Coulomb distortions in the Lead Radius Experiment PREX

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Coulomb distortions in the Lead Radius Experiment
(PREX)
Tim Cooper (Univ. College Fraser Valley) C. J.
Horowitz (Indiana)
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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 VA
  and left handed feels V-A
• Subtract cross sec for V-A from cross sec VA

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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.

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Coulomb distortion results
208Pb at 850 MeV

• 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.

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Vector Analyzing power An

• Test distortion physics with vector analyzing
  power An left right asymmetry for transversely
  polarized beam.
• An0 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).

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850 MeV
An
At forward angles, An grows with increasing Z of
target
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208Pb at 850 MeV
An
Elastic intermediate states only!
An ¼ -.4 ppm comparable to parity violating A¼ .6
ppm because of large Z. Measure An during PREX.
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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

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PREX History

• Electron scattering workshop, INT 1997

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