A consistent calculation of dispersion corrections in elastic electron-deuteron scattering

Abstract:

We calculate the contribution of virtual second-order excitations of the deuteron by integrating numerically over a generalized inelastic structure function S(q ₁ ,q ₂ ,ω). This structure function, as well as the ground state density, are evaluated analytically using the separable Yamaguchi S-wave NN-potential which gives a fair description of low-energy deuteron properties and nuclear polarization shifts. In the static case excellent numerical agreement is found by comparing the second-order Born results with a partial-wave calculation. In the non-static case recoil corrections are also taken into account but only Coulomb excitations, which should be dominant for small momentum transfers, are retained. In contrast to previous calculations the present approach avoids uncontrolled approximations like the closure approximation or mixing of different models for ground and excited states. We show that the closure approximation with a fixed average excitation energy is unable to reproduce our numerical results which are found to be smaller than in previous estimates, negative and dependent both on scattering angle and incident electron energy. An analysis of experimental scattering cross sections at low momentum transfer is performed including static Coulomb and dispersion corrections. In agreement with a recent analysis it is found that the Coulomb corrections increase the charge radius by 0.012 fm whereas our dispersion corrections lead to a decrease of only 0.003 fm. This gives a deuteron radius of (1.968 ± 0.006) fm and a charge radius of (2.130 ± 0.010) fm.