PREX and Bulk Properties of Neutron Rich Matter • The lead radius experiment uses parity v. to measure the neutron radius of 208Pb. • Implications for – nuclear structure. – neutron stars. 208 Pb – atomic parity experiments. FRIB Workshop, MSU, Nov. 2008 C. J. Horowitz, Indiana University 1 Neutron Weak Charge • In Standard Model Z0 boson couples to mixture of weak and E+M currents. − 2 • Weak charge: QW = 2[Weak isospin 2sin ΘW QE+M ] 2 • Important accident? sin ΘW ≈ 0.25 p = 1 − 4sin2Θ ≈ 0 05 QW W . Weak Q Q • Weak interactions (at isospin E+M W 2 2 low Q ) probe neutrons. p 1/2 1 1 − 4sin ΘW n -1/2 0 -1 208Pb Weak + E+M Charge Densities p 3 ! n ! − ! QW p ! − ! ρW (r) = d r [GW (r r)ρn(r ) + n GW (r r)ρp(r )] ! QW ! ! ! ρ (r) = d3r Gp (r − r)ρ (r ) ch ! E p 3 2 QW = d rρW (r) = N − (1 − 4 sin ΘW )Z Total weak charge of nucleus ! Parity Violation Isolates Weak Form Factor D,D,S • Parity violating asymmetry Apv is cross section difference for positive and negative helicity electrons dσ/dΩ+ − dσ/dΩ− Apv = dσ/dΩ+ + dσ/dΩ− 0 • Apv from interference of photon and Z exchange. In Born approximation 2 2 GF Q FW (Q ) 2 3 sin(Qr) Apv = 2 FW (Q ) = d r ρW (r) 2πα√2 Fch(Q ) ! Qr • PREX will measure Apv for 1 GeV e scattering from 208Pb at 5 degrees to 3% (A ¼ 0.6 ppm). This gives neutron radius to 1% (± 0.05 fm). • Purely electroweak reaction is model independent 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 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. CJH + ED Cooper Radiative Corrections e • Tree level diagram is Z0 order QW. Radiative correction is • Q order α/π = 0.2% W Probably not big issue • 0 for PREX but very γ Z important for QWeak experiment on proton Z coupling to inelastic because QW is so small. proton state can be large Radiative correction for • α QWeak = 6% πQW CJH+ M. Gorshteyn PREX in Hall A at JLab Spectometers Lead Foil Target Pol. Source Hall A CEBAF PREX Workshop Aug 08 R. Michaels High Resolution Spectrometers Spectrometer Concept: Resolve Elastic 1st excited state Pb 2.6 MeV Elastic detector Inelastic Left-Right symmetry to Quad control transverse polarization systematic target Dipole Q Q PREX Workshop Aug 08 R. Michaels Systematic Error Challenges • Small asymmetry: 500 ± 15 ppb ± 3% • High precision: δApv/Apv • No backgrounds (not what you might think ---> spectrometers) • 1% normalization (polarimetry). • Analyzing power ~ 10 Apv. Need to measure and control transverse components of polarization. • Need excellent control of helicity correlated beam properties. Measured in previous exp. • Hall A parity group have completed several successful parity experiments. Density FunctionalPREXTheor yand(DFT) Hohenberg-Kohn: ThereNuclearexists an energy functional Evext [ρ] . Structur3 e Evext [ρ] = FHK[ρ] + d x vext(x)ρ(x) ! FHK is universal (same for any external v ) = H to DNA! ext ⇒ 2 Introduce orbitals and minimize energy functional = Egs, ρgs ⇒ Useful if you can approximate the energy functional ConstrExperimentaluct microscopically charge densities or fit a fr“generom electral” onfor mscattering Neutron Skins for Dummies • 208Pb has Z=82 protons and N=126 neutrons. • Where do the N-Z=44 extra neutrons go? In the center of the nucleus? At the surface? Or both places? • Relevant microphysics: A pn 3 pair in bound S1 state has Monty (‘That One’) more attractive interaction than 1 pp or nn pair in unbound S0 state. 12 Spin Skins in Cold Atom Systems • Fermions in asymmetric trap. Call spin up 6Li atoms “neutrons” and spin down “protons”. P=(N-Z)/(N+Z) Neutrons (top) and protons for P=0.14 G. Partridge et al, Science 311(’06) 503 Attractive interaction (zero E bound state) for unlike spins, no interaction for like spins. 13 Pb Radius Measurement •! Pressure forces neutrons out against surface tension. Large pressure gives large neutron Pb radius. 208 •! Pressure depends on derivative of energy with respect to density. •! Energy of neutron matter is E of (fm) for p nuc. matter plus symmetry energy. R - n R Alex Brown et al. • Neutron radius determines P of ! Neutron minus proton rms radius neutron matter at ! 0.1 fm-3 and the density dependence of the of Pb versus pressure of pure symmetry energy dS/d!. neutron matter at !=0.1 fm-3. Pb neutron skin (fm) Density dep. of sym. E, dS/dn Correlation between Pb skin and dS/dn from full error matrix of Skyrme Fit --Witold Nazarewicz 15 PREX and Neutron Stars 208Pb 16 Neutron Star Crust vs Liquid/Solid Transition Pb Neutron Skin Density FP Liquid Neutron Star 208Pb Solid TM1 • Neutron star has solid crust (yellow) over liquid core (blue). • Nucleus has neutron skin. • Thicker neutron skin in Pb means • Both neutron skin and NS energy rises rapidly with density crust are made out of neutron Quickly favors uniform phase. rich matter at similar densities. • Thick skin in Pblow transition • Common unknown is EOS at density in star. subnuclear densities. J Piekarewicz, CJH Pb Radius vs Neutron Star Radius • The 208Pb radius constrains the pressure of neutron matter at sub-nuclear densities. • The NS radius depends on the pressure at nuclear density and above. Central density of NS few to 10 x nuclear density. • Most interested in density dependence of equation of state (EOS) from a possible phase transition. • Important to have both low density and high density measurements to constrain density dependence of EOS. – If Pb radius is relatively large: EOS at low density is stiff with high P. If NS radius is small than high density EOS soft. – This softening of EOS with density could strongly suggest a transition to an exotic high density phase such as quark matter, strange matter, color superconductor… J Piekarewicz, CJH PREX Constrains Rapid Direct URCA Cooling of Neutron Stars • Proton fraction Yp for matter in beta equilibrium depends on symmetry energy S(n). S ≈ µn − µp = µe 208 Rn-Rp in Pb • Rn in Pb determines density dependence of S(n). • The larger Rn in Pb the lower the threshold mass for direct URCA cooling. • If Rn-Rp<0.2 fm all EOS models do not have direct URCA in 1.4 M¯ stars. • If Rn-Rp>0.25 fm all models do If Yp > red line NS cools quickly via have URCA in 1.4 M¯ stars. direct URCA n! p+e+ν J Piekarewicz, CJH !"#"$%$&!'((&)*+&,"+-./&0123& Jorge Piekarewicz 20 Atomic Physics and PREX 21 Atomic Parity Nonconservation • Depends on overlap of electrons with neutron density. • Cs exp. good to 0.3%. • Not limited by Rn but future 0.1% exp would need Rn to 1% • Combine neutron radii from PV e scattering with an atomic PNC exp for Colorado Cs Experiment best low energy test of standard model. Atomic parity violation in ytterbium Dmitry Budker University of California, Berkeley Nuclear Science Division, LBNL Large PNC effect in Yb (~100 Cs) but atomic structure complicated. •! Atomic PV calculation errors cancel in isotopic ratios •! But enhanced sensitivity to the neutron distribution !n(r) •! Atomic PV ! Neutron distributions 170 176 •! For Yb- Yb, QW " -100; #QW(Standard Model) " 6, #QW(Neutron Skin) " 3 23 Francium PNC at TRIUMFA Francium APNC Experiment at TRIUMF Boulder Cs: massive atomic beam • Atomic PNC in Fr 18x (1013 s-1 cm-2) Cs and atomic key figure: 1010 6s-7s excitations /sec continuum structure understood Fr trap: excitation rate per atom: 30 s-1 at same level. but asymmetry 18x larger APNC possible with 106 - 107 atoms! • But no stable isotopes Lifetime of the 8s level and more sensitive to MAGNETICFIELDCOILS neutron radius. • TRIUMF will produce &RIONBEAM FROM)3!# Fr with actinide target. A 506 nm gPRECISIONg-/4 LASERPUSH TRAP • PREX will improve BEAM LASERBEAMS TRAPPED knowledge of n skins. &RATOMS DRYFILMCOATED NEUTRALIZER CELLCAPTURE-/4 MoG.nday, AuGwinnergust 18, 2008 24 11 Neutron Skins for Atomic PNC • A. Brown claims n skins of APNC isotopes track 208Pb. PREX constrains them. 25 Neutron Skins for Atomic PNC • A. Brown claims n skins of APNC isotopes track 208Pb. PREX constrains them. 26 Neutron Skins for Atomic PNC • A. Brown claims n skins of APNC isotopes track 208Pb. PREX constrains them. 27 Brown Skin Scaling • The pressure of neutron matter controls the neutron skins (Rn-Rp) of nuclei of interest for atomic parity experiments. • Therefore all the skins approx. scale with the neutron skin of 208Pb. • “Neutron skins have no finger prints”: nothing identifies skin of given nucleus. • Example: deformation changes proton radius but not skin thickness. • This is a testable hypothesis. 28 Charge Radii of 6He, 8He • Isotope shift of ~1x108 6He+/s Atom Trap Setup precision He ~5x105 8He+/s Transverse! spectroscopy sensitive 389 nm cooling! MOT! 1083 nm Xe Zeeman! to nuclear charge slower! radius. RF -! • Protons recoil against Discharge! neutrons so some PMT sensitivity to neutron distribution. Argonne group P. • Radioactive atoms Mueller et al. measure 6 trapped for He at Argonne and 8 measurement. He at GANIL. 29 Three Neutron Forces • Detailed observations in Neutron matterN ewithutr NNon andma NNNtter fforces.rom NN and 3N light neutron rich nuclei coupled with theoretical and phenomenalogical (phase shift ...) analysis can provide more direct information on three neutron forces.