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

Abstract

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.

Comments: 1 Figure added