Coulomb distortions in the Lead Radius Experiment (PREX)

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