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Register a new userNew method of analytic continuation of elastic-scattering data to the negative-energy region and asymptotic normalization coefficients for $^{17}$O and $^{13}$C
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A new method is proposed for extrapolation of elastic-scattering data to the negative-energy region for a short-range interaction. The method is based on the analytic approximation of the modulus-squared of the partial-wave scattering amplitude. It is shown that the proposed method has an advantage over the traditional one based on continuation of the effective-range function. The new method has been applied to determine the asymptotic normalization coefficients for the $^{17}$O and $^{13}$C nuclei in the $n+^{16}$O and $n+^{12}$C channels, respectively.
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Explicit analytic expressions are derived for the effective-range function for the case when the interaction is represented by a sum of the short-range square-well and long-range Coulomb potentials. These expressions are then transformed into forms convenient for extrapolating to the negative-energy region and obtaining the information about bound-state properties. Alternative ways of extrapolation are discussed. Analytic properties of separate terms entering these expressions for the effective-range function and the partial-wave scattering amplitude are investigated.
The problem of analytic continuation of the scattering data to the negative-energy region to obtain information on asymptotic normalization coefficients (ANCs) of bound states is discussed. It is shown that a recently suggested $Delta$ method [O.L.Ram{i}rez Suarez and J.-M. Sparenberg, Phys. Rev. C {bf 96}, 034601 (2017)] is not strictly correct in the mathematical sense since it is not an analytic continuation of a partial-wave scattering amplitude to the region of negative energies. However, it can be used for practical purposes for sufficiently large charges and masses of colliding particles. Both the $Delta$ method and the standard method of continuing of the effective range function are applied to the $p-^{16}$O system which is of interest for nuclear astrophysics. The ANCs for the ground $5/2^+$ and excited $1/2^+$ states of $^{17}$F are determined.
The $^{13}C(^{14}N,^{13}C)^{14}N$ proton exchange reaction has been measured at an incident energy of 162 MeV. Angular distributions were obtained for proton transfer to the ground and low lying excited states in $^{14}N$. Elastic scattering of $^{14}N$ on $^{13}C$ also was measured out to the rainbow angle region in order to find reliable optical model potentials. Asymptotic normalization coefficients for the system $^{13}C+pto {}^{14}N$ have been found for the ground state and the excited states at 2.313, 3.948, 5.106 and 5.834 MeV in $^{14}N$. These asymptotic normalization coefficients will be used in a determination of the S-factor for $^{7}Be(p,gamma)^{8}B$ at solar energies from a measurement of the proton transfer reaction $^{14}N(^{7}Be,^{8}B)^{13}C$.
The method of asymptotic normalization coefficients is a standard approach for studies of two-body non-resonant radiative capture processes in nuclear astrophysics. This method suggests a fully analytical description of the radiative capture cross section in the low-energy region of the astrophysical interest. We demonstrate how this method can be generalized to the case of three-body $2p$ radiative captures. It was found that an essential feature of this process is the highly correlated nature of the capture. This reflects the complexity of three-body Coulomb continuum problem. Radiative capture $^{15}$O+$p$+$p rightarrow ^{,17}$Ne+$gamma$ is considered as an illustration.
The first study of resonances in $^{17}$O+$alpha$ elastic scattering was carried out using the Thick Target Inverse Kinematics (TTIK) method. The data were analyzed in the framework of an $textit{R}$-matrix approach. Many $alpha$-cluster states were found in the $^{21}$Ne excitation region of the 9-13 MeV excitation energy including the first observation of a broad $textit{l}$=0 state in an odd-even nucleus, which is likely the analog of the broad 0$^+$ at 8 MeV in $^{20}$Ne. The observed structure in $^{21}$Ne appeared to be strikingly similar to that in $^{20}$Ne populated in the resonance $^{16}$O+$alpha$ scattering. The results are also useful for refinement of data on an $^{17}$O($alpha$,$textit{n}$) reaction important for astrophysics.
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