Coulomb Corrections to Elastic Electron-Proton Scattering and the Proton Charge Radius

نویسنده

  • R. Rosenfelder
چکیده

Recent values of the proton charge radius derived from the Lamb shift in electronic hydrogen tend to be larger than those from electron scattering. Therefore low-momentum-transfer scattering data from different groups and laboratories have been reanalyzed with Coulomb and recoil corrections included. This was done by calculating at each scattering angle and scattering energy the corresponding correction obtained from a partial wave program which includes recoil approximately. Corrections due to magnetic scattering were also made before the rms-radius was determined by a fit which allows free normalization for each experiment. It is shown that an analysis of electron scattering data including Coulomb corrections lowers the χ of the fit and increases the proton radius by about (0.008− 0.013) fm depending on the fit strategy. A value of rp = 0.880 (15) fm is obtained which is in good agreement with the one extracted from Lamb shift measurements. ∗E-mail address: [email protected] 1. Traditionally elastic electron scattering data from the proton have been analyzed in the first Born (one-photon-exchange) approximation since Zα ≃ 1/137 was supposed to be small enough. In this way a root-mean-square charge radius of < r > 1/2 e−scatt = 0.862 (12) fm (1) has been deduced from elastic electron-proton scattering experiments at Mainz [1] 20 years ago. This value superseded the nearly canonical value of 0.805(11) fm from Stanford [2] which was based on an (invalid) Q2 → 0 extrapolation of the dipole form factor fitted to data at higher momentum transfer 1. In the last few years atomic Lamb shift measurements in hydrogen have become increasingly more accurate and are now very sensitive to the proton size [5]. Assuming the validity of bound state QED calculations a value for the proton charge radius can be deduced from them; the most recent theoretical evaluation [6] leads to < r > 1/2 Lamb shift = 0.883 (14) fm (2) which is slighthly higher than the value (1). A possible reason of this discrepancy may be the distortion of the scattering waves in the electrostatic field of the proton. Indeed, Coulomb corrections in elastic electron scattering have been shown recently to increase the rms charge radius of the Z = 1, N = 1 hydrogen isotope, the deuteron by 0.012−0.015 fm [7],[8]. Therefore it is of some interest to investigate whether Coulomb corrections also affect the determination of the proton radius. Eventually a muonic hydrogen experiment which has started at PSI [9] will yield this fundamental hadronic quantity with a tenfold higher accuracy than given in (1) or in (2). Even then it will be useful to see whether the value from electron scattering is consistent with the precise value. 2. In the one-photon-exchange approximation the elastic electron-proton scattering cross section in the lab frame is given by dσ dΩ ∣

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تاریخ انتشار 2000