Lepton-neutron interaction and $S$-wave low-energy parameters

A lepton-neutron potential in configuration space is obtained. It is based on the Coulomb plus hyperfine interaction Hamiltonian integrated over the neutron charge and magnetic densities. Different parametrizations of the neutron electromagnetic form factors are compared. It is given in the operator form with central, spin-spin, tensor, and spin-orbit terms. The potentials for lowest partial wave states are presented. We compute the lepton-neutron low-energy parameters for the $S$ waves, estimate the zero-energy cross sections for higher angular momentum states, and point out a possible divergence in the partial wave summation due to the spin-orbit potential.