A new equation for Bondarenko self-shielded cross section sensitivities to nuclide densities

•Bondarenko resonance self-shielded cross sections are discussed.•A new formula for the sensitivities is presented.•A previous formula ignored some dependencies on nuclide density.•The formula is propagated to the adjoint-based keff sensitivity formula.•Results compare favorably with central-difference estimates. This paper derives a new formula for the sensitivities of Bondarenko resonance self-shielded cross sections with respect to nuclide densities and the subsequent adjoint-based sensitivities of keff with respect to nuclide densities. A previous derivation ignored the dependence of the self-shielded cross sections on some of the nuclide densities. The new formula accounts explicitly for tabular interpolation of the self-shielded cross sections. Numerical results for two test problems using the PARTISN multigroup discrete ordinates code and the SENSMG multigroup sensitivity code demonstrate the correctness of the equations and their implementation.