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).

At forward angles, An grows with increasing Z of target

850 MeV

A n

208Pb at 850 MeV

An ¼ -.4 ppm comparable to parity violating A¼ .6 ppm because of large Z. Measure An during PREX.

A n

Elastic intermediate states only!

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