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The method of finding the values of asymptotic normalization coefficients (ANC) is proposed based on the analytic continuation of the -matrix that describes the elastic nuclear scattering into the unphysical region of the negative energy of collision (). The formula is derived, expressing the partial-wave scattering amplitude through the -matrix and modified Coulomb functions. This formula allows, when continuing the amplitude to the region , to overcome difficulties associated with irregular behavior of the scattering amplitude near if the Coulomb interaction is present. The proposed method is used to determine the ANC for the channel C. [ABSTRACT FROM AUTHOR]

Asymptotic normalization coefficients (ANC) determine the overall normalization of cross sections of peripheral radiative capture reactions. In a recent paper [Blokhintsev et al., Eur. Phys. J. A 58, 257 (2022)], we considered the ANC C 0 for the virtual decay 16 O (0 + ; 6.05 MeV) → α + 12 C(g.s.). In the present paper, which can be regarded as a continuation of the previous, we treat the ANCs C l for the vertices 16 O (J π) → α + 12 C(g.s.) corresponding to the other three bound excited states of 16 O ( J π = 3 - , 2 + , 1 - , l = J ). ANCs C l ( l = 3 , 2 , 1 ) are found by analytic continuation in energy of the α 12 C l-wave partial scattering amplitudes, 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 l , the scattering data are approximated by the sum of polynomials in energy in the physical region and then extrapolated to the pole. For a more reliable determination of the ANCs, various forms of functions expressed in terms of phase shifts were used in analytical approximation and subsequent extrapolation. [ABSTRACT FROM AUTHOR]

In quantum theory, amplitudes of the processes are analytic functions of their kinematic variables. The analyticity property of the amplitudes allows, in principle, to continue experimental data into the regions that have not been studied in the experiment, including unphysical domains. One of the most important nuclear characteristics that cannot be directly measured in an experiment is the asymptotic normalization coefficient (ANC). In the present work, we discuss two ways to obtain information about ANCs by analytic continuation of experimental data into unphysical domains. The first method is based on the analytic continuation of the experimental differential cross sections of nuclear transfer reactions in the scattering angle. The second approach uses the analytic continuation in energy of the partial-wave amplitudes of elastic scattering. As an example of using this approach, we present the recently obtained by us average values of the ANCs for the virtual decay of the excited bound states of O which are important for nuclear astrophysics: C(g.s.). We got: fm ; fm ; fm ; fm . [ABSTRACT FROM AUTHOR]

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) → α + 12 C(g.s.), the known values of which are characterized by a large spread (0.29 - 1.65) × 10 3 fm - 1 / 2 . The ANC C is found by analytic continuation in energy of the α 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 Schrödinger equation for the two-body α 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 α + 12 C channel. The values of the ANC C obtained within these two methods lie in the interval (886–1139) fm - 1 / 2 . [ABSTRACT FROM AUTHOR]

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 , where is the scattering angle. Within the framework of this method, using experimental data on the differential cross section for the reaction the ANC for the channel 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. [ABSTRACT FROM AUTHOR]

The asymptotic normalization coefficient (ANC) is a fundamental nuclear characteristic of bound states and resonances. The ANC plays an important role in low-energy elastic scattering, transfer and radiative capture reactions, and provides a powerful indirect method in nuclear astrophysics. In this comprehensive review the main properties of the ANC and the role of the ANC in nuclear reactions and nuclear astrophysics are discussed. Also different experimental and theoretical methods of determining the ANCs are addressed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The formalism of asymptotic normalization coefficients and methods for determining them from experimental nuclear data are discussed. A new method is proposed that uses the continuation of the modulus squared of a partial-wave amplitude. It is shown that the recently proposed method for the continuation of elastic scattering data is not strictly correct. It is argued that, unlike asymptotic normalization coefficients, the values of spectroscopic factors cannot be unambiguously determined from experimental data on nuclear reactions. The Trojan horse method is discussed, which allows one to determine cross sections of binary astrophysical nuclear reactions from the data of reactions with three particles in the final state. [ABSTRACT FROM AUTHOR]

The Single-State HORSE (SS-HORSE) method is applied to studying resonant scattering. The method relies on microscopic calculations of nuclear spectra on the basis of the No-Core Shell Model with realistic nucleon-nucleon interactions and does not involve model approximations. The 3/2− and 1/2− resonances of the 5Li and 5He nuclei are investigated within the SS-HORSE method. The possible existence of a resonance in the four-neutron system is explored. [ABSTRACT FROM AUTHOR]

In the present review work, the main methods of the determination of asymptotic normalization coefficients (or respective nuclear vertex constants) for the A + x → B channel and of threebody asymptotic normalization functions (or respective on-shell vertex functions) for the A + b + c → B channel are briefly discussed. The main attention is paid both to the use of the specific asymptotic normalization coefficients and three-body asymptotic normalization functions as a source of getting the valuable information about the pair (nucleon-nucleon, nucleon-cluster and cluster-cluster) nuclear interactions and to their application for the specific direct nuclear-astrophysical radiative capture and peripheral transfer reactions at low energies. [ABSTRACT FROM AUTHOR]

It is shown that values obtained for asymptotic normalization coefficients by means of a potential fitted to experimental data on elastic scattering depend substantially on the presence and the number n of possible forbidden states in the fitted potential. The present analysis was performed within exactly solvable potential models for various nuclear systems and various potentials without and with allowance for Coulomb interaction. Various methods for changing the number n that are based on the use of various versions of the change in the parameters of the potential model were studied. A compact analytic expression for the asymptotic normalization coefficients was derived for the case of the Hulthén potential. Specifically, the d + α and α + 12C systems, which are of importance for astrophysics, were examined. It was concluded that an incorrect choice of n could lead to a substantial errors in determining the asymptotic normalization coefficients. From the results of our calculations, it also follows that, for systems with a low binding energy and, as a consequence, with a large value of the Coulomb parameter, the inclusion of the Coulomb interaction may radically change the asymptotic normalization coefficients, increasing them sharply. [ABSTRACT FROM AUTHOR]

The method for analyzing resonance states based on the harmonic-oscillator representation of scattering equations (HORSE) and on analytic properties of partial-wave scattering amplitudes which has been proposed earlier, is generalized to the case of charged-particle scattering. The method in question is tested by applying it to the model problem of pα scattering and can be used to study resonance states on the basis of microscopic calculations within various versions of the shell model. [ABSTRACT FROM AUTHOR]

A new method for analyzing resonance states based on the Harmonic-Oscillator Representation of Scattering Equations (HORSE) formalism and analytic properties of partial-wave scattering amplitudes is proposed. The method is tested by applying it to the model problem of neutral-particle scattering and can be used to study resonance states on the basis of microscopic calculations performed within various versions of the shell model. [ABSTRACT FROM AUTHOR]

An exactly solvable potential model is used to study the possibility of deducing information about the features of bound states for the system under consideration (binding energies and asymptotic normalization coefficients) on the basis of data on continuum states. The present analysis is based on an analytic approximation and on the subsequent continuation of a partial-wave scattering function from the region of positive energies to the region of negative energies. Cases where the system has one or two bound states are studied. The α+d and α+C systems are taken as physical examples. In the case of one bound state, the scattering function is a smooth function of energy, and the procedure of its analytic continuation for different polynomial approximations leads to close results, which are nearly coincident with exact values. In the case of two bound states, the scattering function has two poles-one in the region of positive energies and the other in the region of negative energies between the energies corresponding to the two bound states in question. Padéapproximants are used to reproduce these poles. The inclusion of these poles proves to be necessary for correctly describing the properties of the bound states. [ABSTRACT FROM AUTHOR]

Due to the long-range character of the Coulomb interaction theoretical description of low-energy nuclear reactions with charged particles still remains a formidable task. One way of dealing with the problem in an integral-equation approach is to employ a screened Coulomb potential. A general approach without screening requires folding of kernels of the integral equations with the Coulomb wave. A new method of folding a function with the Coulomb partial waves is presented. The partial-wave Coulomb function both in the configuration and momentum representations is written in the form of separable series. Each term of the series is represented as a product of a factor depending only on the Coulomb parameter and a function depending on the spatial variable in the configuration space and the momentum variable if the momentum representation is used. Using a trial function, the method is demonstrated to be efficient and reliable. [ABSTRACT FROM AUTHOR]

An Erratum to this paper has been published: https://doi.org/10.1134/S106377882233002X [ABSTRACT FROM AUTHOR]

In the present work one- and two-channel approaches using the expansion of the effective-range function K( E) in powers of energy E are applied to obtain the asymptotic normalization coefficients (ANCs) and vertex constants (VCs) for the d + α system. The coefficients of the K( E) expansion are found by fitting the d α phase shifts. By analytic continuation of K( E) thus obtained to the corresponding poles the ANCs and VCs for D wave d α resonances with J = 1, 2, 3 are calculated for the first time. The 1-resonance and the bound state of Li ( J = 1) are considered jointly in the two-channel ( S + D) effective-range approach and the ANCs and VCs for the ground Li state are found. [ABSTRACT FROM AUTHOR]

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 H(d,p)H, Li(d, α)He, Li(p, α)He, Li(p, α)He reactions, by using the quasi free reactions after break-ups of different nuclides. Results are compared assuming the Li and He break-up in the case of the d(d,p)t, Li(d, α)He reactions and considering the H and He break-up for Li(p, α)He, Li(p, α)He 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. [ABSTRACT FROM AUTHOR]

The scattering function (effective-range function) for the two-channel elastic scattering of charged particles is used to analyze dα scattering at low energies. In order to construct this function, use is made of various sets of phase shifts and mixing parameter, both those that were obtained by solving Faddeev equations in the three-body ( n, p, α) model and those that were deduced from available phaseshift analyses. By means of an analytic continuation of the scattering function to the point of the pole corresponding to the bound state of the Li nucleus, the values of the vertex constants and asymptotic normalization coefficients are found for the process Li → α + d. Possible means for refining these results are discussed. [ABSTRACT FROM AUTHOR]

All transfer reactions and radiative capture nuclear-astrophysical reactions at low energies measured so far are analysed using a reaction theory that contains overlap functions between the wave functions of the target and residual nuclei. These overlaps are assumed to have an asymptotic form determined by the separation energy of the transferred (or radiative captured) cluster and such an assumption is incorporated into all reaction codes. We point out that although this asymptotic form is dominant for the majority of the transfer reactions and the nuclear-astrophysical radiative capture reactions, for some cases the overlap function has anomalous asymptotic behavior. This behavior originates from virtual decays of the complex nucleus into intermediate channels and, mathematically, is generated by contributions from the singularities of the triangle Feynman diagram and the generalised triangle diagram containing a loop. In the present work, these contributions are investigated in detail and expressions are derived for the strengths of the anomalous terms taking spin variables and the Coulomb effects into account. We present specific examples of nuclear vertices with anomalous asymptotics and discuss their application for peripheral nuclear processes. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The general properties of the three-parametric Woods-Saxon potential and the two-parametric Hulthen and square-well potentials are studied by converting them to dimensionless scaling variables. The relations between the parameters of the potentials and such characteristics of a system as binding energies and the asymptotic normalization coefficients of wave functions are investigated. [ABSTRACT FROM AUTHOR]

A Coulomb-modified matrix of scattering amplitudes (an $\tilde F$ matrix) is considered for the case of two coupled channels of elastic scattering of charged particles with different orbital angular momenta ( l and l = l + 2). Matrix elements of the $\tilde F$ matrix are expressed in terms of the matrix elements of a $\tilde K^{ - 1} $ matrix inverse to a modified reaction K matrix. The elements of the $\tilde K^{ - 1} $ matrix are written as expansions that are generalizations of single-channel effective range expansion with allowance for the Coulomb interaction. If a system of colliding particles involves a bound state, the analytic continuation of these expansions into the region of negative energies makes it possible to obtain both the position of the pole corresponding to the bound state and the scattering amplitude residues in this pole, in terms of which the corresponding vertex constants and asymptotic normalization coefficients are expressed. [ABSTRACT FROM AUTHOR]

Relative motion wave functions in the d + He channel were constructed by the projection method using the two-body αt model of Li nucleus. The asymptotic constants in this channel were calculated using various models of He{αn} wave function. [ABSTRACT FROM AUTHOR]

The dependence of asymptotic normalization coefficients of nuclear wave functions on methods for taking Coulomb interaction into account is studied. Calculations are performed both with the total Coulomb potential and with the Coulomb potential truncated at large distances. Both sharp and smooth truncation is used. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The S matrix and the scattering-amplitude matrix ( F matrix) are considered for the case of two coupled elastic-scattering channels differing by the values of the orbital angular momentum ( l and l = l + 2). The matrix elements of the S and F matrices in the absence of Coulomb interaction are expressed in terms of the matrix elements of the matrix K inverse to the reaction K matrix. The elements of the K matrix are written in the form of expansions that are generalizations of the single-channel effective-range expansion. If there is a bound state in the system of colliding particles, then an analytic continuation of these expansions to the region of negative energies makes it possible to obtain both the position of the pole corresponding to this bound state and the residues of scattering amplitudes at this pole, the respective vertex constants and asymptotic normalization coefficients being expressed in terms of these residues. By way of example, the developed formalism is applied to describing triplet neutron-proton scattering. [ABSTRACT FROM AUTHOR]

H and He nuclei are considered in a two-body model (H = n + d; He = p + d). Two independent approaches are used: in the first, interaction is described by the folding potential, while NN potentials are taken in the Hulthen form with allowance for violations of isotopic invariance. The second approach features phenomenological Hulthen and Yukawa Nd potentials used as Nd interaction. In both approaches, the binding energies, vertex constants, and asymptotic normalization coefficients in the N+d channel are calculated. [ABSTRACT FROM AUTHOR]

new method is proposed for finding the resonance parameters of a nuclear system, obtained from the phase shift analysis of elastic scattering data, by means of a pole representation of an S-matrix in complex momentum space is proposed. This method is based on the expansion of the potential phase shift into a Taylor series within the area of real momentum near the resonance pole. The coefficients of the expansion and resonance parameters are determined by fitting the analytical expression for the experimental phase shift. The proposed method provides reliable values of the energy and width of broad resonances. [ABSTRACT FROM AUTHOR]

In this work, we use a model for describing the dα interaction in a Li nucleus, in which the dα nuclear potential is written as the sum of the local folding potential and a nonlocal term originating from the deuteron exchange mechanism and corresponding to a three-deuteron component of the Li wave function. This model was used to calculate the nuclear vertex constants and the corresponding asymptotic normalization coefficients of Li in the dα channel. Both values L = 0 and L = 2 of relative dα orbital angular momentum L were considered. Calculations were performed with and without allowance for the Coulomb dα interaction. [ABSTRACT FROM AUTHOR]