First Study of Three-body Photodisintegration of with Double Polarizations at

HIS

Xing ZongCommittee members:

Prof. Haiyan Gao (Advisor)Prof. Thomas MehenProf. John ThomasProf. Henry Weller

Prof. Ying WuFeb 19th, 2010

Ph.D. Dissertation Defense

He3

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, intermediat

e attraction, short-range repulsion– Modern NN potentials include: AV18[1] and

CD Bonn[2]. – NN potentials reproduce NN scattering data

base up to 350 MeV with high precision.– They underbind triton

[1] R.B.Wiringa et al. PRC 51, 38 (1995)

[2] R.Machleidt et al. PRC 53, R1483 (1996)

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

.

• 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)

i ji kji

ijkiji VVm

PH

2

2

△

△

Three-nucleon system: 3He

~90% ~2% ~8%

Polarized 3He is an effective neutron target

Movitation I: Test 3-body calculations3He p p n

2005 Nagai data @10.2 and 16 MeV (green)

Deltuva Golak

Calculation framework

AGS Faddeev

NN Potential

CD Bonn AV18

3 NF isobar Urbana IX

Nuclear EM current

Siegert theorem for 1body electric current, explict MEC for magnetic multipoles and h.o. terms E

Expliticit MEC: single nucleon current+ two () body current

Include Coulomb?

Yes Only in bound states

Relativistic treatment?

Yes No

△

Motivation II: Test GDH sum rule

22

22N

N

AN

PN

thrM

d

)26()027.0(23587.0

232 32 32

3

GeV GeV GeV ppnnHeGDHPGDHPGDH

GeV He

GeV

He

He

He

GDH

GDH

GDH

GDH

thr

thr

32

32

3

3

3

3

b496

[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)

3He GDH Sum Rule

Extrapolated from low Q2 3He GDH (E94-010) measurement @ JLab, (E97-110 much lower Q2)

HIS @ DUKE

Fundamental Interpretation: any particle with a nonzero anomalous magnetic moment has internal structure

b38247

???39217 b

b6.99.31

Few-body calculations of GDH integral up to

Deltuva et al. PRC 72, 054004 (2005): Green (with isobar)△ and Blue (without isobar)△

Golak et al. PRC 67, 054002 (2003) (Black curve)

Compare to our simple estimation:

???39217 b

It is crucial to carry out 3-body measurement to provide stringent test of the theories!

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: HIS provides circularly polarized ray @ 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 -ray source

Progress in Particle and Nuclear Physics 62 (2009) 257, Henry R. Weller, et al.

Experimental Setup

Liquid D2O target

Optics

table

Polarization preserving mirror

22mm

collimator

Experiment Setup@ Duke FEL

Spin Exchange Optical Pumping (SEOP)

• Rb vapor in a weak B field is optically pumped

• Spin exchange of hybrid alkali HeRbHeRb 33

KRbKRb HeKHeK 33

Rb only:

Hybrid:

N2 buffer gas

Largest 3He cell ever made!

NMR Polarimetry• A magnetic moment when placed in an

external B-field

• Transform into a rotating frame rotates around the B field at frequency

• The motion of M in the rotating frame

• Apply oscillating RF field

• Effective field in the rotating frame at frequency

xtBx

cos2 1B

gyromagnetic ratio

xBzBBeff ˆˆ)( 10

ytBxtB

ytBxtB

sincos

sincos

11

11

BMdt

Mdlab

|

Mdt

Md

dt

Mdrotlab

||

0| BMdt

Mdrot

z

NMR - Adiabatic Fast Passage (AFP)

• Ramp the holding field from below the resonance to above it

• AFP line shape

zB ˆ0

r/

xBzBBeff ˆˆ)( 10

2/12

02

1

100

/

BB

BB

Amplitude of voltage at resonance, proportional to the sample polarization.

Water calibration to extract 3He Polarization• The ratio of 3He signal to water signal

• The definition of polarization

• The polarization of proton in water is given by

• The polarization of 3He is

pppppn kTP /tanh

pn

hnp

h

nVP

nVPR

0

0

nn

nnpn

pppp kT /

hpp

hp

h

phn pT

RTn

V

VP

22

rf frequency

nP nuclear polarization

n number density

magnetic moment

V volume of the cell

hp pressure of He3 cell

hT temperature of He3cell

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 DetectionImportant info from the signal:

ADC: Pulse-height (energy)

TAC: Pulse-shape discrimination (particle separation)

TDC: Time of flight (time)

The traditional PSD working principle1D TAC: Proportional to the length of the trailing edge of the detector signal, therefore measure the particle type.

n

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:

D2 run: used as a calibration of main experiment

3He run: took spin P and A alternatively to form asymmetry and to reduce systematic uncertainties.

Al run: determine gamma peak position to obtain timing information

N2 run: background subtraction

Data Analysis Overview:

1. Calibration: relate ADC and TDC to PH (energy) and TOF (timing) information.

2. Cuts: separate gammas and neutrons

3. Integrated flux determination

4. GEANT4 simulation to determine the acceptance

Calibration I: ADC

Determine Pedestal (offset resulting from electronics bias)

Compare Cs source runs with simulation to find tune gains (energy per channel)

Calibration II: TDC

Determine Gamma peak TDC position

Compare D2 run and simulation to determine C (TDC Calibration constant)

How to select neutrons?

NeutronCandidates

Gammas Cuts Values

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

pnD b 361257

Principle:

2sinAd

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 5to 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 HIS beamIntegrated 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

The two fits give us very similar results. Using the Bsin2()+C fit result, we obtained tota

l cross section :1247+/-45 bin agreement with world data: 0 = (1257+/-36 b)

A*sin2()

Goal of this run is consistency check:• calibration• data selection (cuts) • simulation• normalization

B*sin2()+C

I. Asymmetry Results

Systematic study includes PSD, PH, TOF cuts variations, beam and target polarization, and integrated photon flux.

Expression:

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 sectionExpression:

Data is from En=1.1 MeV, corrected by simulation (model-dependent) from 0.

Statistical uncertainty:

AV18

AV18+UIX

CD Bonn

CD Bonn+ △ is the detector acceptance which includes both detector efficiency and the extended target effect.

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:

lllPa

d

d

cos

Fit results:

776±18(stat.) ±32(sys.)±11(mod)b

ba 9.27.610

Total cross section result:

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 HIS 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 HIS

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 BackgroundNuclear interactions and Nobel Prizes1949 Hideki Yukawa: exchange of pion accoun

ted for the force between two nucleons1969 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 anti-quark spin antiparallel

Vector Mesons: quark and 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 3

00 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

r

egr

mr

4

Derived from Klein-Gordon eqn.

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,

• 4 charge operators 2...,,,,,, SLSLSLSS jijiijijjijijiji

zjziijijijjiij TSTT ,,,

CD-Bonn

Exchange of mesons! It is based on field theoretical perturbation theory. Completely defined in terms of one-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.

-meson describes multiple-meson contributions in the single boson exchange.

549

770 782

Three-nucleon Force (3NF): UIX

where

Fujita-Miyazawa term

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

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.

Siegert theorem:

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-w

avelength 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 th

e 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 outcome

s is always 1. the S-matrix must be a unitarity operator,

• Unsubtracted dispersion relation: causality. )0(Im

4f

k

GDH sum rule: A simple derivation

0

22

2

22

2 4

1Re

dPf PA

Dispersion Relation for spin-amplitude, the dispersion relation for the spin-averaged amplitude f is the kramers-kronig relation from optics.

222 /

2

10 PPMf

Low-energy theorem

Forward Compton scattering amplitude

eeifeeff

*2

*1 real photon energy

transverse polarization vectors

e

spin vector of nucleon

Gell-Mann etc. related the zero energy limit of spin-flip amplitude to the square of the anomalous magnetic of the nucleon

IM

dN

AN

PN

thr

22

22

GDH sum rule (more)

• The only assumption in deriving the equation: the scattering amplitude goes to zero in the limit, photo energy

• 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 type 0 or 1 2 3 4 5

+1 M1(E2) E2 M3(E4) E4 M5(E6)

-1 E1 M2(E3) E3 M4(E5) E5

I

fi

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 elementDeuteron ground state (spin is 1 and parity is positve):

1J

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 1l

L=1, S=1, J=0,1,or 2

Target Polarization measurement

Hybrid cell “Linda” has a consistent

performance during the run

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%

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

eEEcmE 20

eppp '42

0222 cmpcE ee

cpE 42

022222

0 cos2 cmppppccmpccp

cos111

0

pp

cm

cos10

cm

h

mcm

h 12

0

10426.2

cos112

cm

EE

E

e

My Ph.D. work2003

2004

2005

2006

2007

2008

2009

Set up the polarized 3He target experimental apparatus, started polarization measurement

Sept: first HIS run. Polarization was low. The problem was later traced to the mirror.

Tested a hybrid 3He target, published a target paper. Simulation for projection. Changed the configuration to longitudinal setup and tested target

Worked with Capture group to test detectors. May: first measurement at HIS

Analyzed experimental data and ran simulation

May: Test run of the new target cell at HIS

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