Parity Radius Experiment and Neutron Densities

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C. J. Horowitz Indiana University RIA INT Workshop, Sep. 2007 Neutron Densities

• Introduction: atomic parity. • PREX experiment. • Implications of the neutron density for astrophysics. • PREX details. • Conclusions for neutron densities.

With J. Piekarewicz, E. D. Cooper, R. Michaels, P. Souder ... 2 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% • Future isotope ratio exp may need neutron radii differences. Colorado Cs Experiment

• Possible exp with Fr isotopes • Combine neutron radii from PV e scattering with an atomic PNC exp for best low energy test of standard model. Coherent Weak Charge

• In standard model weak charge Qw is 2 Qw = Z(1 − 4 sin Θw) − N • Weak charge dominated by neutrons and is large for large N nucleus. • Important in Astrophysics. Nu-A elastic scattering has a large cross section ~N2. This first traps neutrinos in core collapse supernovae. Dynamics involve sensitive balance between gravity and lepton Fermi pressure. If nu not trapped, star may collapse to black hole without SN explosion.

4 Neutrino-Nucleus Elastic Scattering

• One way to measure neutron density of nucleus: 0707.419 Amanik+McLaughlin • I strongly support an experiment even if one learns no new info. on neutron density. – Fundamental process never observed before. – Important technology for future. Explore new domain of low threshold experiments. – Use nu-A elastic in osc. exp. sensitive to nu sterile. – Solar nu-A elastic fundamental background for dark matter searches. – Low E solar nu, double beta decay, dark matter ... detectors sensitive to SN nu via elastic scattering. 5 Pb The Parity Radius Experiment

PREX uses parity violating elastic electron scattering to measure the neutron radius of 208Pb Spokespersons: P. Souder, R. Michaels, and G. Urciuoli

208Pb http://hallaweb.jlab.org/parity/prex Parity Radius Experiment

• Parity violation probes neutrons because weak charge of a n À p. • Elastic scattering of 850 MeV e from 208Pb at 6±.

• Measure A ¼ 0.6 ppm to 3%. This gives neutron radius to 1% (± 0.05 fm). • Purely electroweak reaction is model independent 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* conference on PV. • 2001- Relation of neutron density to: – Pressure of neutron matter (Alex Brown), – Density dependence of symmetry energy, – Many neutron star properties, identified. • 2000-5 HAPPEX, HAPPEX II, HAPPEX He run. • 2008-9 PREX runs (?!) Atomic PV was original motivation for PREX. Now nuclear structure, implications for astrophysics, important. 8 Pb Radius Measurement

• Pressure forces neutrons out against surface tension. Large Pb pressure gives large neutron radius. 208 • Pressure depends on derivative of energy with respect to density.

• Energy of neutron matter is E of (fm) for nuc. matter plus symmetry energy. p -R n R Alex Brown et al.

• Neutron radius determines P of neutron matter at ¼ 0.1 fm-3 and Neutron minus proton rms radius the density dependence of the of Pb versus pressure of pure symmetry energy dS/dρ. neutron matter at ρ=0.1 fm-3. Symmetry Energy

• Describes how energy of system rises as one moves away from N=Z.

• Can think about S(n0) and dS/dn or 2 volume symmetry energy Sv=a4(N-Z) /A and surface symmetry energy Ss of semi-empirical mass formula. • Nuclear masses determine some combination of Sv and Ss but ratio Ss/Sv is not well constrained.

10 C. J. Horowitz: Links Between Heavy Ion and Astrophysics 3 elastic electron nucleus scattering. This is the cross sec- NS crusts [13]. The thicker the skin in Pb, the faster the tion difference for the scattering of positive dσ/dΩ+ and energy of neutron matter rises with density, and the more negative dσ/dΩ− helicity electrons, quickly the uniform liquid phase is favored. Therefore, a thick neutron skin in Pb implies a low transition density dσ/dΩ+ − dσ/dΩ− (maximum density) for the NS crust. A = . (2) dσ/dΩ+ + dσ/dΩ− The composition of a neutron star depends on the symmetry energy. In beta equilibrium the neutron chemical In Born approximation A is [8] potential µn is equal to that for protons µp plus electrons µe, µn = µp + µe. Neutron stars are about 90% neutrons 2 GF Q FW (Q) and 10% protons plus electrons. However, a large symme- A = (3) ! 1/2 " 4πα2 Fch(Q) try energy will favor more equal numbers of neutrons and protons and increase the proton fraction. Thus, the com- where GF is the Fermi constant, α the fine structure con- position of matter in the center of a neutron star depends stant and Q the momentum transfer. The charge form fac- on the symmetry energy at high density. tor Fch(Q) is the Fourier transform of the charge density, Neutron stars cool by neutrino emission from the inte- that is known from electron scattering. The weak form rior. If the proton fraction is large, above about 0.13, then factor FW (Q) is the Fourier transform of the weak charge neutrons near the Fermi surface can beta decay to protons density. This is dominated by the neutron density and thus and electrons near their Fermi surfaces and conserve both the neutron density can be deduced from measurements of momentum and energy. This leads to the direct URCA A. Note, coulomb distortions make ≈ 30 % corrections to process n → p+e+ν¯e followed by e+p → n+νe that will A for scattering from a heavy nucleus [9]. However these efficiently cool a NS by rapidly radiating νν¯ pairs. The can be accurately calculated. neutron radius of Pb constrains the density dependence The Jefferson laboratory PREX [10] aims to measure of the symmetry energy near ρ0. This is the crucial piece 208 elastic scattering of 850 MeV electrons from Pb at six of information for extrapolating to find the symmetry en- degrees in the laboratory. The goal is to measure A ≈ 0.6 ergy at large densities. We find that if the neutron minus ppm with an accuracy of 3%. This allows the neutron rms proton rms radii in 208Pb is larger then 0.25 fm, all of the 208 radius of Pb to be deduced to 1%. A full discussion of mean field EOS models considered allow direct URCA for the experiment and many possible corrections is contained a 1.4M" NS [14]. Alternatively, if this skin thickness is in the long paper [11]. less then 0.2 fm, none of the mean field models allow di- We now discuss the implications of the radius measure- rect URCA. ment. Heavy nuclei are expected to have a neutron rich Note, the direct URCA process takes place in the high skin. The thickness of this skin depends on the pressure of density interior of a NS at a few or more ρ0. Therefore, neutron rich matter. The larger the pressure, the larger the the above relation with the skin thickness in Pb involves neutron radius as neutrons are forced out aIsospingainst surface a nDifextrapfusionolation to highe rIndens itHIy. Alt erCollisionsnatively, energetic tension. Alex Brown showed that there is a strong cor- HI collisions can directly produce high densities. Therefore relation between the neutron radius in Pb an•d tBringhe EOS twoit wchunksould be e xoftre mnuclearely useful matterif one co uwithld inf edifr thferente high of pure neutron matter, as predicted by many different density symmetry energy from HI observables. Although mean field interactions [12]. Therefore, the neutroN/Zn rad iratiosus into contact. Symmetry E willmea sdriveuring t he −3 potentially difficult and model dependent, in Pb determines P for neutron matter at ρ ≈ 0isospin.1 fm . difsymfusion.metry energy at high density is perhaps the single most [This is about 2/3ρ0 and represents some average of the important HI experiment for the structure of NS. surface and interior density of Pb.] The press•ureIfd eSpe nsmall,ds WEe independentclose this section wofith N/Za sho andrt dis cisospinussion of o ther on the derivative of the energy with respect to density. ways to determine the density dependence of the symme- The energy of pure neutron matter Eneutron is thdife enfusionergy t rwilly ene rbegy. Islowf one .assumes the symmetry energy depends of symmetric nuclear matter Enuclear plus the symmetry on a power of the density, energy S(ρ), • Measure equilibration of N/Z in asymmetric HI γ collisions vs collision timeS(ρ) (related≈ S0ρ , to energy).(5) Eneutron ≈ Enuclear + S(ρ). (4) • Comparethe ton t hsemi-classicale power γ can be app simulationsroximately relate dandto th finde skin The pressure depends on dEnuclear/dρ (which is small thickness in 208Pb asγfollows, and largely known near nuclear density ρ0) and dS(ρ)/dρS. (n) = S0(n/n0) , γ ≈ 0.7 − 1 Therefore, the neutron radius in Pb determines the density 208 2 1/2 2 1/2 dependence of the symmetry energy dS(ρ)/dρ for denForsities Pb: < rn > − < rp > ≈ 0.22γ + 0.06 fm. (6) near ρ0. Neutron stars are expected to have a so•lidHighneutro nE HITh iscollisionsrelation is a maysimple probefit to sev eSra latm ehighan fiel d calcula- rich crust over a liquid interior, while heavy nuclei have a tions, see also [15]. As discussed by Li et al [16] and by neutron rich skin. Both the skin of a nucleus, anddensities.the NS Co l oCalibratenna and Tsa nHIg [1 results7] in the cwithhapte rPREXon isosp iatn p rno0p - crust are made of neutron rich matter at similar densities. erties of this book, the pow--er B.γ c aTnsangbe de d...uc ed fr1o1m HI The common unknown is the EOS of low density neutron data involving observables such as isoscaling and isospin matter. As a result, we find a strong correlation between diffusion. Finally we mention a recent review article which the neutron radius of 208Pb and the transition density of discusses the symmetry energy in astrophysics [18]. Neutron Star Crusts

• Neutron stars are densest macroscopic objects.

¼1.4 M¯, R¼12 km • Crust is crystal lattice plus neutron gas (superfluid). • Liquid core of neutron rich matter of ~ nuclear density and above with possible exotic interior. • Pasta is at lower limit of inner crust ¼ ½ km down. D. Page

Exotic: quark matter, color superconductor, meson condensate? 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 Pblow transition • Common unknown is EOS at density in star. subnuclear densities. J Piekarewicz, CJH !"#$%&'()$*%(&)+,--*$,&')

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!"#$%&'(()*)+(,-.&&%&+(/0.(1(2%-%&345% Pb Radius vs Neutron Star Radius

• The 208Pb radius constrains the pressure of neutron matter at subnuclear densities. • The NS radius depends on the pressure at nuclear density and above. • 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, kaon condensate…

J Piekarewicz, CJH Measuring Neutron Star Radii

• Deduce surface area from luminosity. T from X-ray spectrum. 2 4 L" = 4#R $SB T • Complications: & R) 2 % F = ( + $ T 4 – Need distance (from parallax forrec nearby' D* SB isolated NS, from cluster membership for F observed "directly" NS in globular clusters ...) rec T "measured" from the shape – Non-blackbody corrections from ! of the spectrum atmosphere models can dependD measure don (HS T parallaxe) composition and B field. ==> R "measured" • Radii major goal of Chandra, XMM.. Drake et al. (200172) got R = 4-6 km ==> Quark Star !

Better spectral models + new parallaxe distance ==> R = 24 km !?!?! "Anti Quark Star" ? 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 NeutronCom Starpari sLuminosityon with D vsat Agea

Mag H fits: 1) RX J0822-4247 (in Puppis A) D. Page 2) 1E 1207.4-5209 (in PKS 1209-52) SN 1987A 3) PSR 0538+2817 4) RX J0002+6246 (in CTB 1) 5) PSR 1706-44 6) PSR 0933-45 (in Vela) BB fits: 7) PSR 1055-52 8) PSR 0656+14 9) PSR 0633+1748 "Geminga" 10) RX J1856.5-3754 11) RX J0720.4-3125

Upper limits: A) CXO J232327.8+584842 (in Cas A) B) PSR J0205+6449 (in 3C58)

C) PSR J1124-195916 (in G292.0+1.8) D) RX J0007.0+7302 (in CTA 1) Hadronic Probes of Neutron Density

• Anti-protons are sensitive to low density tail, not rms radius. [Model dependent to fit wood-saxon ... to tail and use it to calculate rms radius.] • Proton and or alpha elastic scattering can measure neutron density. – What are systematic errors of rxn mechanism? – Calibrate with PREX 208Pb result. – Measure n densities of rare isotopes in

inverse kinematics. 20 PREX Details

21 angle. The calculations take into account the averaging over the ﬁnite acceptance and the energy resolution needed to discriminate inelastic levels. Figure 2 shows the product FOM !2 for 208Pb which peaks at E = 0.85 GeV. Similar calculations for 138Ba shows an optimu×m at 1.0 GeV (ﬁgure 3). For both these nuclei the running time T in days to reach 2 a 1% accuracy in Rn is approximately T 7/(P IΩ) days, where P is the polarization (P 0.8 is achievable), I is the average ≈beam current in µA (I 50µA is achievable) and≈Ω is the solid angle acceptance of the spectrometer in steradian≈s. This optimum point corresponds to q = 0.45 fm−1 and 0.53 fm−1 for Pb and Ba respectively. In the plots of FOM !2 one can see a secondary ridge where one might want to perform a second measurem×ent at higher Q2 to check the shape dependence. Here the experimental running time becomes longer but the required accuracy in Rn can be reduced. As an example, for 208Pb at E = 1.3 GeV, θ = 8◦, corresponding to q = 0.92 fm−1 the running time to reach 2% in R is T 19/(P 2IΩ) days. n ≈ Optimize 208 Pb Cross Section Asymmetry Kinematics at E = 0.85 GeV • Maximize (mbarn) A (ppm) "

figure of merit /d ! times square d of sensitivity to neutron radius. q (fm -1) q (fm -1) FOM x 2 Sensitivity # • Minimizes run to R_n = dA/A time for 1% # sensitivity to neutron radius. 6 • 850 MeV, 10 0.5 $ 1 6 degrees. E (GeV) q (fm -1)

208 FIG. 2. Cross section, parity violating asymmetry, and sensitiv22ity to Rn for Pb elastic scattering at 0.85 GeV. The fourth plot shows the variation of FOM !2 with energy and angle, × showing an optimum at 0.85 GeV for a 6◦ scattering angle which corresponds to q = 0.45 fm−1.

To reduce the running time, a thick target is needed; the main issues are: 1) For a given energy resolution required to discriminate excited states, there is an optimum target

11 Pb Target Test • A thinner version of the Pb- diamond foil target 208was Pb tested recently by a different group. • Diamond foils did not suffer 12 radiation damage. C Electron Beam • Target melted near 80 micro-amps! Diamond Backing: Presumably because of poor thermal• High Thermal Conductivity contact Pb to diamond. • Negligible Systematics Target did not use vacuum grease! • Earlier, shorter, test with grease was ﬁne. PREX Measured Asymmetry

Physics Correct for Coulomb -1 Distortions q=0.45 fm Impact

Weak Density at one Q2 EOS of n Small Corrections for Mean Field n s G G MEC & Other rich Atomic E E Parity Models matter 2 Violation Neutron Density at one Q

Assume Surface Thickness Good to 25% (MFT) Heavy Neutron Ions Stars

R n Coulomb Distortions 208Pb at 850 MeV

• In Born approx, A is ratio of weak to EM form factor.

• Coulomb distortions reduce A by ~30% (largest correction), but still sensitive to n density.

• Analyzing power An is, parity allowed, left right asymmetry for normal polarized beam. – This is potential systematic error from small normal P of beam.

– An approx. same size as A – E.D. Cooper, CJH, PRC72 (2005)034602. – Need to include excited intermediate states. – Dispersion calc underway An

ppm PREX: 2 Measurement at one Q is sufficient to measure R N

( R.J. Furnstahl )

PREX error bar (1σ )

R. Michaels HE06 July 2006 PREX at Atomic Parity Overlap

1.5 Atomic PV depends 10!

1-j0(qr), q=.3 on overlap of elec. 1-j (qr), q=.45 0 6(1-f(r)) axial transition 4.1(1-f(r)) matrix element with 1

nuclear weak density. (qr) 0 1-j ≈ † f(r) ψp(r)γ5ψs(r) 0.5 For Pb, f(r) looks like -1 j0(qr) for q~0.3 fm 0 0 2 4 6 8 10 r (fm)

FIG. 7. Approximate nuclear weak density ρ(r) for Pb, along with the function multiplying ρ(r) in the integrals for the weak form factor (namely, j0(qr)) and in the atomic correction factor qn (namely f(r)). In both cases the function is subtracted from one to eliminate the volume integral of the weak charge density. Curves for 1 j (qr) are shown for two diﬀerent values of q in fm−1. − 0 Note 4.1(1-f(r)) is almost identical to 1 j (qr) for q=0.30fm−1. − 0

VII. CONCLUSION

With the advent of high quality electron beam facilities such as CEBAF, experiments for accurately measuring the weak density in nuclei through parity violating electron scattering (PVES) are feasible. The measurements are cleanly interpretable, analogous to electromag- netic scattering for measuring the charge distributions in elastic scattering. From parity violating asymmetry measurements in elastic scattering, one can extract the weak density in nuclei after correcting for Coulomb distortions, which have been accurately calculated [24].

By a direct comparison to theory, these measurements test mean ﬁeld theories and other models that predict the size and shape of nuclei. They therefore can potentially have a fundamental and lasting impact on nuclear physics.

Furthermore, PVES measurements have important implications for atomic parity nonconservation (PNC) experiments which in the future may become the most precise tests of the Standard Model at low energies. We have shown that to a good approximation, suﬃ- cient for testing the Standard Model, the dependence on nuclear shape parameters enters the

35 PREX Status

• Control of helicity correlated beam parameters ok from HAPPeX. • Target (with vacuum grease) seems ﬁne. Radiation in hall is ok. • Plan to build warm septum magnets (bend 6 deg. scattered electrons to 12 deg. to enter spectrometers). • Plan to upgrade polarimetry including green laser for Compton e-gamma polarimeter. • Full run early ’09 (?) P. Souder, R. Michaels, G. Urciuoli Extrapolation from one nucleus to another • Two nuclei with “simple” nuclear structure. Strong 208 132 correlation in MFT Rn in Pb vs Ba. IE Rn in Pb constrains density dep. of symmetry E and this determines Rn in other nuclei. PV on Ba is possible but may not provide much more info then Pb. • Large SCIDAC program to calculate an improved energy density functional for nuclei. This will agree with (or be tuned to?) PREX for Pb and then may provide the best neutron densities in other systems (Fr?). Neutron Densities • Have many implications for nuclear structure and astrophysics including for the radius, crust transition density, and cooling of neutron stars. • The neutron radius in Pb depends on the density dependence of the symmetry energy.

• PREX aims to measure Rn in Pb to 1% using PV electron scattering. • What n density would you like? Let’s work on it. What one thing should • Bobatomic asks... physicists take • Ansawwaer: yAstr fronomersom this should talk? ask nuclear theorists: • Are your results model independent? • Through advances in nuclear theory, a parity violating measur• Whatement, are your and theor otheretical measurementserror with bars? strongly interacting probes, our knowledge of neutron densities is improving signiﬁcantly. PREX

• Implications of PREX in astrophysics done with J. Piekarewicz. • Coulomb distortion and analyzing power calculations done with E. D. Cooper. •