Few body studies @HIgS below
20 MeV
Henry R. Weller
Duke University and Triangle Universities Nuclear Laboratory
HIgS PROGRAM
Chiral 09, Bern Switzerland
HIgS
Nearly Mono-energetic g-rays from 2 to 100 MeV
Up to 65 MeV now
Up to ~100 MeV in 2010
•
•
~100% Linearly and Circularly Polarized g-rays
High Beam Intensities
(Ran with 2x108 on target at 15 MeV -June 2009)
Chiral 09, Bern Switzerland
Chiral 09, Bern Switzerland
The Upgraded HIgS Facility
• 1.2-GeV Booster Injector
• RF System with HOM Damping
Chiral 09, Bern Switzerland
Some typical beam intensities
•
Eg(MeV)
1-2
8 – 16
20 – 45
50 – 95
Beam on target (DE/E = 3%)
2 x 107 g/s
8 x 107 (total flux of 2 x 109)
8 x 106
4 x 106 (by 2011)
Chiral 09, Bern Switzerland
Photodisintegration of the deuteron
The E1 gammas are absorbed on the 1+ (3S1) state, exciting 0-, 1-, and 2- strength,
which then decays into n+p having S=1 (since DS=0) and l=1 (p-waves).
There are 3 different p-wave terms corresponding to J= 0-, 1-, and 2- . No
information about the splittings of these has been available—until now.
Chiral 09, Bern Switzerland
d(g,n)p at 14 and 16 MeV
(Dissertation topic of Dr. Matthew Blackston)
Used the 88 neutron detector array Blowfish (had
TOF and PSD).
Heavy water target.
100% linearly polarized beams.
A full simulation was performed using Geant4 to
correct the data for finite geometry and multiple
scattering effects.
Chiral 09, Bern Switzerland
The upgraded BLOWFISH array
Chiral 09, Bern Switzerland
Chiral 09, Bern Switzerland
Chiral 09, Bern Switzerland
Chiral 09, Bern Switzerland
Chiral 09, Bern Switzerland
Phase shifts from the SAID n-p scattering analysis
For Eg= 14 MeV (En (lab) = 23.6 MeV)
1
50.74o
3
8.61o
3
-4.88o
3
2.86o
3
-2.9o
3
4.12o
3
0.13o
S0
P0
P1
P2
D1
D2
D3
Chiral 09, Bern Switzerland
Chiral 09, Bern Switzerland
•First determination of the splittings in the p-wave (E1) amplitudes in
photodisintegration of the deuteron at 16 MeV.
Chiral 09, Bern Switzerland
The Gerasimov Drell Hearn Sum Rule

4  2
(

P  A)dE / E 

S

I
GDH
2
th
m
2
Chiral 09, Bern Switzerland
GDH Sum Rule studies @ HIgS
Measure the GDH integrand on d below pion
threshold.
• Compare to theoretical predictions. Provides
extremely sensitive test of spin dependent
effects such as relativistic spin-orbit
currents.
• Combine with the global effort to measure
this for n, p and d. Our piece is essential for
a test of consistency and a search for new
physics.
Chiral 09, Bern Switzerland
The Gerasimov-Drell-Hearn (GDH) Sum
Rule for Deuteron
P/A(E) are the total cross sections for the absorption of circularly polarized
photons on a target with spin Parallel/Antiparallel to the spin of the photon;
 = anomalous magnetic moment (of the deuteron).
IGDH Predicted = 0.65b
d = -0.143 m
Chiral 09, Bern Switzerland
Chiral 09, Bern Switzerland
The GDH integrand can be written in terms of the
contributing T-matrix elements
[if no p or d-wave splitting, P – A = -3 (M1)]
Chiral 09, Bern Switzerland
At very low energies, s-waves will dominate. If p and d-waves are
present but don’t split, their contributions drop out.
Chiral 09, Bern Switzerland
Extracting the fractional M1 contribution S(M1) from the measured
analyzing power at 90o
Chiral 09, Bern Switzerland
Obtaining a point near threshold from thermal neutron
capture data
Thermal neutron capture cross section is well measured and known to
be pure M1.
cap = 332 +/- 0.60 mb @ En ~ 0.025 eV.
The detailed balance factor is 1.6 x 10-6 giving
(M1) = 0.547 b @ Eg = 2.2246 MeV.
Using P – A = - 3 (M1) gives
P – A = -1.641 +/- 0.003 b @ 2.2246 MeV
Chiral 09, Bern Switzerland
Chiral 09, Bern Switzerland
Results for the GDH integral at low energies
The solid black curve was a fit to the data using a
Lorentzian line shape parameterized by amplitude,
centroid and width. The GDH integral of this function up
to 6 MeV gave a value of
GDH (thresh6 MeV)exp = -603 +/- 43 b
(note: already much larger than -436 b)
Theory (Arenhoevel et al.) gives -627 b (full)
and -662 b (s-wave only)
Chiral 09, Bern Switzerland
A second “sum-rule” which can be extracted is the forward spin
polarizability g0
Chiral 09, Bern Switzerland
Xiangdong Ji and Yingchuan Li have calculated the forward spin
polarizability of the deuteron to next-to-leading order in pionless EFT.
(Phys. Letts. B 591 (2004) 76 -82)
(determined by deut BE, isovector nucl. mag. mom., 1S0 scatt length)
Chiral 09, Bern Switzerland
Chiral 09, Bern Switzerland
Chiral 09, Bern Switzerland
Comparison with this experiment
The NLO calculation gives a value of
go = 4.26 fm4
If we integrate from threshold up to 6 MeV
we obtain
go = 3.75 +/- 0.18 fm4
Chiral 09, Bern Switzerland
Chiral 09, Bern Switzerland
Predicted behavior (Ahrenhovel) of the GDH
integrand. Solid line includes a relativisitic
correction.
Chiral 09, Bern Switzerland
Relativistic contributions
Leading order relativistic contributions are required to give
the correct form of the term linear in photon momentum
in the low-energy expansion of the Compton amplitude.
The relativistic spin-orbit current effects the splitting of the
p-wave amplitudes, leading to a positive value of the
GDH integrand. (It increases the relative strength of the
3p term.)
2
Chiral 09, Bern Switzerland
•First determination of the splittings in the p-wave (E1) amplitudes in
photodisintegration of the deuteron at 16 MeV.
Chiral 09, Bern Switzerland
The GDH integrand can be written in terms of the
contributing T-matrix elements
[if no p or d-wave splitting, P – A = -3 (M1)]
Chiral 09, Bern Switzerland
Results for the GDH integrand from the two solutions. Without p-wave
splittings the value at 14 MeV is predicted to be -50 b (from the s-wave M1
term). Positive values are predicted only when the relativistic contribution is
included.
Chiral 09, Bern Switzerland
Requirements for direct measurements of
The GDH
integrand on the Deuteron
Circularly Polarized gamma rays—available NOW!
Neutron detection array—Blowfish –ready to go!
Polarized frozen-spin target—Under construction in collaboration
with Don Crabb and Blaine Norum of U. Va. Scheduled to be
installed this spring.
Chiral 09, Bern Switzerland
The upgraded BLOWFISH array
Chiral 09, Bern Switzerland
Frozen Spin Polarized Deuterium Target --target and
installation (loading dock system) are fully funded.
Butanol
Polarization ~ 80 %
Polarizing Field ~ 2.5 T
Holding Field ~ 0.6 T
Thickness ~ 3.5 x 1023 d/cm2
Chiral 09, Bern Switzerland
Chiral 09, Bern Switzerland
The GDH integrand for deuterium
A 300 hour run will allow us to measure the GDH
integrand between 5 and 50 MeV to an overall
accuracy of about 5% or better, assuming a beam
of 1 x 107 g/s with ~5% energy spread.
Besides being a crucial piece of the world’s data
on the GDH sum rule, the integrand will provide
important tests of potential and EFT calculations,
being more sensitive to spin physics and
relativistic contributions than any previously
measured observable.
Chiral 09, Bern Switzerland
Anticipated schedule
The HIFROST target will be installed in
2010.
We (the GDH @HIgS Collaboration) expect
to begin taking data in mid 2010, with
preliminary results between 5 and 50 MeV
by the end of the year.
Chiral 09, Bern Switzerland
3He(g,p)d
and 3He(g,pp)n cross sections
(obtained with 104 g/s and 4% energy spread)
S. Naito, Y. Nagai, T. Shima, et al.
Chiral 09, Bern Switzerland
Chiral 09, Bern Switzerland
Measured (g,pp)n cross section to be 0.15(5) mb at 10.2 MeV
which is 3 times smaller than theory (AV18 + Urbana IX predicts
0.5 mb). The value at 16.0 MeV is about 15% below theory.
(a) two-body; (b) three-body; (c) total cross section
Chiral 09, Bern Switzerland
Momentum-space description of three-nucleon breakup
reactions including the Coulomb interaction
A. Deltuva, A.C. Fonseca, and P.U. Sauer
Phys. Rev. C 72, 054004 (2005).
• Extended the technique of solving the three-particle Alt-GrassbergerSandhas equation to include the (screened) Coulomb potential between
the protons. Used the CD-Bonn + D potential.
• Found that the value of (g,pp)n decreased by
~25% when Coulomb effects in the final state were
included at 10.2 MeV.
• Factor of 3 is unaccounted for!
Chiral 09, Bern Switzerland
Final state Coulomb interaction decreases the cross
section by ~15% @ 12.8 MeV
from A. Deltuva et al.
Chiral 09, Bern Switzerland
The HIgS experiment:
3He(g,n)pp @ 11.4,12.8, 13.5, 14.7 MeV
Chiral 09, Bern Switzerland
Efficiency corrected (using Geant4 simulation) absolute cross sections--@ 12.8
MeV, experiment is 22% below theory, but in good agreement at higher
energies
Chiral 09, Bern Switzerland
Conclusions and future studies
Coulomb corrected theory is in good agreement with data
down to ~13.5 MeV.
At 12.8 MeV, data are ~22% below theory. The
discrepancy is primarily in the higher energy neutrons.
The observed neutron energy distribution is consistent
with pure 3-body phase space.
Data at 11.4 MeV are being analyzed. Data at lower
energies will be taken in the near future to verify and try
to understand the discrepancy of a factor of 3.
Chiral 09, Bern Switzerland
Conclusions and future studies
Precision data on photodisintegration of the deuteron with 100%
linearly polarized beams @HIgS has given us the first
determination of the splittings of the E1 p-wave amplitudes.
These results confirm the positive value of the GDH integrand
which arises theoretically from relativistic spin-orbit currents.
The results also allow for the first determination of the forward spinpolarizability of the deuteron. The value deduced is in reasonable
agreement with EFT and potential model predictions.
The deduced GDH integrand provides a direct experimental signature
of the 1S0 state of the deuteron.
Extension of GDH measurements up to 100 MeV will be performed
starting next year.
Chiral 09, Bern Switzerland
Special thanks to: Mohammad Ahmed,
Matthew Blackston, Don Crabb, Blaine
Norum, Brent Perdue and Rob Pywell
Chiral 09, Bern Switzerland
Chiral 09, Bern Switzerland
Chiral 09, Bern Switzerland