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We establish semiclassical resolvent estimates for Schrödinger operators with long-range matrix-valued potentials. As an application, we prove a resonance-free domain in trapping situations. These results generalize the well-known results of [4] [N. Burq, Lower bounds for shape resonances widths of long range Schrödinger operators, Amer. J. Math. 124(4) (2002) 677–735] in the case of scalar Schrödinger operators. In addition, we give an estimate on the scattering amplitude for Schrödinger operators with compactly supported matrix-valued potentials. [ABSTRACT FROM AUTHOR]

Rayleigh scattering from a spherical object located near a planar rigid boundary at distances smaller than the wavelength is calculated. Low frequency analysis reduces a scattering problem to a sequence of potential problems. An analytical solution based on expansion in spherical solid harmonics and the use of addition theorem is presented. Analytical perturbation approach is validated by comparison with numerical calculations. The velocity of the center of the particle and the scattering amplitude are determined. In the lowest order in wavenumber, the scattering amplitude is expressed in terms of the monopole and dipole components. In contrast to the behavior of a bubble, under the same conditions, dipole oscillations of the particle in the direction normal to the boundary are not excited and the monopole component of the scattering amplitude does not depend on the location of the particle relative to the boundary. [ABSTRACT FROM AUTHOR]

Features of Rayleigh scattering by a solid particle at a small distance compared to the wavelength from an impenetrable plane boundary are revealed. The choice of the Green's function in the integral representation of the Helmholtz equation makes it possible to reduce integration only over the particle surface and eliminate the contribution of the interface surface. When expanding over a small wave parameter, a well-known approach is used, making it possible to represent the solution of a given order as the sum of a potential function and a component expressed in terms of lower-order approximations. The potential component is found, expressed in terms of solid irregular harmonics centered on the particle and its mirror image. The vibrational velocity of the center of a particle and the scattering amplitude are determined. In the lowest order of the wavenumber, the scattering amplitude is expressed in terms of the monopole and dipole components. [ABSTRACT FROM AUTHOR]

We propose a novel method to determine the structure of symbols for any family of polylogarithmic Feynman integrals. Using the d log-bases and simple formulas for the leading order and next-to-leading contributions to the intersection numbers, we give a streamlined procedure to compute the entries in the coefficient matrices of canonical differential equations, including the symbol letters and the rational coefficients. We also provide a selection rule to decide whether a given matrix element must be zero. The symbol letters are deeply related to the poles of the integrands and also have interesting connections to the geometry of Newton polytopes. Our method can be applied to many cutting-edge multi-loop calculations. The simplicity of our results also hints at the possible underlying structure in perturbative quantum field theories. [ABSTRACT FROM AUTHOR]

The spherical and parabolic wave functions are calculated for the generalized MIC–Kepler system in the continuous spectrum. It is shown that the coefficients of the parabola–sphere and sphere–parabola expansion are expressed in terms of the generalized hypergeometric function . The quantum mechanical problem of scattering in the generalized MIC–Kepler system is solved. [ABSTRACT FROM AUTHOR]

The paper presents the multipole expansion for the electron-nucleus scattering cross section at high energies within the framework of the unified electroweak theory. The electroweak currents of the nucleus are expanded into the simple components with definite angular momenta, called the multipole form factors. The multipole expansion of the cross section is a consequence of the above expansion. Besides the familiar electromagnetic form factors, there are also the vector and axial form factors, respectively, related to weak interactions. To determine multipole form factors, general formulas for the calculation of reduced matrix elements are established using the fractional parentage coefficient method and the multiparticle shell model. Calculation of them enables us to obtain more detailed information about the nuclear structure and elucidate the role played by the weak interaction in the high-energy reaction mechanisms.

It is known that the Real Extended Bialas–Bzdak (ReBB) model describes the proton–proton ( p p ) and proton–antiproton ( p p ¯ ) differential cross-section data in a statistically non-excludible way, i.e., with a confidence level greater than or equal to 0.1% in the center of mass energy range 546 GeV ≤ s ≤ 8 TeV and in the squared four-momentum transfer range 0.37 GeV2 ≤ −t ≤ 1.2 GeV2. Considering, instead of Gaussian, a more general Lévy α -stable shape for the parton distributions of the constituent quark and diquark inside the proton and for the relative separation between them, a generalized description of data is obtained, where the ReBB model corresponds to the α = 2 special case. Extending the model to α < 2 , we conjecture that the validity of the model can be extended to a wider kinematic range, in particular, to lower values of the four-momentum transfer − t . We present the formal Lévy α -stable generalization of the Bialas–Bzdak model and show that a simplified version of this model can be successfully fitted, with α < 2 , to the non-exponential, low − t differential cross-section data of elastic proton–proton scattering at s = 8 TeV. [ABSTRACT FROM AUTHOR]

Using the ambitwistor string theory, we study graviton scattering amplitudes in a light-like linear dilaton background of 10-dimensional supergravity. At the tree level, we find that the three-graviton amplitude coincides with the type-II superstring theory, and the four-graviton or more amplitudes differ from the superstring theory but satisfy the scattering equations. Due to a modified momentum conservation law different at each order in genus expansion, a nonzero amplitude is determined solely from the particular order in perturbation theory without further corrections. [ABSTRACT FROM AUTHOR]

In this research, the chiral perturbation theory and the mechanism of three-body forces, which are of great importance, are employed through simulations to investigate the chain interaction. In the following, important parameters such as scattering amplitude ratio, decay rate, and scattering cross section of this decay have been calculated. Due to the fact that in nuclear processes, accuracy up to the next to leading order (NLO) can reduce the error rate to a high extent, the calculations performed in this research have been done up to (NLO). The obtained results are highly consistent with the experimental results.

Based on the work of Fu et al. (2020), we derive the rest seven scattering‐state solutions to the Dirac equation when E=−im$$ E=- im $$ and establish a relation between differential scattering cross‐section, σi*(p,θ,φ)$$ {\sigma}_{i\ast}\left(p,\theta, \varphi \right) $$, and stellar matter density, μ$$ \mu $$, using the long‐wave approximation. It is found that the sensitivity of average scattering cross‐sections σ‾i(p,θ)$$ {\overline{\sigma}}_i\left(p,\theta \right) $$ to the change in the stellar matter density is proportional to μ2$$ {\mu}^2 $$. We find that the average scattering amplitudes f‾i(p,θ)$$ {\overline{f}}_i\left(p,\theta \right) $$, as well as average scattering cross‐sections σ‾i(p,θ)$$ {\overline{\sigma}}_i\left(p,\theta \right) $$, are independent of the masses of particles, m$$ m $$, for four scattering states χ(i)$$ {\chi}^{(i)} $$, i = 0, 1, 2 and 3, while f‾i(p,θ)$$ {\overline{f}}_i\left(p,\theta \right) $$ and σ‾i*(p,θ)$$ {\overline{\sigma}}_{i\ast}\left(p,\theta \right) $$ depend on m$$ m $$, for the rest four scattering states, ϕ(i)$$ {\phi}^{(i)} $$, i = 0, 1, 2 and 3. By measuring the scattering cross‐section, we can determine the density of the ellipsoid and obtain its gravitational properties. This work will be useful in understanding the properties of anti‐Dirac spinors and the physical effects in a rotating spheroid. [ABSTRACT FROM AUTHOR]

We measured a set of π±Σ∓, π0Σ0, and π−Σ0 invariant mass spectra below and above the K¯N mass threshold in K−-induced reactions on deuteron. The measured πΣ mass spectral shape is well reproduced via the two-step mechanism, i.e., a neutron knocked out at a forward angle from a deuteron by an incident K−, with the K¯ recoiled backward reacting with the residual nucleon to produce π and Σ. We deduced the S-wave K¯N→πΣ and K¯N→K¯N scattering amplitudes in the isospin 0 channel in the framework of a K¯N and πΣ coupled channel. We find that a resonance pole corresponding to Λ(1405) is located at 1417.7−7.4+6.0 (fitting errors)−1.0+1.1 (systematic errors) + [−26.1−7.9+6.0 (fitting errors)−2.0+1.7 (systematic errors)] i MeV/c2, closer to the K¯N mass threshold than the value determined by the Particle Data Group.

The post-Minkowskian expansion of Einstein's general theory of relativity has received much attention in recent years due to the possibility of harnessing the computational power of modern amplitude calculations in such a classical context. In this brief review, we focus on the post-Minkowskian expansion as applied to the two-body problem in general relativity without spin, and we describe how relativistic quantum field theory can be used to greatly simplify analytical calculations based on the Einstein–Hilbert action. Subtleties related to the extraction of classical physics from such quantum mechanical calculations highlight the care which must be taken when both positive and negative powers of Planck's constant are at play. In the process of obtaining classical results in both Einstein gravity and supergravity, one learns new aspects of quantum field theory that are obscured when using units in which Planck's constant is set to unity. The scattering amplitude approach provides a self-contained framework for deriving the two-body scattering valid in all regimes of energy. There is hope that the full impact of amplitude computations in this field may significantly alter the way in which gravitational wave predictions will advance in the coming years. [ABSTRACT FROM AUTHOR]

It is known that the Real Extended Bialas–Bzdak (ReBB) model describes the proton–proton (pp) and proton–antiproton (pp¯) differential cross-section data in a statistically non-excludible way, i.e., with a confidence level greater than or equal to 0.1% in the center of mass energy range 546 GeV ≤s≤8 TeV and in the squared four-momentum transfer range 0.37 GeV2 ≤ −t ≤ 1.2 GeV2. Considering, instead of Gaussian, a more general Lévy α-stable shape for the parton distributions of the constituent quark and diquark inside the proton and for the relative separation between them, a generalized description of data is obtained, where the ReBB model corresponds to the α=2 special case. Extending the model to α<2, we conjecture that the validity of the model can be extended to a wider kinematic range, in particular, to lower values of the four-momentum transfer −t. We present the formal Lévy α-stable generalization of the Bialas–Bzdak model and show that a simplified version of this model can be successfully fitted, with α<2, to the non-exponential, low −t differential cross-section data of elastic proton–proton scattering at s=8 TeV.

In this paper, we propose a Regge-pole model with a Gaussian potential to study hadron scattering at high energies. In the diffraction approximation, considering the consequences of the analyticity and unitarity of the scattering amplitude, expressions are obtained for the matrix of the scattering amplitude, the cross section, and the slope of the diffraction cone for reactions a + A → B + b. The resulting expressions are applied to p-p scattering. The results obtained show that the model describes well the slope coefficient of the diffraction cone at energies below 102 GeV. To obtain agreement with the experiment at high energies, the parameters should be adjusted. [ABSTRACT FROM AUTHOR]

We describe a more rigorous formulation of the 3D semiclassical approach, corresponding to deformed potentials, which leads to the exact results and we also compare them with the much simpler expressions given by the angular Wentzel–Krames–Brillouin (WKB) and linearized WKB with its approximation, known as Fröman WKB method. We define the semiclassical fundamental matrix of solutions, describing the effect of the deformed field. Its inverse, proportional to the so-called propagator matrix, connects the solution in two points. A comparison between the coupled channels fundamental matrix of solutions to various semiclassical counterparts evidences close results in the barrier region. We express the scattering amplitudes in terms of the propagator matrix multiplied by the ratio between internal wave function components and irregular Coulomb waves. The relative influence of nuclear and Coulomb action terms together with nuclear and Coulomb centrifugal barriers upon the penetration process reveals the dominance of the Coulombian parts. An analysis of alpha-emission processes between ground states and to excited states of even–even nuclei in terms of the propagator matrix evidenced the important role played by deformation of the Coulomb field and the shape of the nuclear interaction. [ABSTRACT FROM AUTHOR]

Dark energy and dark matter are two of the biggest mysteries of modern cosmology, and our understanding of their fundamental nature is incomplete. Many parametrizations of couplings between the two in the continuity equation have been studied in the literature, and observational data from the growth of perturbations can constrain these parametrizations. Assuming standard general relativity with a simple Yukawa-type coupling between dark energy and dark matter fields in the Lagrangian, we use the Boltzmann equation to analytically express and calculate the interaction kernel Q in the continuity equation and compare it to that of a typical parametrization. We arrive at a comparably very small result, as expected. Since the interaction is a function of the dark matter mass, other observational data sets can be used to constrain the mass. This calculation can be modified to account for other couplings of the dark energy and dark matter fields. This calculation required obtaining a distribution function for dark energy that leads to an equation of state parameter that is negative, which neither Bose–Einstein nor Fermi–Dirac statistics can supply, and this is the main result of this paper. Treating dark energy as a quantum scalar field, we use adiabatic subtraction to obtain a finite analytic approximation for its distribution function that assumes the FLRW metric and nothing more. [ABSTRACT FROM AUTHOR]

We comment on phase selection of the scattering amplitude, emphasizing that the elastic overlap function should have a central impact parameter profile at high energies and highlighting the role of the reflective scattering mode at the LHC energies. Emerging problems with the use of peripheral impact parameter dependence of the elastic overlap function are explicitly indicated. Their solution is an elimination of the phases connected to peripheral form of the elastic overlap function. Contrary, we adhere to a relative peripheral form of the inelastic overlap function with an additional new feature of a maximum at nonzero value of the impact parameter at the highest energies. Phenomenologically, the dynamics of hadron scattering is motivated by a hadron structure with a hard central core presence.

We consider the fixed angle inverse scattering problem and show that a compactly supported potential is uniquely determined by its scattering amplitude for two opposite fixed angles. We also show that almost symmetric or horizontally controlled potentials are uniquely determined by their fixed angle scattering data. This is done by establishing an equivalence between the frequency domain and the time domain formulations of the problem, and by solving the time domain problem by extending the methods of [Rakesh and M. Salo, Inverse Problems, 36 (2020), 035005] which adapts the ideas introduced in [A. Bukhgeim and M. Klibanov, Soviet Math. Dokl., 24 (1981), pp. 244-247] and [O. Imanuvilov and M. Yamamoto, Comm. Partial Differential Equations, 26 (2001), pp. 1409-1425] on the use of Carleman estimates for inverse problems. [ABSTRACT FROM AUTHOR]

We study explicit formulas for phaseless inverse scattering in the Born approximation at high energies for the Schrödinger equation with compactly supported potential in dimension d ≥ 2 . We obtain error estimates for these formulas in the configuration space. [ABSTRACT FROM AUTHOR]

A polynomial basis for parity-even three-point amplitudes of higher-spin massless fermions and bosons are derived in four-dimensional space–time from first principles. This basis can be used to construct three-point amplitudes of polarizations of any rank. The results are presented using polarization tensors and tensor-spinors, which is convenient when they are applied to Lagrangian construction. [ABSTRACT FROM AUTHOR]

Formula for the size of the scatterer is derived explicitly in terms of the scattering amplitude corresponding to this scatterer. By the scatterer either a bounded obstacle D or the support of the compactly supported potential is meant. [ABSTRACT FROM AUTHOR]

We discuss possible modes of the asymptotic behavior of hadron scattering amplitudes in QCD. We show that the triviality condition for the scattering matrix with the interaction of the fundamental fields turned off leads to the impossibility of cross sections nondecreasing with energy in the case of pure gluodynamics. We also show that this ban is lifted in the presence of at least one type of massive quark. We also discuss some consequences of the presence of an infrared fixed point. [ABSTRACT FROM AUTHOR]

Abstract The process of scattering of fast charged particles in thin crystals is considered in the transitional range of thicknesses, between those at which the channeling phenomenon is not developed and those at which it is realized. We demonstrate the possibility of application of the methods of geometrical optics for description of the scattering process. In particular, we study the dependence of the total scattering cross-section of ultrarelativistic positrons on target thickness in this range of crystal thicknesses. In the case of channeling of ultrarelativistic particles we indicate the possibility of the existence of an effect analogical to the Ramsauer-Townsend effect of conversion into zero of the total scattering cross-section at some values of crystal thickness. An important role is noted of the Morse-Maslov index that makes part of the wave function expression in the geometrical optics method. [ABSTRACT FROM AUTHOR]

The elastic proton scattering cross section depending on the impact parameter b is discussed. Using the Gaussian quasipotential in the diffraction approximation and conclusions following from analyticity and unitarity of the scattering amplitude, the equation for the matrix of the scattering amplitude and the formula for the scattering cross section have been obtained. A relationship between analytical properties of the scattering amplitude characterizing momentum transfer and of the impact parameter is studied. The ratio of the real component of the forward scattering amplitude to its imaginary component is also discussed as a function of the momentum t. [ABSTRACT FROM AUTHOR]

The paper presents the multipole expansion for the electron-nucleus scattering cross section at high energies within the framework of the unified electroweak theory. The electroweak currents of the nucleus are expanded into the simple components with definite angular momenta, called the multipole form factors. The multipole expansion of the cross section is a consequence of the above expansion. Besides the familiar electromagnetic form factors, there are also the vector and axial form factors, respectively, related to weak interactions. To determine multipole form factors, general formulas for the calculation of reduced matrix elements are established using the fractional parentage coefficient method and the multiparticle shell model. Calculation of them enables us to obtain more detailed information about the nuclear structure and elucidate the role played by the weak interaction in the high-energy reaction mechanisms. [ABSTRACT FROM AUTHOR]

In the present work the first and second order scattering amplitudes and the related phase were calculated in the charge transfer channel. The positronium formation, with the impact of molecular hydrogen ion, has been carried out using multiple channel scattering formulation and transition matrix. The calculation of differential cross section has been done by varying the scattering angle from 0 to 180 in the fixed orientation of the molecule. In the next calculation the scattering angles were fixed while the spatial molecular orientation was varied. At last the calculated differential cross section was compared with available results in the literature. The scattering angle spanned from 0 to 180 degrees in the second order nuclear and electronic terms were calculated while the molecular orientation was assumed to be fixed. Otherwise, the scattering angles were fixed in the calculation of the corresponding amplitudes while the orientation was varied. At last our calculations were compared with available results