the phase shift data, we introduce a new renormalization method; we assume that those large terms should be renormalized by counter terms, the role of which we assign to the effective range terms. Thus we include the effective range parameters up to third order ($n=3$ in powers of $k^{2n}$) for the $l=0,1,2$ channels and up to fourth order ($n=4$) for the $l=3$ channel. After fitting the parameters to the phase shift data, we calculate the ANCs of the $0_2^+$, $1_1^-$, $2_1^+$, $3_1^-$ states of $^{16}$O and compare our results to the existing ones.

This paper is organized as the following: In Sec. 2, the approach based on an EFT for the radiative capture reaction is briefly reviewed, and the expression of equations related to the elastic scattering amplitudes, the phase shifts, and the effective range parameters are displayed. In Sec. 3, we introduce a new renormalization method and describe the details of the numerical fitting to the elastic scattering data. In Sec. 4, the numerical results obtained in this work are exhibited, and finally in Sec. 5, the results and discussion of the work are presented. In Appendix, the structure of the UV divergence and the counter terms of the 