three effective range parameters of the elastic scattering for $l=0,1,2$ channels by fitting them to the phase sift data, but not included the excited bound states of $^{16}$O in the study. Though the phase shift data below the resonance energies can be reproduced very well by using the fitted parameters, we find that significant uncertainties in the elastic amplitudes are remained when extrapolating them to $T_G$.

In the present work, we incorporate the excited binding energies for $0_2^+$, $1_1^-$, $2_1^+$, $3_1^-$ ($l^\pi_{i-th}$) states of $^{16}$O in the parameter fitting to the phase shift data of the elastic scattering for $l=0,1,2,3$ channels. Our assumption for the parameter fitting is that fitted curves which interpolate the amplitude between the phase shift data and the excited binding energies can be represented by several terms of a polynomial function. As will be discussed in detail below, however, we find a mismatch between the strength of the amplitudes estimated from the phase shift data and the first few terms of a polynomial function obtained from the Coulomb self-energy term in the dressed $^{16}$O propagator. Because those terms from the Coulomb self-energy are larger, at most by two order of magnitude, than the term estimated by 