The Rouse model has recently been modified to take into account the excluded volume interactions that exist between various parts of a polymer chain by incorporating a narrow Gaussian repulsive potential between pairs of beads on the Rouse chain (Prakash, Macro molecules. 2001. 34, 3396-3411). The narrow Gaussian potential is characterized by two parameters: z*-which accounts for the strength of the interaction, and d*-which accounts for the range of the interaction. In the limit of d* going to zero., the narrow Gaussian potential tends to the more commonly used delta -function repulsive potential. The influence of the parameter d*. in the limit of infinite chain length, on equilibrium and linear viscoelastic properties, and on universal ratios involving these properties, is examined here. A renormalization group calculation of the end-to-end vector Suggests that the Value chosen for the variable d* will not affect critical exponents, or universal ratios. A similar trend is also observed for results obtained with all approximate solution, which is based on the assumption that the non-equilibrium configurational distribution function is Gaussian.