Spin-Dependent Isovector Giant Resonances as a Possible Precursor of the Pion-Condensation in Finite Nuclei

The pion-condensation is an instability of the nuclear medium through a softening of the spin-isospin sound mode with high momentum (~1.5PF, PF being the Fermi momentum) due to the attractive OPEP (OnePion-Exchange-PotentiaI).') It means that the precursor of the condensation is a softening of the mode. Here we examine the possiblity that it manifests itself directly in finite nuclei as a softening of spin-dependent isovector giant resonances (M-mode). Following Dabrowski and Haensel;) we adopt an extended version of the SteinwedelJensen (S-]) model) to describe the mode in the simplest way: The neutron (proton) fluid is replaced by the A+(A-) fluid consisting of neutrons with the up (down) spin and protons with the down (up) spin. The restoring force is given by the spin-isospin (S1) symmetry energy Cd7: in place of the isospin symmetry energy C 7: in the S-J model. In this way for the energy of the or-mode of a given multipolarity L and node n, we have CliP = cq';,L) with c=/2cd7:/M and q~L)=z~L)/R. Here, M is the nucleon mass, R the radius of the nucleus and z~L) the n-th zero of the derivative of the spherical Bessel function of order L. The corresponding difference between the local densities of A+ and Afluids with a multipolarity L has a spatial form of