New aid to the classification Feshbach resonances. Application to Ne, Kr, Ar, and Xe

It is shown that the energies $E_{\mathrm{Nl}{l}^{\prime }}\mathrm{}\left(m\right)\mathrm{}$ of Feshbach resonances in Ne, Kr, Ar, and Xe are related to their respective ionization potentials via an equation of the type $E_{\mathrm{Nl}{l}^{\prime }}\mathrm{}\left(m\right)=A_{\mathrm{Nl}{l}^{\prime }}I\left(m\right)+B_{\mathrm{Nl}{l}^{\prime }}$, where $E_{\mathrm{Nl}{l}^{\prime }}\mathrm{}\left(m\right)\mathrm{}$ is the energy of the $N\mathrm{th}$ resonance with excited electron angular momenta $l$ and $l^{\prime }$ in species $m$, $I\left(m\right)\mathrm{}$ is the ionization potential of species $m$, and $A_{\mathrm{Nl}{l}^{\prime }}$ and $B_{\mathrm{Nl}{l}^{\prime }}$ are independent of atomic species $m$. It is shown how the above linear relation simplifies grouping of families of resonances with similar configurations in Ne, Kr, Ar, and Xe. The linear relation implies that for Feshbach resonances electron-electron interactions external to the ion core dominate over electron-ion-core interactions within the ion core.