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Abstract A method is discussed for determining the asymptotic normalization coefficients (ANC) using the analytic continuation of experimental differential cross sections for nuclear transfer reactions to the pole point of the reaction amplitude with respect to the variable $$\cos\theta$$, where $$\theta$$ is the scattering angle. Within the framework of this method, using experimental data on the differential cross section for the reaction $${}^{12}\textrm{C}(0^{+};0\textrm{ MeV})(d,p){}^{13}\textrm{C}(1/2^{+};3.09\textrm{ MeV})$$ the ANC for the channel $${}^{13}\textrm{C}(1/2^{+};3.09\textrm{ MeV})\to{}^{12}\textrm{C}(0^{+};0\textrm{ MeV})+n$$ was determined. When determining the ANC, the corrections caused by the Coulomb interaction in the initial, final and intermediate states of the reaction were taken into account. It is shown that these corrections significantly affect the extracted ANC value.

Asymptotic normalization coefficients (ANC) determine the overall normalization of cross sections of peripheral radiative capture reactions. In the present paper, we treat the ANC $C$ for the virtual decay $^{16}$O$(0^+; 6.05$ MeV)$\to \alpha+^{12}$C(g.s.), the known values of which are characterized by a large spread $(0.29-1.65)\times 10^3$ fm$^{-1/2}$. The ANC $C$ is found by analytic continuation in the energy of the $\alpha^{12}$C $s$-wave scattering amplitude, known from the phase-shift analysis of experimental data, to the pole corresponding to the $^{16}$O bound state and lying in the unphysical region of negative energies. To determine $C$, two different methods of analytic continuation are used. In the first method, the scattering data are approximated by the sum of polynomials in energy in the physical region and then extrapolated to the pole. The best way of extrapolation is chosen on the basis of the exactly solvable model. Within the second approach, the ANC $C$ is found by solving the Schr\"odinger equation for the two-body $\alpha^{12}$C potential, the parameters of which are selected from the requirement of the best description of the phase-shift analysis data at a fixed experimental binding energy of $^{16}$O$(0^+; 6.05$ MeV) in the $\alpha+^{12}$C channel. The values of the ANC $C$ obtained within these two methods lie in the interval (886--1139) fm$^{-1/2}$., Comment: arXiv admin note: text overlap with arXiv:1710.10767

Abstract It is shown that the Schrödinger equation for the sum of the potential of a square well and the Coulomb potential of a uniformly charged sphere admits an analytical solution for arbitrary values of the orbital angular momentum. An explicit form of this solution has been found. Using the obtained solution, the influence of the Coulomb interaction for both point and distributed nuclear charges on the values of asymptotic normalization coefficients for various nuclear systems is investigated. It is shown that taking into account the non-point distribution of the nuclear charge has little effect on the calculated values of the asymptotic normalization coefficients, provided that the binding energy of the system is assumed to be fixed.

The astrophysical $^{7}\mathrm{Be}(p,\ensuremath{\gamma})\phantom{\rule{0.16em}{0ex}}^{8}\mathrm{B}$ direct capture process is studied in the framework of a two-body single-channel model with potentials of the Gaussian form. A modified potential is constructed to reproduce the new experimental value of the $S$-wave-scattering length and the known astrophysical $S$ factor at the Gamow energy, extracted from the solar neutrino flux. The resulting potential is consistent with the theory developed by Baye [Phys. Rev. C 62, 065803 (2000)] according to which the $S$-wave scattering length and the astrophysical $S$ factor at zero energy divided by the square of the asymptotic normalization coefficient are related. The obtained results for the astrophysical $S$ factor at intermediate energies are in good agreement with the two data sets of Hammache et al. [Phys. Rev. Lett. 86, 3985 (2001); Phys. Rev. Lett.80, 928 (1998)]. Linear extrapolation to zero energy yields ${S}_{17}(0)\ensuremath{\approx}20.{51}_{\ensuremath{-}1.85}^{+2.02}\phantom{\rule{0.28em}{0ex}}\mathrm{eV}\phantom{\rule{0.16em}{0ex}}\mathrm{b}$ consistent with the Solar Fusion II estimate. The calculated reaction rates are substantially lower than the results of the NACRE II Collaboration.

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.

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 $\mathrm{\ensuremath{\Delta}}$ method [O. L. Ram\'{\i}rez Su\'arez and J.-M. Sparenberg, Phys. Rev. C 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 $\mathrm{\ensuremath{\Delta}}$ method and the standard method of continuing of the effective range function are applied to the $p\ensuremath{-}^{16}\mathrm{O}$ system, which is of interest for nuclear astrophysics. The ANCs for the ground $5/{2}^{+}$ and excited $1/{2}^{+}$ states of $^{17}\mathrm{F}$ are determined.

The approach called the single-state harmonic oscillator representation of scattering equations (SS-HORSE) to analyze resonant states is generalized to the case of charged particle scattering by using the analytical properties of partial scattering amplitudes and is applied to the study of resonant states in the $^{5}\mathrm{Li}$ nucleus and nonresonant $s$-wave proton-$\ensuremath{\alpha}$ scattering within the no-core shell model using the JISP16 and Daejeon16 $NN$ interactions. We present also the results of calculations of neutron-$\ensuremath{\alpha}$ scattering and resonances in the $^{5}\mathrm{He}$ nucleus with Daejeon16 and compare with results published previously using JISP16.

A problem of analytical continuation of scattering data to the negative-energy region to obtain information about bound states is discussed within an exactly solvable potential model. This work is continuation of the previous one by the same authors [L. D. Blokhintsev et al., Phys. Rev. C 95, 044618 (2017)]. The goal of this paper is to determine the most effective way of analytic continuation for different systems. The $d+\alpha$ and $\alpha +^{12}$C systems are considered and, for comparison, an effective-range function approach and a recently suggested $\Delta$-method [O. L. Ram\'{\i}rez Su\'arez and J.-M. Sparenberg, Phys. Rev. C 96, 034601 (2017)] are applied. We conclude that the $\Delta$-method is more effective for heavier systems with large values of the Coulomb parameter, whereas for light systems with small values of the Coulomb parameter the effective-range function method might be preferable.

In the last decades, the Trojan Horse method (THM) has played a crucial role for the measurement of several particle (both neutron and charged one) induced cross sections for reactions of astrophysical interest. To better understand its cornerstones and its applications to physical cases, many tests were performed to verify all its properties and the possible future perspectives. The Trojan Horse nucleus invariance proves the relatively simple approach allowed by the pole approximation and sheds light in the involved reaction mechanisms. Here we shortly review the complete work for the binary 2H(d,p)3H, 6Li(d,α)4He, 6Li(p,α)3He, 7Li(p,α)4He reactions, by using the quasi free reactions after break-ups of different nuclides. Results are compared assuming the 6Li and 3He break-up in the case of the d(d,p)t, 6Li(d,α)4He reactions and considering the 2H and 3He break-up for 6Li(p,α)3He, 7Li(p,α)4He reactions. These results, regardless of the Trojan Horse particle or the break-up scheme, confirms the applicability of the standard description of the THM and suggests the independence of binary indirect cross section on the chosen Trojan Horse nuclei for a whole spectra of different cases. This gives a strong basis for the understanding of the quasi-free mechanism which is the foundation on which the THM lies.

Deuteron induced quasi-free scattering and reactions have been extensively investigated in the past few decades. This was done not only for the study of the nuclear structure and processes but also for the important astrophysical implication (Trojan Horse Method, THM). In particular the width of the neutron momentum distribution in deuteron will be studied as a function of the transferred momentum. THM applications will also be discussed because the momentum distribution of the spectator particle inside the Trojan horse nucleus is a necessary input for this method. The impact of the width variation on the extraction of the astrophysical S(E)-factor is discussed as well as the relevance of the s and d wave component in the deuteron wave function.

The study of energy production and nucleosynthesis in stars requires an increasingly precise knowledge of the nuclear reaction rates at the energies of interest. To overcome the experimental difficulties arising from the small cross sections at those energies and from the presence of the electron screening, the Trojan Horse Method has been introduced. The method provides a valid alternative path to measure unscreened low-energy cross sections of reactions between charged particles, and to retrieve information on the electron screening potential when ultra-low energy direct measurements are available.

Trojan Horse method plays an important part for the measurement of several charged particle in- duced reactions cross sections of astrophysical interest. In order to better understand its cornerstones and the related applications to different astrophysical scenarios several tests were performed to verify all its proper- ties and the possible future perspectives. The Trojan Horse nucleus invariance for the binary reactions d(d,p)t, 6,7 Li(p,α) 3,4 He was therefore tested using the appropriate quasi free break- ups, respectively. In the first cases results from 6 Li and 3 He break up were used, while for the lithium fusion reactions break-ups of 2 H and 3 He were compared. The astrophysical S(E)-factors for the different processes were then extracted in the framework of the Plane Wave Approximation applied to the different break-up schemes. The obtained results are compared with direct data as well as with previous indirect investigations. The very good agreement between data coming from different break-up schemes confirms the applicability of the plane wave approximation and suggests the independence of binary indirect cross section on the chosen Trojan Horse nucleus also for the present cases. Moreover the astrophysical implications of the results will also be discussed in details.

In the last decades the Trojan Horse method has played a crucial role for the measurement of several charged particle induced reactions cross sections of astrophysical interest. To better understand its cornerstones and its applications to physical cases many tests were performed to verify all its properties and the possible future perspectives. The Trojan Horse nucleus invariance for the binary d(d,p)t reaction was therefore tested using the quasi free 2 H( 6 Li, pt) 4 He and 2 H( 3 He,pt)H reactions after 6 Li and 3 He break-up, re- spectively. The astrophysical S(E)-factor for the d(d,p)t binary process was then extracted in the framework of the Plane Wave Approximation applied to the two di erent break-up schemes. The obtained results are compared with direct data as well as with previous indirect investigations. The very good agreement confirms the applicability of the plane wave approximation and suggests the independence of binary indirect cross section on the chosen Trojan Horse nucleus also for the present case.

In the current picture of nuclear astrophysics indirect methods and, in particular, the Trojan Horse Method cover a crucial role for the measurement of charged particle induced reactions cross sections of astrophysical interest, in the energy range required by the astrophysical scenarios. To better understand its cornerstones and its applications to physical cases many tests were performed to verify all its properties and the possible future perspectives. The key to the method is the quasi-free break-up and some of its properties will be investigated in the present work. In particular, the Trojan Horse nucleus invariance will be studied and previous studies will be extended to the cases of the binary d(d,p)t and 6 Li(d,α) 4 He reactions, which were tested using different quasi-free break-up's, namely 6 Li and 3 He. The astrophysical S(E)-factor were then extracted with the Trojan Horse formalism applied to the two different break-up schemes and compared with direct data as well as with previous indirect investigations. The very good agreement confirms the independence of binary indirect cross section on the chosen spectator particle also for these reactions.

This paper describes some of the authors' practical experiences in the on-line measurement of partial discharges in medium voltage motor and generator stator windings. Economic considerations are discussed as well as the use of traditional and nontraditional sensor applications. Comparisons and practical recommendations are provided.

Few-body methods provide very useful tools to solve different problems important for nuclear astrophysics. Some of them are discussed below.

The Trojan Horse nucleus invariance for the binary d(d,p)t reaction was tested using the quasi free $^2$H($^6$Li, pt)$^4$He and $^2$H($^3$He,pt)H reactions after $^6$Li and $^3$He break-up, respectively. The astrophysical S(E)-factor for the d(d,p)t binary process was then extracted in the framework of the Plane Wave Approximation applied to the two different break-up schemes. The obtained results are compared with direct data as well as with previous indirect investigations. The very good agreement confirms the applicability of the Plane Wave Approximation and suggests the independence of binary indirect cross section on the chosen Trojan Horse nucleus also for the present case.