Sciences • TUNL MEP group, Capture group, TUNL staff & FEL staff • Dr. Deltuva and Dr. Golak and their collaborators Historical Background Nuclear interactions and Nobel Prizes 1949 Hideki Yukawa: exchange of pion accounted for the force between two nucleons 1969 Murray Gell-Mann: existence of more fundamental particles, ie. quarks 2004 Gross/Politzer/Wilczek: discovery of asymptotic freedom in QCD Photos are from nobelprize.org Mesons Pseudoscaler Mesons: quark and Vector Mesons: quark and anti-quark spin antiparallel anti-quark spin parallel Baryons J=1/2 J=3/2 Nuclear force • Range of nuclear force is ~ radius of alpha particle, 1.7 fm • Intermediate attraction: nuclear binding • Repulsive core. Proof: NN scattering data, energies above 300 MeV, the s-wave phase shifts becomes negative • Nuclear force has a tensor component. Proof: the presence of the a quadrupole moment for the deuteron ground state • Nuclear force has a strong spin-orbit component. The triple p-waves from phase shift analysis at high energies can only be reproduced by adding a spin-orbit term to the central and tensor nuclear force component. Yukawa potential g e mr r Derived from Klein-Gordon eqn. 4p r With the increase of r, potential decreases very fast, which implies the short- range characteristics of nuclear force. AV18: • It contains an EM interaction & a phenomenological short and intermediate range • NN interaction describe by V(r, p, 1, 2) where terms are the relative position, relative momentum, spin. • It is based on AV14, 14 operators not related to charge, j i , i j i j , i j , S , S ij ij i j , L S, L S i j ...L S 2 • 4 charge operators Tij , i j Tij , SijTij , zi zj CD-Bonn 549 Exchange of mesons! It is 770 782 based on field theoretical perturbation theory. Completely defined in terms -meson describes multiple- of one-boson exchange! meson contributions in the single boson exchange. Nonlocality: the potential acting at one point may depend on the the value of the wavefunction at a different point. It essentially describes the relativistic treatment. All mesons with mass below nucleon mass are included. Interaction between nucleons in the same spin-angular momentum is identical for pp, np, and nn system. ----charge independence. Three-nucleon Force (3NF): UIX Fujita-Miyazawa term where Urbana IX potential: Short range repulsive term: Multiple-pion exchange and repulsive contributions Nuclear current operator • One-body current with Siegert operator • Meson Exchange Currents (MEC) include non-relativistic In my calculations MEC means that meson exchange currents were included directly, i.e., (transversal) E and M multipoles were calculated from spatial 1-body and 2-body currents. In my all other calculations (RCO) Siegert theorem was used, that assumes current conservation and replaces dominant parts of electric multipoles by the Coulomb multipoles. In case of exact current conservation MEC and Siegert would be identical (and I verified this practically with simple meson exchange model). However, it is very hard to achieve exact current conservation with realistic NN models, especially if they are nonlocal like CD Bonn. Therefore MEC and Siegert yield different results. Since the charge operator is theoretically known better than MEC's, it is advantageous to use Siegert approach, where, in fact, dominant contribution of not well known MEC's are replaced by better known 1N charge (you probably know all that). Therefore our standard calculation is Siegert. The first relativistic corrections are of order (p/m)**2 and are charge corrections, i.e., they have entirely no effect on MEC results. The large difference between MEC and RCO results means that the considered observable is very sensitive to relativistic corrections. I remember, that when I did first calculations without RCO, MEC and Siegert were quite similar. Once again: my MEC does not includes 1N charge relativistic corrections, but others two do so. One more remark: the calculations named "Siegert" have different meaning in my and Golak calculations. Nuclear current operators Siegert theorem: Electric multipoles = matrix elements of spatial current operator, Coulomb multipoles = matrix elements of charge operator. electric multipoles = Coulomb multipoles + higher order terms. The advantage of Siegert form is that Coulomb multipoles (charge), being strongly dominated by 1-body operators, are known better than spatial current operator. The uncertanties from spatial current operators enter then only in higher order terms and magnetic multipoles. Currents and nuclear forces are connected by continuity equation!!! More on nuclear current operators • The current is expanded in electric and magnetic multipoles. • The magnetic multipoles are calculated from the one- and two-baryon parts of the spatial current. • The electric multipoles use the Siegert form of the current without the long- wavelength approximation; assuming current conservation, the dominant parts of the one-baryon convection current and of the diagonal $\pi$- and $\rho$-exchange current are taken into account implicitly in the Siegert part of the electric multipoles by the Coulomb multipoles of the charge density; the remaining non-Siegert part of the electric multipoles not accounted for by the charge density is calculated using explicit one- and two-baryon spatial currents. • The potential and currents are related via continuity equation (charge conservation). Transversal MEC that do not contribute to the continuity equation are not constrained by this. • Potential and MEC's have to include the same meson exchanges. The same meson-nucleon coupling parameters have to be used for the potential and MEC's. Faddeev • Original Faddeev equations are for wave function components, their sum is the full wave function. In the differential form one needs to impose desired boundary conditions on the trial solutions. The scattering amplitudes can be extracted from the wave function, either from its asymptotic or from an additional integral with potentials. AGS • AGS equations are formulated not for observables, but for the transition operators • If one wants to calculate the observables for a given reaction, one needs the amplitude for that reaction. On-shell elements of transition operators are those needed amplitudes, that's why transition operators are so important. • They incorporate standard boundary conditions, so in some sense they are Faddeev equations in integral form. Particular (so-called on-shell) matrix elements of the transition operators are scattering amplitudes from which all observables can be calculated. On-shell means that initial and final state momenta and reaction energy satisfy energy conservation. • On the other hand, from the half-shell matrix elements of the transition operators one can construct the full wave function. Half-shell means that only initial state momenta and reaction energy satisfy energy conservation. Deltuva’s RCO treatment • one has to start with fully relativistic expression for one- nucleon e.m. current (4-dim. Dirac matrices and spinors) and then make an expansion in powers of (k/m_N). Nonrelativistic charge is of 0th order, nonrelativistic spatial current is of 1st order, whereas the leading relativistic corrections are of 2nd (charge) and 3rd (spatial) order. In the RCO calculations charge operator is a sum of those 0th and 2nd order terms. GDH sum rule • Anomalous magnetic moment: The difference between the observed gyromagnetic ratio of the electron and the value of exactly two predicted by Dirac's theory of the electron. The discrepancy is resolved using quantum electrodynamics. • Low energy theorem: from Lorentz and gauge invariance. • Unitarity means that the sum of probabilities of all possible outcomes is always 1. the S-matrix must be a unitarity operator, 4p Im f (0) k • Unsubtracted dispersion relation: causality. GDH sum rule: A simple derivation Forward Compton scattering amplitude f f1 e * e f 2 i e * e real photon energy e transverse polarization vectors spin vector of nucleon Dispersion Relation for spin-amplitude, the dispersion relation for the spin- averaged amplitude f is the kramers-kronig relation from optics. Re f 2 2 1 P A P d 2 4p 2 0 2 2 Gell-Mann etc. related the zero energy limit of spin-flip d 2p 2 2 amplitude to the square of the anomalous magnetic of P N A N M 2 N I the nucleon thr Low-energy theorem f 2 0 1 2 / MP P 2 2 GDH sum rule (more) • The only assumption in deriving the equation: the scattering amplitude goes to zero in the limit, photo energy g • The weakest argument of the derivation, no- subtraction hypothesis • Validity of no-subtraction hypothesis!!!! • It is the only “QCD-input” to the sum-rule • For fundamental charged particles with g=2 the no-subtraction hypothesis is applicable FEL principle Selection Rule of Gamma transition transition 0 or 1 2 3 4 5 type I p ip f +1 M1(E2) E2 M3(E4) E4 M5(E6) -1 E1 M2(E3) E3 M4(E5) E5 NMR • Gyromagnetic ratio: ratio of the magnetic dipole moment to the mechanical angular momentum/spin. g = -2 B/hbar, • AFP conditions the sweep rate slow enough rate fast enough: In this way, the magnetization of 3He follows the effective B field (“adiabatic”), while it is fast enough so the spin relaxation at resonance is minimal (“fast”). Here T1 and T2 are the longitudinal and transverse relaxation times. EPR SEOP • the Rb number density is ~10^15 cm-3 in the pumping cell and ~10^11 cm-3 in the target cell because of the different temperatures inside in each cell. Neutron detection: PSD, MPD4 module PMT 倍增器电极 D2 run Transition matrix element Deuteron ground state (spin is 1 and parity is positve): J p 1 L is the multipolarity of the incoming polarized gamma-ray. The mode of the gamma-ray is P. p=0 magnetic multipoles, p=1 electric multipoles. *** E1 radiation leads to l 1 L=1, S=1, J=0,1,or 2 Target Polarization measurement Two methods for cross calibration: 1. Water calibration S_water=6.6 uV, S_NMR=15.1 mV -> P=41.1% 2. EPR measurement P=38.2% So: two methods agree within 7% Hybrid cell “Linda” has a consistent performance during the run For more, please refer to our targer paper: K.Kramer et al, NIMA 582, Issue 2 (2007) backup Comparison of NMR with/no detectors Remove detectors, peak shift from 23.4G-> 25.4G Expected change: 8.5% signal increase Measurement: 15.13 mV->15.31 mV Actual change: 1.2% increase, plus 0.8% measurement loss So: mu metal results in 6.5% polarization loss Compton scattering E m0 c 2 E E e p p ' p e Ee c 2 pe m0 c 4 2 22 E cp cp cp m0 c 2 2 c 2 p 2 2 pp cos p 2 m0 c 4 2 1 1 m0 c 1 cos p p E h E 1 cos 1 E 1 cos m0 c 2 h me c 2.426 10 12 m m0 c My Ph.D. work 2003 Set up the polarized 3He target experimental 2004 apparatus, started polarization measurement 2005 Sept: first HIgS run. Polarization was low. The problem was later traced to the mirror. 2006 Tested a hybrid 3He target, published a target paper. Simulation for projection. Changed the configuration 2007 to longitudinal setup and tested target Worked with Capture group to test detectors. 2008 May: first measurement at HIgS Analyzed experimental data and ran simulation 2009 May: Test run of the new target cell at HIgS 2010 Checked data analysis and finalized results III. Helicity-dependent diff. cross section difference Expression: definition of the variables are the same as before It is calculated directly from the above expression, but can be verified by combining asymmetry and DXS results. The statistical uncertainty is Systematic uncertainty is obtained in the same way as before. Theory curves are the same as before

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