On the helium-4 charge rms-radius. Ingo Sick

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1 /helium/elba08q On the helium-4 charge rms-radius Ingo Sick Recent interest in Helium charge radii: measurement isotope shift 3 He 4 He (Shiner et al. ) measurement isotope shift of unstable 6 He 4 He (Wang et al. ) measurement of halo nucleus shift 8 He 4 He (talk Peter Mueller)... plus interesting behavior of matter radii... plus ability to accurately predict using GFMC need most accurate 4 He radius to convert shifts to absolute radii

2 Upcoming interest: measurement of 2S-1S energy difference using 4 He + ion in Paul trap M. Herrmann, Munich, Hänsch group goal measure 2S-1S with relative accuracy use for QED tests better than hydrogen as He rms-radius potentially better known no HFS-splitting can access two-loop terms which scale with (Zα) 5 interpretation limited by precision of 4 He charge rms-radius 4 He radius from (e,e) determined 1982 from then available data Frosch et al. McCarthy et al. Erich et al. r rms = 1.676±0.008 fm

3 4 He radius from µ-x-ray data Carboni et al., 1977, CERN µ stopped in He gas at pressure p He =40bar 2S-2P (Lamb shift) transition induced by light from laser r rms =1.673±0.001 fm apparently much more precise Problem: two follow-up experiments Eckhause et al. Orth et al. find at p He >1 bar that lifetime 2S-state un-measurably short (collisional quenching) much too short to allow for 2S-2P measurement evolution of lifetime τ with pressure: theory predicts very short lifetime τ at 40bar theory correctly predicts evolution with p He at low p He where τ measurable Experiment of Hauser et al. performed at PSI at p He = 0.04 bar there 2S-lifetime big enough for measurement of 2S-2P data exclude value of r rms =1.673± fm with 3.5σ Consequence: cannot believe the Carboni result need most accurate value from (e,e) to make progress

4 Today s (e,e) data data listed above, plus: v. Gunten et al., q < 0.5fm 1, precise but much too low in q finite size effect very small not helpful Ottermann et al., 0.5 < q < 2fm 1, covers ideal range 0.8 < q < 1.6fm 1 see sensitivity study precise ratios relative to proton systematic error 0.7% Conversion to absolute cross sections use own fit to world e-p data made including Coulomb distortion

5 Today s data v.gunten Ottermann McCarthy Frosch Arnold additional data helps, but would like to do better

6 Density at large radii gives large contribution to r rms r 4 -weight in r 2 -integral density there quite uncertain, as small e.g. for r>1.9 fm: ρ < 0.1 ρ(0), yet contributes 55% to r 2 constraint on ρ(r >>) would help Constraint on shape of ρ(r) outside range of V NN : R(r) W η,1/2 (2κr )/r κ and η given by proton separation energy fixes shape of ρ(r), can use in fit Special case of 4 He know not only shape know also absolute value of ρ(r >>) from FDR World data on elastic p- 4 He scattering very extensive data set available analyzed by Plattner et al. using Forward Dispersion Relations FDR yields residue of p- 3 H pole at E p < 0 (exchange amplitude) asymptotic normalization of p wave function = constant in front of W 2 (..)/r 2, known to ±5% can use as constraint in fit

7 Technicalities use point density of 4 He calculated in WS-potential fit WS-parameters to: at large r: FDR-density at small r: GFMC density of Pieper et al. To get charge density fold WS point density with modern charge density of proton fold n point density (± same WS-potential) with n density add (effect small) Use resulting ρ ch for r > 2.4fm as data there ρ(r) < 3% of ρ(0) = asymptotic region according to GFMC calculation Fit of (e,e)+fdr-data use SOG parameterization fit all available data (q 8 fm 1 ) use phase-shift code (Coulomb distortion) find perfect fit: χ 2 =133 for 168 d.o.f. find perfect agreement of (e,e) with FDR

8 Ratio data/fit on expanded scale

9 Treatment of errors statistical errors: use error matrix systematic errors: change individual data sets by syst. error, refit add changes quadratically (most conservative treatment) add quadratically stat. + syst. errors Result r rms = 1.681±0.004 fm error includes statistics and systematics Comparison to earlier value from (e,e) r rms =1.676±0.008 fm has changed by 1/2 of previous error bar reason: additional data folding of point density with proton with larger r rms Observation due to FDR-constraint r rms of 4 He = most accurate radius from (e,e) for any nucleus!

10 Some references D. Shiner et al. Phys. Rev. Lett. 74:3553, L.B. Wang et al. Phys. Rev. Lett. 93:142501, P. Mueller et al. Phys. Rev. Lett. 99:252501, I. Sick, Phys. Lett. B 116:212, G. Carboni et al. Nucl. Phys. A 278:381, M. Eckhaus et al. Phys. Rev. A 33:1743, H. Orth, Electromagnetic Cascade and Chemistry of Exotic Atoms, Plenum 1990 H.P. vonarb et al. Phys. Lett. B 136:232, P. Hauser et al. Phys. Rev. A 46:2363, R. Frosch et al. Phys. Rev. 160:874, U. Erich et al. Z. Phys. 209:208, J.S. McCarthy et al. Phys. Rev. C 15:1396, R.G. Arnold et al. Phys. Rev. Lett. 40:1429, A. von Gunten, thesis, TH Darmstadt, C.R. Ottermann et al. Nucl. Phys. A 435:688, G.R. Plattner et al. Nucl. Phys. A 206:513, I. Sick, Phys. Rev. C, 77 (2008) (R)

11 Plausibility consideration: could signal of Carboni et al. be fake? Test with random numbers: in 1/200 cases get peak of similar significance 1/200 unlikely? peak found after peak-optimizing cuts (cannot simulate after the fact) have seen many similar peaks many dibaryon resonances GSI e + e peaks pentaquarks... which have all gone away