Realistic Transverse Images of the Proton Charge and Magnetic Densities

Details Realistic Transverse Images of the Proton Charge and Magnetic Densities Realistic Transverse Images of the Proton Charge and Magnetic Densities

2010-10-18

arxiv.org/abs/1010.3629v2

Phys.Rev.C83:015203,2011

Physics

Nuclear Physics

Nuclear Theory

11 pages, 9 figures

Scientific paper

10.1103/PhysRevC.83.015203

We develop a technique, denoted as the finite radius approximation (FRA), that uses a two-dimensional 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.

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