Transposition of a local-density-dependent pion-nucleus potential to an effective density-linear potential - generalized Seki-Masutani relations

We have shown that a local-density-dependent term, $F[\rho(r)] \rho(r)$, of the pion-nucleus potential with a nuclear density, $\rho(r)$, can be transposed to a conventional density-linear term, $F(\rho_e) \rho(r)$, with an effective nuclear density, $\rho_e$, which is close to $\sim 0.6 \rho(0)$ for most $\pi^-$ bound states. The presently found relations, {\it generalized Seki-Masutani relations}, for the density-quadratic term, the medium-modified isovector term and the double-scattering isoscalar term of the s-wave pion-nucleus interaction assure that the constant parameters in the conventional pion-nucleus potential are interpreted as being effective ones in the light of density-dependent effects.