On the relation between the Deuteron Form Factor at High Momentum Transfer and the High Energy Neutron-Proton Scattering Amplitude

Abstract

A non-relativistic potential-model version of the factorization assumption, used in perturbative QCD calculations of hadronic form factors, is used, along with the Born approximation valid at high energies, to derive a remarkably simple relationship between the impulse approximation contribution to the deuteron form factor at high momentum transfer and the high energy neutron-proton scattering amplitude. The relation states that the form factor at a given value of $Q^2$ is proportional to the scattering amplitude at a specific energy and scattering angle. This suggests that an accurate computation of the form factors at large $Q^2$ requires a simultaneous description of the phase-shifts at a related energy, a statement that seems reasonable regardless of any derivation. Our form factor-scattering amplitude relation is shown to be accurate for some examples. However, if the potential consists of a strong short distance repulsive term and a strong longer ranged attractive term, as typically occurs in many realistic potentials, the relation is found to be accurate only for ridiculously large values of $Q$. More general arguments, using only the Schroedinger equation, suggest a strong, but complicated, relationship between the form factor and scattering amplitude. Furthermore, the use of recently obtained soft potentials, along with an appropriate current operator, may allow calculations of form factors that are consistent with the necessary phase shifts.