Algorithm for the asymptotic nuclear coefficients calculations using phase shift data for charged particles scattering

Abstract: A new algorithm for the asymptotic nuclear coefficients calculation, which we call the $\Delta$-method, is proved and developed. This method was proposed in Ref. [O. L. Ram\'irez Su\'arez and J.-M. Sparenberg, arXiv: 1602.04082 nucl-th] but no proof was given. We apply it to the bound state situated near the channel threshold when the Sommerfeld parameter is quite large within the experimental energy region. As a result, the value of the conventional effective-range function $K_l(k<sup>2)$ is actually defined by the Coulomb term. One of the resulting effects is the wrong description of energy behavior of the elastic scattering phase shift $\delta_l$ reproduced from the fitted total effective-range function $K_l(k<sup>2)$. This leads to an improper value of the asymptotic normalization coefficient (ANC) value. No such problem arises if we fit only the nuclear term. The difference between the total effective-range function and the Coulomb part at real energies is the same as the nuclear term. Then we can proceed using just this $\Delta$-method to calculate the pole position values and the ANC. We apply it to the vertices $$^4\rm{He}+ {^{{12}\rm{C}}\longleftrightarrow} {<sup>{16}\rm{O}}$$ and $$^3\rm{He}+ {^{4\rm{He}}\longleftrightarrow} {<sup>7\rm{Be}}$$. The calculated ANCs can be used to find the radiative capture reaction cross sections of the transfers to the $<sup>{16}\rm{O}$ bound final states as well as to the $$^{7\rm{Be}\longleftrightarrow} {<sup>7\rm{Be}}$$. The calculated ANCs can be used to find the radiative capture reaction cross sections of the transfers to the $<sup>{16}\rm{O}$ bound final states as well as to the $<sup>7\rm{Be}$.