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We discuss the sensitivity of fission barrier for heavy neutron-rich nucleito fission paths in the two dimensional neutron-proton quadrupole plane. Tothis end, we use the constrained Skyrme-Hartree-Fock + BCS method, and examinethe difference of fission barriers obtained with three constraining operators,that is, the neutron, proton, and mass quadrupole operators. We investigate$^{220}$U, $^{236}$U, and $^{266}$U, %from proton-rich to neutron-rich uraniumisotopes, that is relevant to r-process nucleosynthesis. We find that thefission barrier heights are almost the same among the three constrainingoperators even for neutron-rich nuclei, indicating that the usual way tocalculate fission barriers with the mass quadrupole operator is well justified.We also discuss the difference between proton and neutron deformationparameters along the fission paths.

Fission barriers in neutron-proton isospin plane for heavy neutron-rich nuclei