ORNL- 7/14/05 Puzzling Over Intricacies of the Few Nucleon Force Thomas B. Clegg University of North...

ORNL- 7/14/05

Puzzling Over Intricacies of the

Few Nucleon Force

Thomas B. CleggUniversity of North Carolina and

Triangle Universities Nuclear Laboratory

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 Ay puzzle in 3N and 4N systems

– Tensor force in few-nucleon scattering

ORNL- 7/14/05

Outline of Talk

• Introduction

• NN scattering and potential models




ORNL- 7/14/05

A Simple Example

• p + 3He elastic scattering

• Differential cross section measured below 11.5 MeV

• Data described with a 3-parameter phase shift analysis

Cro

ss S

ecti

on

(m

b/s

r)

Center-of-mass scattering angle

T B Clegg, et al., Nucl. Phys 50 (1964) 621

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Parameterization of Data

Cro

ss S

ecti

on

(m

b/s

r)

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

Ep = 7.51 MeV

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Partial Wave Analysis

/ and )/(

)/(tan ,0

)]2exp(1)[2exp(

)12)((cos)](ln(cscexp[)(csc4

1

221

1

10

2

02

122

12

vkveZZ

s

iiU

where

UlPiikd

d

l

sl

lll

lll

Phase shift

Coulomb scattering term Nuclear scattering term

L=0, s-wave

L=1, p-wave

L=2, d-wave

• Data are parameterized by phase shifts for individual partial waves.

Ep (MeV)

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Conclusion?

• Nuclear scattering from 3He is basically pretty simple.

Right?

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Conclusion?

• Nuclear scattering from 3He is basically pretty simple.

Right?

Not quite! What about spin?

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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

33

23

13

21

23

13

03

11

13

01

3

2

1

0

scattering Hepor np, nn, pp,For

DDDDL

PPPPL

SSL

SLJS L 12

NotationMultiplicity

Total Angular MomentumSinglet States

Triplet States

…

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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

33

23

13

21

23

13

03

11

13

01

3

2

1

0

scattering Hepor np, nn, pp,For

DDDDL

PPPPL

SSL

SLJS L 12


Total Angular MomentumSinglet States

Triplet States

…1

Mixing Parameter

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Mixing Parameter

• Presence of a tensor component mixes states with and

• The scattering matrix then has the form

1J1J

shifts. eigenphase theare and

and ,parameters mixing theare

0

0 ,

cossin

sincos

where,

J

J

11

11

21

J

J

J

i

U

UeUS

ORNL- 7/14/05

Outline of Talk

• Introduction





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N-N Scattering - 1959 • p-p scattering cross sections measured

with absolute accuracy ~ 0.2%

E = 3.037 MeV

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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

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• 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 phaseshifts, with ~40 parameters with overall χ2 = 1.

NN Interactions

From J. Carlson and R. Schiavilla, Rev. Mod. Phys. 70 (1998) 743

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Comparison of Phase Shifts


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Deuteron Properties• Experimental bound-state properties of

the deuteron are well predicted by all models.

As = Asymtotic S-state wave function normalization

η = Asymtotic D-to-S state ratio

rd = Radius μd = Magnetic moment

Qd = Quadrupole moment Pd = D-state probability


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Energy Levels of Light Nuclei

AV18 – Deletes 3-N force termsAV8’- Deletes electromagnetic termsAV6’ - 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

ORNL- 7/14/05

Outline of Talk

• Introduction





ORNL- 7/14/05

What Does Polarization Mean?

• For protons, neutrons, or 3He with , one defines

2

spin

)/()(on Polarizati NNNNPz

+1/2

-1/2

Pz = +0.602

Inte

nsit

y

Bz (mTesla ) B z (mTesla )

Inte

nsit

y+1/2

-1/2Pz =-0.689 Pz=+ 0.602 Pz=-0.689

+1/2

-1/2

ORNL- 7/14/05

What Does Polarization Mean?

• For deuterons with , one definesspin

)]/()3[(1on PolarizatiTensor

)/()(on PolarizatiVector 1010

10111

NNNNP

NNNNNP

zz

z

-1

P z = 0.518

P zz = -0.034-

+10

Inte

nsit

y

B z (mTesla )

P z = -0.073

P zz = -1.352

0

-1

+1Inte

nsit

y

B z (mTesla )

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Polarized Sourcery -1965First acceleration of polarized ions in tandem accelerator

Ibeam 5-20 pA Pbeam 0.45

Polarization preserved with foil stripper

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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,

SL

Modified from H.H. Barschall, Am J. of Phys 35 (1967) 119

Spin up, L down

Spin up, L up

Incident Beam

Scattered Beam

r

p

down

L pr

pr

up

L pr

rightleft

rigntlefty NN

NNA

ORNL- 7/14/05

• Simplest measureable is the vector analyzing power.

• New measurementsfor p-p scatteringshowed that global phase-shifts were not

correct at low energy.

Types of Data

RL

RLy NN

NNA

J.D. Hutton, et al., Phys. Rev. Lett. 35 (1975) 429

p + p scattering – 10.0 MeV

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• 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?

)])((3[1

2211212rmrmmm

rU tensor

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Types of Data - 1968 First spin correlation measurement with polarized beam & target

Ptarget 0.1

Ibeam 0.5 nA

Two points in 48 hours!

Axz

θcm

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Outline of Talk

• Introduction





ORNL- 7/14/05

Atomic Beam Polarized Source

Atomic Beam SystemsIonizer Systems

Acceleration & Spin Precession Systems

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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 -1

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Low Energy Target Area – E=20-680 keV

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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

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p + d Elastic Scattering

• Cross section measured at Ecm = 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

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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.

Ay

iT11

T21

T21

T20

Ayy

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 2P3/2 states, i.e.

the spin-spin interaction strength is also wrong.

2/74

2/54

2/34

2/14

2/52

2/32

2/54

2/34

2/14

2/32

2/12

2/34

2/12

2

1

0

1 ofspin has d since ,scattering pdFor

DDDDDDL

PPPPPL

SSL

SLJS L 12


Total Angular Momentum

Doublet States

Quartet States…

M. Wood, et al., Phys Rev 65 (2002) 34002

3/2

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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 1017 atoms/cm2 obtained– 1018 atoms/cm2 possible

• Very low backgrounds in spectra

• Used for 3He + p scattering – B. Fisher, TUNL Ph.D. thesis, 2003

Nozzle

Catcher

ORNL- 7/14/05

p + 3He Elastic Scattering

• New, low-energy cross section data taken with high accuracy, ~1%

• Cross-normalized topp scattering

• Data are fit extremely well by calculations which include a 3N force

B Fisher, Ph.D Thesis, UNC-CH, 2003

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p + 3He 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

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The Ay Puzzle – Status • Spin-dependent effects in these systems are not

small.

• Larger Ay 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+d667 keV

p+3He1.20 MeV 1.69 MeV

Viviani et al, PRL 86 (2001) 3739

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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

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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

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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

ORNL- 7/14/05

P.W. Lisowski et al., Nucl. Phys A232 (1975) 298

Polarized Neutron Beam

d + d 3He + n

n

p

n

p npp

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.

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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

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n-p Tensor Force

• The 3S1-3D1 coupling parameter ε1 measures strength of the tensor force.

• Modern n-p potentials underpredict ε1;

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

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A0y

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 50 100 150

No change

1P1 -10%

1P1 +10%

3P0 -10%

3P0 +10%

3P1 -10%

3P1 +10%

3P2 -10%

3P2 +10%

Alley and KnutsonAlley and Knutson

Refining Spin Dependence in p + 3He

p + 3He Phase-Shift Calculation: Curves show effect on Aoy at Ep = 5 MeV when optimum p-wave phase shifts are changed by ±10 %.

cm

ORNL- 7/14/05

Spin Correlation Ayy

Ayy

00.02

0.040.060.080.1

0.120.140.16

0.180.2

0 50 100 150

Ayy1P1 -10%1P1 +10%3P0 -10%3P0 +10%3P1 -10%3P1 +10%3P2 -10%3P2 +10%Alley and Knutson

p + 3He Phase-Shift Calculation: Curves show effect on Ayy at Ep = 5 MeV when optimum p-wave phase shifts are changed by ±10 %.

Alley and Knutson

No change

cm

ORNL- 7/14/05

• Essential needs for 3He 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 3He 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

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New Polarized 3He Target• New spin-exchange

optically-pumped, 3He polarizer

– Pyrex target cell with Kaptonwindows placed inside sine-theta coil

– Polarized 3He Pressure ~1ATM

– 3He polarization ~ 25 to 30%

monitored on-line with NMR

• First use – 3He(p,p)3He• Goal: Measure strength of

the tensor force coupling Katabuchi et al., Rev Sci Instrum 76 033503 (2005).

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3He Spin-Exchange Polarizer

Polarize 3He by spin-exchange with optically pumped Rb vapor

Diaphragm pump

3He Storage cells

Laserbeam Optical Pumping Cell

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Details of Target

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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

cmx

B

B

310

1

7.5 cm

24 current rods (3 mm

diam)

mu-metal(1 mm thick)

5 cm

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Sine-Theta Coil – Design Details

12" (30 cm)

1/8" Copper Rods

Mu Metal Shield

3 1/8 " (8 cm)

Windows

• 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.

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Beam Polarimetry – 1971First absolute calibration method for spin-1/2 particle polarization

Ay

Proton Lab Energy

p + 4He

Ay = 1 points

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Calibration for NMR System

• Using 3He + 4He scattering at a known Ay=1 point, the NMR coil sensitivity to 3He polarization was calibrated

ORNL- 7/14/05

p + 3He Data Taken

Energy (MeV) Observables Lab Angles (deg) 5.52 Axx 30-150

5.50 Ayo,Aoy,Ayy 30-150

4.04 Ayo,Aoy,Ayy 30-150

3.18 Axx 30-150

2.74 Ayo,Aoy,Ayy 70-150

2.74 Axx 30-130

2.68 Ayo,Aoy,Ayy 30-130

2.29 Axx 30-90

ORNL- 7/14/05 Puzzling Over Intricacies of the Few Nucleon Force Thomas B. Clegg University of North...

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Transcript of ORNL- 7/14/05 Puzzling Over Intricacies of the Few Nucleon Force Thomas B. Clegg University of North...