Dynamical Question Bearing on Calculations of Mass Shifts inS-Matrix Theory

It is argued that the $N{D}^{-1\mathrm{}}$ method is inadequate for determination of the basic dynamical inputs, $A_1^{}{}_{}{}^{\mathrm{exch}}$, in the Dashen and Frautschi theory of octet enhancement in the reciprocal bootstrap model. Some models are developed which have the properties: a pole in the $u$ channel as a Born term, two- and three-particle unitarity with pole terms for production, a rather general form for an unknown short-range force. In these models it is proved that the $A^{\mathrm{exch}}$ coefficients have consistently the opposite signs to those given by the $N{D}^{-1\mathrm{}}$ approximation (with the identical Born term). The qualitative interpretation of our result is that an increase in an attraction gives rise to a greater binding energy, as contrasted with the results of Dashen and Frautschi, which seem to have the opposite interpretation.