MeV, the convergence of the expansion series should be carefully examined when the elastic scattering data are used for the parameter fitting. In addition, because we do not explicitly include the resonance states of $^{16}$O in the theory, we restrict data sets for the parameter fitting below the resonance energies, $T_\alpha=6.52$, 3.23, 3.57, 5.09 MeV for $0_3^+$, $1_2^-$, $2_2^+$, $3_2^-$ states, respectively; the corresponding momenta are $k=166$, 117, 123, 146 MeV for the $l=0$, 1, 2, 3, channels, respectively. (We will mention data sets we choose for the parameter fitting in detail below.)

We are now in position to discuss a new renormalization method. The effective range parameters in $K_l(k)$ are expanded in powers of $k^2$ whereas the real part of the function $H_l(k)$ can be expanded in powers of $k^2$ as well. For the function $H(\eta)$ in $H_l(k)$, one has Re H() &=& k\^2 + k\^4 + k\^6 + k\^8 + , where $\eta = \kappa/k$; $\kappa$ is the inverse of the Bohr radius, $\kappa\simeq 245$ MeV, and is regarded as another large scale of the theory. This expansion is reliable in our study for the elastic scattering at low energies along with the effective range expansion in $K_l(k)$. 