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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

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.

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 dα phase shifts. By analytic continuation of K(E) thus obtained to the corresponding poles the ANCs and VCs for D wave dα resonances with Jπ = 1+, 2+, 3+ are calculated for the first time. The 1+-resonance and the bound state of 6Li (Jπ = 1+) are considered jointly in the two-channel (S + D) effective-range approach and the ANCs and VCs for the ground 6Li state are found.

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 problem of determining asymptotic normalization coefficients (ANC) from experimental data is considered. It is shown that the ANC could be extracted from the single partial-wave phase shift if one applies the analyticity requirement. A new method of determining ANCs is suggested, which makes use both of the experimental information on phase shifts and of the analytic properties of scattering amplitudes.

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 widths of the spectator momentum distributions in several nuclei, which have been used as Trojan Horses, have been obtained as a function of the transferred momentum. Applications of Trojan Horse method will also be discussed.

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.

It is suggested to use the integral Faddeev equations in the Alt-Grassberger-Sandhas form to calculate the muon transfer reactions relevant to muon-catalyzed fusion. Similar equations derived while neglecting the electron mass compared to the ion masses, were successfully used for the description of the electron transfer reactions in the ion-atomic collisions. The corrections due to the finiteness of the muon mass are discussed.

A variant of stochastic space is considered, which reveals the specific feature that the field when averaged over this space turns into the nonlocal field leading to macrocausal and unitary S-matrix.

The functional equations of a renormalization group are formulated for theories for dimensional coupling constants. The structure of the general solutions of the equation is determined for an invariant charge. Particular attention is paid to models with a negative mass dimensionality of the coupling constants (i.e., to models which are unrenormalizable in ordinary perturbation theory). The correspondence between the general solutions in the UV region with ordinary perturbation theory leads to nonanalyticity in terms of the coupling constant. An additional assumption that the number of invariant charges is finite leads to limitations on the parameters of the Bogolyubov R operation. The possibility of scale invariance at small distances is discussed. As an illustration of these hypotheses, an exactly solvable unrenormalizable nonrelativistic model is analyzed.

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.

The form of causality used in present-day theory follows from basic space-time concepts. It has been borrowed from macroscopic physics and, in view of the nature of the singularities in the Green's functions, it is carried over automatically to infinitely small scales. This leads to divergencies (infinities) in a number of the more important physical quantities associated with elementary particles. In this paper we have discussed some of the preliminary theoretical schemes which, while retaining macroscopic causality, produce substantial changes in causality for small space-time scales.

It is shown that the nonlocal potential deduced from quantum field theory may be replaced by a local, complex refraction index for large wave numbers.

A brief survey is made of the design of the experimental fast neutron reactor and of its basic experimental and auxiliary equipment. The reactor was designed for physical experimentation with fast neutrons. The core is composed of plutonium rods; the lateral reflector is filled with depleted uranium. Heat is removed from the core by mercury and from the uranium reflector by air. The total rated power of the reactor is 150 kw of which about 100 kw is derived from the core.

The atomic power plant of the USSR Academy of Sciences was set in operation on June 27, 1954. During the time of its operation not a single fuel element has gone out of order. There has been a rupture of an operating channel tube from which no dangerous consequences resulted. The emergency shielding of the reactor proved to be fully adequate. There have been stoppages of primary feeding of the circulating pumps but the emergency shielding fulfilled its purpose.

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 June, 1960, criticality was reached on the fast-neutron pulse reactor constructed at the United Institute of Nuclear Studies.

This paper is concerned with the study of the analytic properties of the scattering amplitude under the assumption that the signal propagates not only inside the light cone but also outside it, however near its surface or its vertex. The conditions of macroscopic causality and spectrality were fulfilled. It is shown that the dispersion relations are violated throughout the energy region. Therefore, a check of these dispersion relations may be of principal importance for the theory.

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).

In March of this year, the Joint Institute for Nuclear Studies, the international scientific organization of the socialist countries, completed five years of existence. On this occasion, the Editorial Board publishes an abridged text of the main report delivered by the Institute's Director Prof. D. I. Blokhintsev to the Committee of Authorized Representatives of the Member Nations in November, 1960.

The present day theory in a formal way permits one particle states which are localized in space with any degree of accuracy. This gives the possibility to formulate conditions of macroscopic causality directly forS-matrix.

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).