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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 $$\Delta$$ 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.

The method for analyzing resonance states based on the harmoni©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.

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.

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.

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+12C 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. Padeapproximants are used to reproduce these poles. The inclusion of these poles proves to be necessary for correctly describing the properties of the bound states.

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.

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 6Li nucleus, the values of the vertex constants and asymptotic normalization coefficients are found for the process 6Li → α + d. Possible means for refining these results are discussed.

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.

In view of projected experiments on the production of relativistic hypernuclei and the investigation of reactions induced by them, the characteristics of the hypernucleus and low-energy parameters of the Λ 5 He hyperon scattering from 4He were calculated. The interaction of the Λ hyperon and the α particle is described by the effective Λα potential in two different forms. The root-mean-square radius of the Λ hyperon in the Λ 5 He hypernucleus, the vertex constant for the Λ 5 He ↔ 4He + Λ process, and the corresponding asymptotic normalization coefficient of the Λ 5 He wave function were calculated by solving the radial Schrodinger equation. The scattering length and the effective radius for the scattering of Λ from 4He were calculated by two methods. The calculated characteristics turn out to be sensitive to the form of the Λα potential.

The characteristics of bound states of hypernuclei were calculated in [1] in a wide range of mass numbers within the potential model for three different potentials. In this study, the phase shifts and low-energy parameters for scattering of Λ hyperons from core nuclei, considered in [1], have been calculated for the same potentials. The calculated scattering lengths and effective radii are compared with their values found in [1] on the basis of the data on the binding energies and vertex constants of hypernuclei.

N/D equations taking into account the Coulomb interaction effects are used to consider the phase analysis data on 3He4He scattering and determine the nuclear vertex constants for the 7Be ↔ 3He4He vertex, where the beryllium nucleus is in the ground (3/2−) or first excited (1/2−) states. Information about the asymptotic normalization coefficients of the wave functions of the 7Be nucleus in the noted states is derived. The data obtained are used to calculate the astrophysical S factor for the 4He(3He, γ)7Be reaction.

The approach to the problem of constructing effective local operators of interaction between systems of strongly interacting particles, based on the requirement of proper analytical structure of partial-wave scattering amplitudes, has been developed. The approach has been applied to constructing effective potentials for N 4 He, N 3 H, N 3 He, and 3 He 4 He scattering.

The S matrix and the f matrix amplitudes are considered for the case of two coupled elastic scattering channels, which differ in values of orbital angular momenta. Matrix elements of S and f matrices are parametrized in terms of scattering phases δ i (i = 1, 2) and a mixing parameter $${\epsilon}$$ and are expressed in terms of matrix elements c ij = (K −1) ij where K is the reaction K matrix. Quantities $${g_{ij}(k)=k^{l_i+l_j+1}c_{ij}(k)}$$ are expanded in powers of k 2, k being the relative momentum of colliding particles B and C. Then functions g ij (k) and c ij (k) are continued analytically to the pole of amplitudes f ij corresponding to the bound state A of colliding particles. This procedure allows to get the position of the pole as well as the residues of amplitudes f ij at that pole which are related directly to vertex constants and asymptotic normalization coefficients corresponding to the vertex A → B + C.

The two-body transfer mechanism for elastic rearrangement scattering from the three-body bound state i + { jkl } → j + { ikl } has been investigated on the basis of 4-dimensional formalism of covariant nonrelativistic graphs. The relation between this approach and the 3-dimensional graph formalism has been analyzed in detail. This approach is applied to describing backward elastic p 3 He scattering in the energy range 0.5 – 1.7 GeV. The Faddeev 5-channel wave function is used for the bound state of the 3 He nucleus. Numerical calculations show that the mechanism of sequential transfer of a noninteracting np-pair dominates while transfer of an interacting pair as well as nonsequential transfer of a noninteracting np-pair give a negligible contribution. The dominating mechanism is insensitive to the D-components of the 3 He wave function and relativistic effects in spite of high momentum transfer. Taking into consideration Glauber rescatterings in the entrance and exit channels one obtains agreement with the experimental data in energy and angular dependence of the differential cross section at energies 0.9 – 1.7 GeV.

Deuteron induced quasi-free scattering and reactions have been extensively investigated in the past few decades. This was done not only for nuclear structure and processes study 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. The same will be done for other nuclides of possible use as Trojan Horse particles. Trojan horse method 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 (FWHM) variation on the extraction of the astrophysical S(E)-factor is discussed.

The three-body eikonal approach to ion-atom collisions based on the Alt-Grassberger-Sandhas equations is developed. The amplitudes for scattering and charge exchange, written in the impact parameter representation and using the eikonal approximation, are represented as a sum of two terms. One of them describes the scattering via the Coulomb potential acting between the colliding heavy particles. The second one could be factored into a product of two terms. One is an explicitly known factor which contains all the information about the interaction between the heavy particles. The remaining part does not contain any reference to this interaction any longer. For these residual amplitudes effective-two body equations are written down. Explicit expressions for the effective potentials occurring therein, for both the scattering and the transfer channels, are derived in the lowest order approximation. This approach is then used to calculate total and partial cross sections for the electron capture processes in collisions of the ions H+, He2+ and Li3+ with atomic hydrogen. The latter is taken to be in its ground state, except for the case of incident H+ when the target hydrogen atom is considered also in some low-lying excited states.

Recently, a new measurement of the $^{6}\mathrm{Li}$ (150 A MeV)dissociation in the field of $^{208}\mathrm{Pb}$ has been reported [Hammache et al., Phys. Rev. C 82, 065803 (2010)] to study the radiative capture $\ensuremath{\alpha}+d\ensuremath{\rightarrow}{}^{6}\mathrm{Li}+\ensuremath{\gamma}$ process. However, the dominance of the nuclear breakup over the Coulomb one prevented the information about the $\ensuremath{\alpha}+d\ensuremath{\rightarrow}{}^{6}\mathrm{Li}+\ensuremath{\gamma}$ process from being obtained from the breakup data. The astrophysical ${S}_{24}(E)$ factor has been calculated within the $\ensuremath{\alpha}\ensuremath{-}d$ two-body potential model with potentials determined from the fits to the $\ensuremath{\alpha}\ensuremath{-}d$ elastic scattering phase shifts. However, the scattering phase shift, according to the theorem of the inverse scattering problem, does not provide a unique $\ensuremath{\alpha}\ensuremath{-}d$ bound-state potential, which is the most crucial input when calculating the ${S}_{24}(E)$ astrophysical factor at astrophysical energies. In this work, we emphasize the important role of the asymptotic normalization coefficient (ANC) for ${}^{6}\mathrm{Li}\ensuremath{\rightarrow}\ensuremath{\alpha}+d$, which controls the overall normalization of the peripheral $\ensuremath{\alpha}+d\ensuremath{\rightarrow}{}^{6}\mathrm{Li}+\ensuremath{\gamma}$ process and is determined by the adopted $\ensuremath{\alpha}\ensuremath{-}d$ bound-state potential. Since the potential determined from the elastic scattering data fit is not unique, the same is true for the ANC generated by the adopted potential. However, a unique ANC can be found directly from the elastic scattering phase shift, without invoking intermediate potential, by extrapolation the scattering phase shift to the bound-state pole [Blokhintsev et al., Phys. Rev. C 48, 2390 (1993)]. We demonstrate that the ANC previously determined from the $\ensuremath{\alpha}\ensuremath{-}d$ elastic scattering $s$-wave phase shift [Blokhintsev et al., Phys. Rev. C 48, 2390 (1993)], confirmed by ab initio calculations, gives ${S}_{24}(E)$, which at low energies is about $38%$ less than the other one reported [Hammache et al., Phys. Rev. C 82, 065803 (2010)]. We recalculate also the reaction rates, which are lower than those obtained in that same study [Hammache et al., Phys. Rev. C 82, 065803 (2010)].

The $^{6}\mathrm{Li}$(${1}^{+}$0)${\ensuremath{\rightarrow}}^{4}$He+d virtual decay vertex constant ${\mathit{G}}_{0}$ and the respective asymptotic coefficient ${\mathit{C}}_{0}$ of the $^{6}\mathrm{Li}$ wave function in the $^{4}\mathrm{He}$+d channel are found using the analytic continuation of the solution of a novel energy-dependent phase-shift analysis of elastic d${\mathrm{\ensuremath{-}}}^{4}$He scattering to the pole corresponding to the $^{6}\mathrm{Li}$ ground state. The reliability and accuracy of the method used have been corroborated independently by three other ways: by directly solving the inverse problem for d${\mathrm{\ensuremath{-}}}^{4}$He scattering and by two different methods for finding a solution for the three-body (\ensuremath{\alpha}+n+p) problem. The values ${\mathit{G}}_{0}^{2}$=0.42\ifmmode\pm\else\textpm\fi{}0.02 fm and ${\mathit{C}}_{0}$=2.93\ifmmode\pm\else\textpm\fi{}0.15 have been found, which seem to be the most accurate and reliable among the values obtained so far.

Deuteron elastic scattering and stripping processes off a target nucleus consisting of A nucleons are treated within the framework of the few-body integral equations theory. By projecting the (A+2)-body operators onto target states, matrix three-body integral equations are derived that allow for the incorporation of the excited states of the target nucleons. This approach is applied to deuteron scattering off {sup 12}C when the latter is in its ground state before and after the reaction. For the nucleon-{sup 12}C subsystem three sets of (quasi-separable) potentials are employed. The first such potential is based on the one derived by Cattapan et al. [Nucl. Phys. A241, 204 (1975)] for orbital angular momentum states with L{

The method of the analytic continuation of the effective range function is applied to obtain the asymptotic normalization coefficients for 6 Li nucleus in the α+d channel. Several sets of scattering phases obtained from the phase-shift analyses as well as from Faddeev calculations are used as an input. Since the α+d system possesses the low-lying inelastic threshold due to the dissociation of a deuteron, the approach used is generalized to include inelastic channels. The sensitivity of the obtained values of asymptotic normalization coefficients to the elastic channels coupling and to account of the inelastic channel is investigated.

The two-body transfer amplitude for the rearrangement process i+(jkl) - j+(ikl) is constructed on the basis of technique of 4-dimensional covariant nonrelativistic graphs. The developed formalism is applied to describing backward elastic $p^3He$ scattering in the energy range 0.5 - 1.7 GeV. Numerical calculations performed using the 5- channel wave function of the $^3He$ nucleus show that the transfer of a noninteracting np- pair dominates and explains satisfactorily the energy and angular dependence of the differential cross section at energies 0.9 - 1.7$ GeV. A weak sensitivity to high momentum components of the $~^3He$ wave function in spite of large momentum transfer as well as a very important role of rescatterings in the initial and final states are established., Comment: 7 pages, Latex, 3 Postscript figures

The recently developed three‐body eikonal approach to ion‐atom collisions, based on the Alt‐Grassberger‐Sandhas equations, is applied to the scattering at medium and high energies of H+ off hydrogen atoms. The latter are considered in the ground as well as in some low‐lying excited states.

It is assumed that the main contribution to the reaction K matrix for elastic alpha t scattering comes from the pole Feynman graph corresponding to the proton transfer mechanism. The differential cross section calculated under this assumption furnishes a satisfactory description of the experiment and allows one to obtain the value 10.0 fm for the vertex constant Galpha tp2 of the process alpha to or from t+p. Taking account of the infinite series of graphs describing the multiple proton exchange improves agreement with the experiment and leads to Galpha tp2=12.2 fm.

A description of nuclear reactions is suggested based on the assumption that the main contribution to the reaction K -matrix elements, regarded as analytic functions of the variable z = cos (being the scattering angle), comes from the singularities of these functions which are nearest to the physical region. Analytic properties of K -matrix elements with respect to z are discussed. As an illustration, elastic Nα scattering is examined and vertex constants values are found for the vertices α ⇄t + p and α ⇄ τ + n.

Elastic scattering of low-energy positive kaons by2H,3He, and4He is considered in terms of theN/D equations, the “inverse amplitude” method, and the dispersionK-matrix approach. The influence of the Coulomb effects and of the multiple scattering terms on the partial-wave amplitudes has been studied. The calculated values ofK + d andK + 4He scattering lengths are 0·45 fm and 0·48 fm respectively. The Coulomb effects contribute about 20% to the Coulombnuclear part of the amplitude for the kaon energy of 5–20 MeV.

A new method for analysing the diffraction π N-scattering is given. It is based on the idea of the effective π N-interaction potential. The application of this method to 6.8 GeV/ c pion scattering points to strong ππ -interaction.

The condition of macroscopic causality for the scattering matrix is formulated. An example of the unitary but nonlocal scattering matrix which satisfies the requirements of macroscopic causality is given.

In this paper the role of the peripheral ππ interaction in πN collisions is studied when the momentum of the primary pion is about 7 GeV. It has been shown that in elastic πN scattering the contribution of the peripheral ππ interaction is not great, and that it is fully camouflaged by the diffraction scattering from the nucleon core. In the case of inelastic collisions the contribution of the ππ interaction is already quite noticeable and, therefore, it is possible to determine the cross sections for ππ interaction from the experimental data on multiple pion production. The distribution of the transverse momentum of the recoil nucleon has been calculated in the processes π +N→N+2 π and of Λ 0 for the process π +N→ Λ 0 +K+ π . It has been shown also that this distribution is in agreement with the experimental data.

The change in the position of the leading singularities of non-relativistic Feynman graphs with their successive complications has been investigated using the block method proposed by Rudik and Simonov. Graphs describing the interaction in the final (or initial) state of a nuclear reaction, ladder graphs consisting of identical blocks and some other four-point graphs are considered as examples. From these examples it is concluded that with increasing number of internal lines the singularities of non-relativistic four-point diagrams in the cosine of the scattering angle move away fairly rapidly from the boundary of the physical region. The singularities of two-loop three-point graphs corresponding to the virtual processes of A ⇄ B+C type are also discussed.

A method is proposed for calculating the amplitude M(s, t) of the direct nuclear reaction 1 + 2 → 3 + 4 taking into account the interactions in the initial and final states (the method of summing diagrams). The amplitude M(s, t) is based on the initial Born amplitude B(s, t) which is described by one or several non-relativistic Feynman graphs and which does not take into account the interaction effects in the initial and final states. The method of summing diagrams is compared with the method of distorted waves and the dispersion method. The analytical properties of the amplitudes M(s, t) in the variables s and t are discussed in detail.

On the basis of the optical model, under very general assumptions, it is shown that in the backward scattering there must be a peak of width ∼\(\mathchar'26\mkern-10mu\lambda \)/R (R is the nucleon « diameter »). The cross-section for the backward scattering, unlike the forward scattering, is constant or decreases with increasing energy (depending on the type of the optical model).

It is shown that under rather general assumptions the largea ngle elastic scattering cross-sections must decrease as 1/E0 (E0 is the energy of an incident particle in the laboratory system).

Deuteron induced quasi‐free scattering and reactions have been extensively investigated in the past few decades as well as 6Li, 3He and 9Be induced ones. This was done not only for nuclear structure and processes study but also for the important astrophysical implication (Trojan Horse Method, THM). In particular the width of the spectator momentum distribution in 6Li and deuterium, which have widely been used as a Trojan Horse nuclei, will be studied as a function of the transferred momentum. Trojan horse method applications will also be discussed in these cases.