other effective range parameters as - &=& 12 r\_l\_l\^2 + 14 P\_l\_l\^4 + Q\_l \_l\^6 + R\_l \_l\^8 + +2H\_l(k\_b), \[eq;moneoveral\] and we remove the $a_l$ dependence from the amplitude. Thus, we have $D_l(k)$ as D\_l(k) &=& 12r\_l(k\^2+\_l\^2) - 14P\_l(k\^4-\_l\^4) + Q\_l(k\^6 + \_l\^6) -R\_l(k\^8 -\_l\^8) +\
&& -2. The remaining effective range parameters are fixed by using the phase shift data of the elastic scattering.

The differential cross section of the elastic scattering is represented in terms of the pure Coulomb scattering part and the Coulomb modified nuclear scattering part, as presented in Eq. (3) in Ref. [@a-epja16], where the scattering function $U_l$ is $U_l=\exp[2i(\delta_l+\omega_l)]$ where $\delta_l$ are the phase shifts for $l$-th partial waves and $\omega_l=\sigma_l-\sigma_0$ with $\sigma_l=\arg \Gamma(1+l+i\eta)$. Thus the scattering amplitudes are represented in terms of $\delta_l$ as [@l-rmp57] A\_l &=& . \[eq;Al-delta\] By comparing two expressions of the amplitudes $A_l$ in Eqs. (\[eq;Al\]) and (\[eq;Al-delta\]), one has a relation between the phase shift and the effective range parameters in $D_l(k)$ as W\_l()C\_\^2 k\_l = Re D\_l(k). \[eq;dell\]

To estimate the ANC, $|C_b|$, for the $0_2^+$, $1_1^-$, $2_1^+$, $3_1^-$ states of $^{16}$O, we employ the definition of $|C_b|$ from Eq. (14) in Ref. [@scb-prc10]: |C\_b| &=& 