Nucleon-nucleon and nucleon-<i>Δ</i>-isobar forces in a Skyrme model with higher derivative terms

The static properties of the skyrmion and the skyrmion-skyrmion (SS) interaction are investigated within a modified Skyrme model in which the symmetric quartic and the \ensuremath{\omega}-coupling terms are both included. We approximate the latter term by the infinitely large limit for the \ensuremath{\omega}-meson mass. The model is considered to be an effective Lagrangian of pions at low energies. A good agreement of the static properties of the nucleon is obtained using the coupling constants to fit the \ensuremath{\pi}\ensuremath{\pi} scattering data. The SS interaction potential is expressed by means of the generalized spin and isospin operators. As a result, the potential is easily projected onto the potentials for NN, N\ensuremath{\Delta}, and \ensuremath{\Delta}\ensuremath{\Delta} states with definite spin and isospin. It is shown that the SS potential has a good correspondence with the one-boson-exchange potential of the \ensuremath{\pi} and \ensuremath{\rho} mesons at large distances. The symmetric quartic term, which is necessary to achieve agreement with the S- and D-wave \ensuremath{\pi}\ensuremath{\pi} scattering data, has been expected to give rise to an ``\ensuremath{\sigma}-meson''-like attractive contribution at the intermediate range of the central potential. There exists, however, no such contribution, even if the strength of the symmetric quartic term is increased. This is because we must also increase the \ensuremath{\omega}-coupling term to stabilize the skyrmion. We need further study of this problem.

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