CHIRALLY CONSTRAINING THE PI-PI INTERACTION IN NUCLEAR-MATTER

A general prescription for the construction of pi pi interaction poten tials which preserve scattering length constraints from chiral symmetr y when iterated in scattering equations is derived. The prescription i nvolves only minor modifications of typical meson-exchange models, so that coupling constants and cut-off. masses in the models are not grea tly affected. Calculations of s-wave pi pi scattering amplitudes in nu clear matter for two models are compared with those for similar models which violate the chiral constraint, While the prescription tends to suppress the accumulation of the near sub-threshold strength of the pi pi interaction, an earlier conjecture that amplitudes which satisfy c hiral constraints will not exhibit an instability towards pi pi s-wave pair condensation appears to be incorrect. At the same time, however, conventional pi pi interaction models which fit scattering data well can readily be adjusted to avoid the instability in nuclear matter wit hout recourse to exotic mechanisms.