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## Few-body studies at HI g S

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Few-body studies at HIgS

Sean Stave

Duke University & Triangle Universities Nuclear Laboratory (TUNL)

And Mohammad Ahmed, Henry Weller

Supported in-part by DOE grant DE-FG02-97ER41033

www.tunl.duke.edu www.tunl.duke.edu/higs/

Few-body experiments at HIgS

Exploring A=2 and 3

Photodisintegration of the Deuteron & 3He

- Importance
- Theoretical understanding of A=2,3 systems
- Global state of the experiments
- The role HIGS plays in the understanding of these systems
- What is on the horizon for HIGS

Overview of A=2

The Deuteron

Fundamental

Sum Rules

The BBN Importance

Ideal Laboratory for

the study of 2-body

NP system

“Baryometer”

- Test of EFT and PM
- Calculations

d

Target

Beam

d

Understanding Few-Nucleon Systems

2H, the simplest of Few-Body Systems

The Theoretical Framework, A=2

- Potential Model
- Effective Field Theory
- Sum Rules for Deuteron:
- Gerasimov-Drell-Hearn (GDH) &
- Forward Spin Polarizability (g0)

The A=2 Theoretical Framework

Potential Model Calculations [H. Arenhovel, M. Schwamb et al.]

- High precision NN-potentials, MEC, RC and D degrees of freedom

The Pion-less Effective Field Theory Approach (EFT)

[M. Savage, J-W. Chen & G. Rupak]

- E1 is computed up to N4LO and M1 is calculated up to N2LO,
- n-p radiative capture cross section predicted to an accuracy of
- 1% at CM energies ~ 1 MeV

Most accurate theory describing 2-Nucleon system,

Minimal data exist to test the predictions in this energy region

The Experimental Effort at HIgS

Few-Body Studies at TUNL are carried out at HIgS

Duke Free-Electron Laser Laboratory

(HIgS)

HIgS g-ray beam generation

RF Cavity

Optical Klystron

FEL

Booster Injector

Mirror

LINAC

High Intensity Gamma-Ray Source:

HIgS Parameters

- Circularly and Linearly Polarized nearly monoenergetic g-Rays
- from 2 to 60 MeV (90 MeV in the next 1 to 2 years)
- Total Gamma-Ray Flux ~ 108 to 109g/s

A=2 Experiments at HIgS

- S(135°) Eg = 3.58 MeV Eric Schrieber et al., 2000
- S(90°) Eg = 2.39 to 4.05 MeV Werner Tornow et al., 2003
- s(q); S(q) Eg = 4 to 10 MeV Brad Sawatsky et al., 2005
- S(90°) Eg = 2.44 to 4.0 MeV Mohammad Ahmed et al., 2007
- s(q); S(q) Eg = 14 and 16 MeV Matthew Blackston et al., 2007
- s(q); stotalEg = 2.44 to 4.0 MeV Mohammad Ahmed et al., 2008

All experiments were performed using linearly polarized beams

Liquid Scintillating

Detectors in

Blowfish Array

Li-Glass

Detectors in

an Array

Liquid Scintillating

Detectors

Schreiber

Tornow

Sawatsky

Blackston

Sawatsky

Blackston

Ahmed

Status of the “baryometer”

- Very little data in energy region for BBN

d(g,n)p Cross section Expansion

Polarized beam, unpolarized target

(M1)

(E1)

Photon analyzing power measurement is proportional to

the %E1 contribution to the total cross section

A=2 Results at HIgS

Tornow et al.

[PLB 574, 8 (2003)]

Excellent agreement between data and PM and EFT

4-neutron detectors at a

polar angle of 90 degrees and

azimuthal angles of

0,90,180, and 270 degrees

PRC 61, 061604 (2000)

Curves from EFT (Rupak et al.)

d(g,n)p at HIgS: Ahmed et al.

No significant

d-wave

contributions

are present

at these low

energies

4.0 MeV

3.5 MeV

2.44 MeV

Sum Rules for the Deuteron

Spin-flip part of forward Compton scattering amplitude:

GDH :

Arenhoevel et al.

GDH on the deuteron: Theory

With

relativistic

corrections

Without

relativistic

corrections

Negative at

low energies

Crosses zero

at low energies

Arenhoevel et al.

[NPA 631, 612c (1998)]

Cross section difference expansion

Polarized beam, polarized target

]

If ignore d-waves and splitting of p-waves

at low energies then

A=2 Global Impact

First-ever indirect determination of the GDH Sum Rule

for Deuteron at low energies: -603 ± 43 mb (Fit from thr. to 4 MeV, integrated from thr. to 6 MeV)

Remember Ds =-3s(M1)

Ahmed et al. [PRC 77, 044005 (2008)]

A=2 GDH Comparison: Data and Theory

- Theory and Data integrated from threshold to 6 MeV
- Data: -603 ± 43 mb
- Arenhoevel: -627 mb
- -3sM1: -662 mb
- Experimentally confirmed negative value at low energy

Ahmed et al. [PRC 77, 044005 (2008)]

A=2 Results at HIgS

Blowfish

- 88-cell Liquid Scintillating
- detector array
- 25% of 4p coverage
- q = 22.5 to 157.5 degrees

d(g,n)p: Weller/Blackston’s Results

Blackston et al. [PRC 78, 034003 (2008)]

16 MeV

- Cross section and analyzing power at 16 MeV as a function of angle compared with Schwamb/Arenhoevel potential model
- High quality of data allowed a fit using 7 reduced transition matrix element amplitudes (phases fixed by np elastic scattering, SAID)

d(g,n)p: Weller/Blackston’s Results

16 MeV

First-ever observation of the splittings of the

E1 (p-wave) amplitudes in low energy

deuteron photo-disintegration

[PRC 78, 034003 (2008)]

Note: d-wave results negligible and consistent with theory

Value if no

p-wave splitting

Compared with Schwamb/Arenhoevel Potential Model

A=2 Global Impact

First-ever observation of the p-wave splittings and

confirmation of the relativistic corrections in the theory

[PRC 78, 034003 (2008)]

Sum Rules for the Deuteron

Spin-flip part of forward Compton scattering amplitude:

Forward Spin-Polarizability:

NLO, EFT calculation by X. Ji et al.

A=2 g0 Comparison: Data and Theory

First-ever indirect determination of g0 for deuteron at low energies

Data integrated from threshold to 6 MeV

- Data: 3.75 ± 0.18 fm4
- Ji-LO: 3.762 fm4
- Ji-NLO: 4.262 fm4
- Arenhoevel: 4.1 fm4

Ahmed et al. [PRC 77, 044005 (2008)]

What is our understanding of Few-Nucleon systems?

3He, the simplest of Few-body Systems with

3NF and no excitation spectrum

System being considered

- 3He breakup
- Two-body
- Three-body

The A=3 Experiments at HIgS

- Photodisintegration of 3He between 7 and 20 MeV
- Total and differential Cross Section

- Total cross section for the 2-body breakup from 7 to 20 MeV,
- Tornow et al.
- Total and differential cross sections for the 3-body breakup,
- 12.8, 13.5, and 14.7 MeV, Perdue et al.

The A=3 Theoretical Framework

Recent efforts in understanding 3-body systems

[Deltuva, Fonseca, Sauer]

- Coulomb Interaction in the 2- and 3-body
- photodisintegration channels
- CD-Bonn + D, with D isobar mediating an effective 3NF and
- 2-, 3-nucleon currents, and still consistent with 2NF
- Still has issues at low-energies (3 Nucleon Analyzing Power Puzzle still stands!)

The problem is also being worked upon by

[Witala, Glockle, Nogga, and Golak, et al.]

Current Status of the 3He breakup cross section

Shima & Nagai

[PRC 73, 034003 (2006)]

Compared with previous data

and AV18 and AV18+Urbana IX

2-body

- No measurement that is consistent across the energy range
- Clearly calls for a set of measurements with the same experimental conditions across the energy range

3-body

total

Factor of 3

below theory

A=3 at HIgS: 2-body breakup of 3He, Tornow et al.

- High Pressure 3He/Xe cell

Data are still under analysis for absolute normalization

Two-body peaks clearly separated

3He 3-body Breakup at HIgS: Weller, Perdue et al.

12.8, 13.5, and 14.7 MeV

3He 3-body Breakup: Theoretical Framework

No coulomb

interaction

With coulomb

interaction

No sensitivity to

coulomb interaction

in the analyzing

power

Deltuva et al.

[PRC 72, 054004 (2005)]

Weller, Perdue et al. Initial Results

From an APS talk by B. Perdue

- HIgS Data

- Deltuva

- 3-body phase space

- Phase-Space (PS) to
- PS + NP transition near
- 12.8 MeV
- About 25% below theory

Summary

What have we accomplished?

- Confirmation of PM/EFT for the deuteron near BBN region
- First determination of the splitting of the p-waves in the
- photodisintegration of the deuteron
- First confirmation of GDH sum rule for the deuteron
- Confirmed large negative strength
- Confirmed positive going above 8 MeV and that it arises fromthe splitting of the p-waves
- First determination of the g0 sum rule for deuteron
- Precision 3-body photodisintegration cross section for 3He
- disagree with state-of-the-art theory at low energies

Future plans at HIgS

New era of precision measurements at HIgS - PAC-09 has approved the following

experiments for the next two years:

- Continue to measure deuteron photodisintegration cross section
- at lower energies (below 2.4 MeV) (Using OTPC)
- Direct measurements of the GDH on deuteron
- Compton scattering on the deuteron
- Measurement of two- and three-body cross sections of g + 3He
- GDH Sum rule for 3He
- Cross section measurement of g + 4He

Weller, Perdue et al. Initial Results

- Results from Gorbunov (1976) coarsely binned but consistent with current results

8-12 MeV

12-16 MeV

A. N. Gorbunov, Proc. Of the P.N. Lebedev Phys. Inst., p. 1 (1976)

A=2 Introduction

(

(

(

(

(

(

)

)

)

)

)

)

d

d

d

n

n

p

γ

p

n

p

p

γ

,

,

,

,

,

,

Few-Nucleon Systems and BBN Network

Light-element abundances depends

on

WMAP determines

and11 nuclear reaction rates

n-p capture reaction rate becomes a “baryometer”

Understanding the photodisintegration of the deuteron

In 1936, H. A. Bethe and R. F. Bacher wrote …

“… the transition from the ground state to the state of positive energy . . .

can be produced by a magnetic moment, this ‘magnetic dipole’ photoelectric

effect is, however, small compared to the ‘electric dipole’ effect …, except for

very low energies . . . the final state must be a P-state”

[ Rev. Mod. Phys. 8, 82-229 (1936) ]

The A=2 Experiments at HIgS

In the near-threshold region, the photodisintegration

cross section can be expanded in terms of S and P wave

amplitudes. We can ignore the D-waves and

The P-wave splittings (evidence will be presented soon) :

Bethe, 1936

Photon analyzing power measurement is proportional to

the %E1 contribution to the total cross section

A=2 Global Impact (Ahmed et al.)

- First-ever indirect determination of g0 for deuteron at low energies

Ahmed et al. [PRC 77, 044005 (2008)]

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