Download Coulomb distortions

Coulomb distortions in the Lead
Radius Experiment (PREX)
Tim Cooper (Univ. College Fraser Valley)
C. J. Horowitz (Indiana)
Coulomb distortions
• Interested in neutron densities of heavy nuclei.
These have large Z and important coulomb
distortions.
• Solve Dirac equ for electron in both coulomb V(r)
and weak axial A(r) potentials.
• In helicity basis, right handed e feels pot V+A
and left handed feels V-A
• Subtract cross sec for V-A from cross sec V+A
Numerics
• Crucial help from E. D. Cooper! His code RUNT for
relativistic proton-nucleus scattering in S, V optical pots
Helped B. C. Clark with Dirac phenom. numerics.
• Worry about subtraction of two large cross sections???
• Each cross sec is very hard numerical problem because
convergence of partial waves is poor. Standard tricks to
speed convergence.
• Backward cross section is much much harder numerical
problem (need phase shifts to many places) than
forward angle asymmetry.
• Now several independent codes agree.
Coulomb distortion results
• Distortions reduce
asym. by ~30% and
somewhat reduce
sensitivity to neutron
density.
• Largest correction to
asymmetry.
• Can be accurately
calculated and
charge density is
known.
208Pb
at 850 MeV
Vector Analyzing power An
• Test distortion physics with vector analyzing power An:
left right asymmetry for transversely polarized beam.
• An=0 in Born approx. from time reversal. Nonzero value
only from 2 or more photons.
• An is large for high Z of nucleus, since distortions large .
• An is potential systematic error for parity experiments.
• We exactly solve Dirac equation to sum photon
exchanges to all orders. Only keep elastic
intermediate states. These are coherent / Z2 for
heavy nucleus.
• Hard numerical problem: two independent codes RUNT
(E.D. Cooper) and ELASTIC (CJH). Agree with
published results at lower energies (15 MeV).
An
850 MeV
At forward angles, An grows with increasing Z of target
at 850 MeV
An
208Pb
Elastic
intermediate
states only!
An ¼ -.4 ppm comparable to parity violating A¼ .6
ppm because of large Z. Measure An during PREX.
PREX History
• 1989 Donnelly, Dubach, Sick  PV for n densities.
• 1998 CJH calculates PV asy with Coulomb
distortions.
• 1999 Michaels + CJH optimize PREX kinematics.
• 2000 PREX discussed at ECT* PV conference.
• 2001 Relation of neutron density to:
– Pressure of neutron matter (Alex Brown)
– Density dependence of symmetry energy
– Many neutron star properties
• 2000- HAPPEX, HAPPEX II, HAPPEX He
…experiments
PREX History
• Electron scattering workshop, INT 1997