We develop a technique, denoted as the finite radius approximation (FRA), that uses a twodimensional version of the Shannon-Nyquist sampling theorem to determine transverse densities and their uncertainties from experimental quantities. Uncertainties arising from experimental uncertainties on the form factors and lack of measured data at high Q 2 are treated. A key feature of the FRA is that a form factor measured at a given value of Q 2 is related to a definite region in coordinate space. An exact relation between the FRA and the use of a Bessel series is derived. The proton Dirac form factor is well enough known such that the transverse charge density is very accurately known except for transverse separations b less than about 0.1 fm. The Pauli form factor is well known to Q 2 of about 10 GeV 2 , and this allows a reasonable, but improvable, determination of the anomalous magnetic moment density.
We report new measurements of the parity-violating asymmetry A(PV) in elastic scattering of 3 GeV electrons off hydrogen and 4He targets with approximately 6.0 degrees . The 4He result is A(PV)=(+6.40+/-0.23(stat)+/-0.12(syst))x10(-6). The hydrogen result is A(PV)=(-1.58+/-0.12(stat)+/-0.04(syst))x10(-6). These results significantly improve constraints on the electric and magnetic strange form factors G(E)(s) and G(M)(s). We extract G(E)(s)=0.002+/-0.014+/-0.007 at =0.077 GeV2, and G(E)(s)+0.09G(M)(s)=0.007+/-0.011+/-0.006 at =0.109 GeV2, providing new limits on the role of strange quarks in the nucleon charge and magnetization distributions.
We studied simultaneously the 4 He(e, e p), 4 He(e, e pp), and 4 He(e, e pn) reactions at Q 2 = 2 (GeV/c) 2 and xB > 1, for an (e, e p) missing-momentum range of 400 to 830 MeV/c. The knocked-out proton was detected in coincidence with a proton or neutron recoiling almost back to back to the missing momentum, leaving the residual A = 2 system at low excitation energy. These data were used to identify two-nucleon short-range correlated pairs and to deduce their isospin structure as a function of missing momentum, in a region where the nucleon-nucleon (N N ) force is expected to change from predominantly tensor to repulsive. The abundance of neutron-proton pairs is reduced as the nucleon momentum increases beyond ∼500 MeV/c. The extracted fraction of proton-proton pairs is small and almost independent of the missing momentum. Our data are compared with calculations of two-nucleon momentum distributions in 4 He and discussed in the context of probing the elusive repulsive N N force.
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