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arXiv · 1702.04933

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

Yu. V. Orlov·B. F. Irgaziev·Jameel-Un Nabi
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Abstract

A new algorithm for the asymptotic nuclear coefficients calculation, which we call the $Δ$-method, is proved and developed. This method was proposed in Ref. [O. L. Ramírez Suárez and J.-M. Sparenberg, arXiv: 1602.04082 [nucl-th] (2016)] 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 $K_l(k^2)$ 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 $δ_l$ reproduced from the fitted total effective-range function $K_l(k^2)$. 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 $Δ$-method to calculate the pole position values and the ANC. We apply it to the vertices $^4\rm{He}+ {^{12}\rm{C}}\longleftrightarrow {^{16}\rm{O}}$ and $^3\rm{He}+ {^4\rm{He}}\longleftrightarrow {^7\rm{Be}}$. The calculated ANCs can be used to find the radiative capture reaction cross sections of the transfers to the $^{16}\rm{O}$ bound final states as well as to the $^7\rm{Be}\longleftrightarrow {^7\rm{Be}}$. The calculated ANCs can be used to find the radiative capture reaction cross sections of the transfers to the $^{16}\rm{O}$ bound final states as well as to the $^7\rm{Be}$.

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Yu. V. Orlov, B. F. Irgaziev, Jameel-Un Nabi. 2017-07-16. Algorithm for the asymptotic nuclear coefficients calculations using phase shift data for charged particles scattering. https://doi.org/10.1103/physrevc.96.025809

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