Representation dependence of the neutron-proton kinetic energy in adiabatic deuteron stripping

Abstract

The adiabatic distorted-wave approximation (ADWA), the standard model for deuteron stripping and pickup, depends on the neutron-proton interaction through the form factor $V_{np}ϕ_d$. With nonlocal nucleon potentials, the neutron-proton kinetic energy averaged with this form factor shifts the energy at which the nucleon-target potentials are evaluated, and ADWA cross sections become sensitive to the choice of interaction. I ask whether this sensitivity reflects short-range neutron-proton structure. A unitary transformation of the neutron-proton Hamiltonian with the AV18 interaction, confined to short distances, represents the same interaction differently and preserves the two-body scattering matrix, the deuteron binding energy, and both asymptotic normalizations. It raises the weighted kinetic energy from 218 to 313 MeV, a change equal to more than half the range spanned by the five realistic interactions studied, while the finite-range coefficient, which controls low-momentum transfer, hardly moves. The weighted kinetic energy is dominated by the variance of the kinetic energy, which the high-momentum components control, whereas the finite-range coefficient is set by the spatial extent of the form factor. A dependence on $V_{np}$ carried by the weighted kinetic energy can therefore arise from the representation of the interaction alone, and does not by itself measure its short-range content.