Amplitudes of multichannel scattering on a two-dimensional potential barrier with constant height

The immersing method is applied to solve the N-channel scattering problem for concrete potential. In particular, we consider the particle scattering on a two-dimensional potential barrier, which is constant in the scattering direction and arbitrary in the cross-section direction. For this case the scattering amplitudes t _m and r _m (1,2, m= ...,N) are determined. A transition from the obtained formulas to the case of ?-potential is performed. For this case transmission amplitudes t _m and reflection amplitudes r _m are obtained. It is also shown that the product of transmission and reflection amplitudes along the channel m does not depend on the scattering channel.     

Amplitudes of two-channel scattering by a two-dimensional potential barrier with a constant height

The immersing method is used to solve the two-channel scattering problem in the case of concrete potential. In particular, we consider the particle scattering by a two-dimensional barrier which is constant in the scattering direction and is arbitrary in the transverse direction. For this case the scattering amplitudes t ₁, t ₂, r ₁, and r ₂ are determined. Expressions for the transmission and reflection amplitudes are obtained for the case of δ-potential. The behavior of the scattering amplitudes in the limit k ₂ → 0 is studied. It is also shown that the ratio of products of transmission and reflection amplitudes for two channels does not depend on the coordinate of the middle of coordinate.     

Multichannel scattering of a particle in a quantum wire of cylindrical symmetry

The Schrödinger equation for a scattering particle in a quantum wire is considered. We discuss two geometrical forms of cross-section of the wire: the rectangular section and the cylindrical one. It is shown that scattering of the particle on an arbitrary potential V = V (x, y, z,), given in the wire, can be considered as a multichannel scattering, where the index of the channel coincides with the index which determines energy levels of the confined transverse motion of the particle. A method for determination of the amplitudes of transmission T _i and reflection R _i in the case of multichannel scattering is proposed. The case of two-channel scattering is considered in detail and a method for determination of the scattering amplitudes T ₁, T ₂ and R ₁, R ₂ is proposed.     

Change in the shape of a symmetric light pulse passing through a quantum well

A theory for the response of a 2D two-level system to irradiation by a symmetric light pulse is developed. Under certain conditions, such an electron system approximates an ideal solitary quantum well in a zero field or a strong magnetic field H perpendicular to the plane of the well. One of the energy levels is the ground state of the system, while the other is a discrete excited state with energy ?ω₀, which may be an exciton level for H=0 or any level in a strong magnetic field. It is assumed that the effect of other energy levels and the interaction of light with the lattice can be ignored. General formulas are derived for the time dependence of the dimensionless “coefficients” of the reflection ?(t), absorption A(t), and transmission ?(t) for a symmetric light pulse. It is shown that the ?(t), A(t), and ?(t) time dependences have singular points of three types. At points t ₀ of the first type, A(t ₀)=T(t ₀)=0 and total reflection takes place. It is shown that for γ_r?γ, where γ_r and γ are the radiative and nonradiative reciprocal lifetimes, respectively, for the upper energy level of the two-level system, the amplitude and shape of the transmitted pulse can change significantly under the resonance ω_l=ω₀. In the case of a long pulse, when γ_l<γ_r, the pulse is reflected almost completely. (The quantity γ_l characterizes the duration of the exciting pulse.) In the case of an intermediate pulse duration γ_l?γ_r, the reflection, absorption, and transmission are comparable in value and the shape of the transmitted pulse differs considerably from the shape of the exciting pulse: the transmitted pulse has two peaks due to the existence of the point t ₀ of total reflection, at which the transmission is zero. If the carrier frequency ω_l of light differs from the resonance frequency ω₀, the oscillating ?(t), A(t), and ?(t) time dependences are observed at the frequency Δω=ωl?ω₀. Oscillations can be observed most conveniently for Δω?γ_l. The position of the singular points of total absorption, reflection, and transparency is studied for the case when ω_l differs from the resonance frequency.     

Transfer-matrix for the two-channel scattering problem

The transfer-matrix for the two-channel scattering problem is obtained. The elements of this matrix are expressed in terms of transmission T ₁, T ₂ and reflection R ₁, R ₂ amplitudes. The transfer-matrix for N localized and nonoverlapping scattering centers is presented. Recurrent equations for matrix elements are derived and initial conditions for them are defined.     

Immersing method for the multichannel scattering problem

We propose a method for solution of the multichannel scattering problem. In particular, the scattering problem is considered when a particle makes a finite motion in the transverse direction of the scattering. In this case the scattering becomes multichannel, which is connected with the presence of discrete energy levels of the transverse movement of the particle. For the case of two-channel scattering, the problem is formulated up to the end. A method for determination of scattering amplitudes for the potential V=V(x,y) is proposed.     

Summation of partial waves for large-angle scattering

For large-angle elastic scattering different methods of summing partial wave amplitudes are investigated for their accuracy and simplicity of computation. It is found that among the approximations considered, the method of expanding the T-matrix in terms of the weighted orthogonal polynomials proposed by Brysk is the most accurate way of calculating the scattering amplitude in the backward direction. If the two-particle interaction is assumed to be a Yukawa potential, then the lth partial sum of the T-matrix with the weighted polynomials can be expressed as the lth partial sum with the Legendre polynomials and a correction term which depends on the phase shift for the lth partial wave.     

Finite energy sum rules for π-N backward scattering

Finite energy sum rules for the A and S,π-N scattering amplitudes are saturated in the region ?0.4 GeV²< u <0 with a number of s andt channel resonances. It turns out that one needs a rather large π—π s wave contribution, to get agreement with the high energy Regge pole analysis, which explains the dip structure in π⁺p scattering atu ₀=?0.15 GeV² by a zero in theN _α contribution. The coupling of theN _α trajectory seems to be much stronger than the coupling of theN _γ andΔ _δ trajectories.     

Transfer-matrix for the multichannel scattering problem

A transfer-matrix for the multichannel scattering problem is obtained. The elements of this matrix are expressed in terms of transmission and reflection amplitudes. On the basis of the matrix for a system of N localized and nonoverlapped scattering centers the recurrent equations for the transfermatrix elements are derived and the initial conditions are defined.     

Correlation between the properties of the deuteron and the low-energy triplet parameters of neutron-proton scattering

The correlation between the asymptotic normalization constant for the deuteron, A_S, and the neutron-proton scattering length for the triplet case, a_t, is investigated. It is found that 99.7% of the asymptotic constant A_S is determined by the scattering length a_t. It is shown that the linear correlation between the quantities A _S ^?2 and 1/a_t provides a good test of correctness of various models of nucleon-nucleon interaction. It is revealed that, for the normalization constant A_S and for the root-mean-square deuteron radius r_d, the results obtained with the experimental value recommended at present for the triplet scattering length a_t are exaggerated with respect to their experimental counterparts. By using the latest experimental data obtained for phase shifts by the group headed by Arndt, it proved to be possible to derive, for the low-energy parameters of scattering (a_t, r_t, P_t) and for the properties of the deuteron (A_S, r_d) results that comply well with experimental data.     

N-point functions and low-energy scattering by N centres

The scattering of a low-energy particle by a potential of a small range is known to be described satisfactorily by the s-wave alone. In the present paper we give a method of describing low-energy scattering by N potentials with the aid of N waves. For this purpose, a special system of Laplacian eigenfunctions is suggested. The scattering amplitude depends on only N parameters, irrespective of overlapping of potentials. The physical significance of these parameters δ_λ, λ=1,2,…N, is shown by exp (2iδ_λ)=S_λ where S_λ is the eigenvalue of the S matrix. The parameters δ_λ may be obtained by direct methods and perturbation theory.The low-energy scattering by an arbitrary configuration of N centres is discussed. The differential cross-section is averaged over all orientations of the configuration and radially about the direct beam, giving it as a function of the scattering angle. This formula may be used for the phase shift analysis.     

The infrared structure of the quark-antiquark scattering kernel in quantumchromodynamics: A clue to the nature of the quark binding potential?

The equal rate, near-mass-shell behavior of the two particle irreducible, spin-independent, color singlet channel quark-antiquark (qq?) scattering kernel is studied to all orders in perturbation theory. A general functional form in terms of the long-distance Yang-Mills invariant charge g(t),t→0, t being the momentum transfer, is determined. Under certain conditions, the behavior of the Bethe-Salpeter iteration of this kernel in the qq? threshold regime suggests the existence of a universal qq? effective potential of the form g²_eff[g(t)]/t.     

Low momentum transfer theorem for two photon exchange in lepton hadron scattering

The two photon exchange contribution to lepton-hadron scattering is considered. Under the assumptions of Lorentz covariance, gauge invariance, unitarity and analyticity, we prove a low momentum transfer theorem for the relevant amplitudes. Fixed energy dispersion relations tell us that their nonanalytic part, in the neighbourhood of t = 0, is given by the contribution of the two photon cut in the t-channel. The t-channel absorptive parts are obtained from unitarity. Their calculation has as input the two amplitudes corresponding to Compton scattering on the hadron with a pole contribution, and the continuum controlled at low t by the electromagnetic polarizabilities. By means of the dispersion integral, one proves the expansion $\text{k}{}_1\text{(s)+k}{}_2\text{(s)}\text{?t}\text{+k}{}_3\text{(s)t}\text{log}\text{(?t)+O(t)}$ for the continuum contribution, where k₁(s) is the only unknown. Explicit expressions are obtained for the pole contribution as M → ∞, where M is the hadron mass, and for the continuum when (?t) <Λ and (?t) < 4m², where m is the muon mass and Λ is a characteristic parameter of the hadron structure.     

Connection between the immersing and transfer-matrix methods in one-dimensional scattering problems

We show that application of the immersing and transfer-matrix methods to one-dimensional problems of particles scattering leads to the system of two linear equations for the functions F and Φ expressed by means of the transmission and reflection amplitudes. The expressions of these functions are derived. The offered method is illustrated by the finding of transmission and reflection coefficients for the potential barrier with a constant height. The developed method can be applied in solving the quasi-one-dimensional and two-dimensional problems of scattering.     

Antiproton-nucleus scattering with self-consistent model for medium corrections

The antiproton-nucleon t-matrix with propagation in the nuclear medium is calculated selfconsistently and applied to the construction of optical potentials for the elastic scattering of antiprotons from nuclei. We find that this treatment gives results that are sensitive to medium corrections even though the strong absorption acts to mask these corrections partially. The agreement with scattering experiments at 46.8 MeV on ¹²C is very good. We compare potentials containing medium corrections to those based on free $\text{p}\text{N}$ amplitudes for ¹²C and ⁴⁰Ca. The local approximation to the optical potential is found attractive at low energies, becoming shallower with increasing bombardment energy in the range considered here (up to about E_L = 120 MeV).     

Neutron transport in ultradisperse copper layers under strong scattering conditions

The character of neutron transport in ultradisperse copper near the total reflection boundary is studied. The dependence of the ultracold neutron transmission on the thickness of a nonuniform layer under the strong scattering condition kl≤10 (k is the wave vector and l is the mean free path) is obtained for the first time.     

Light-light scattering in vector electrodynamics

Expressions for scattering amplitudes with definite polarizations in the approximation ω² ? m² are found. The asymptotic γγ→γγ total cross section is evaluated for the scattering of unpolarized photons. Also the forward scattering amplitudes and the differential cross section for forward scattering are obtained.     

New determination of the neutron-proton scattering amplitude and precise measurements of the scattering amplitudes on carbon,chlorine, fluorine and bromine

After an improvement on the theory of the neutron-gravity-refractometer and after refinements of the experimental procedure we have performed new measurements of the absolute value of the neutron-proton scattering amplitude at low neutron energies. In order to obtain and to confirm a very high accuracy we carried out neutron-reflection experiments on 18 various liquids of 11 different organic substances containing the elements carbon, hydrogen and/or chlorine. Compounds with fluorine and bromine were used to measure the scattering amplitudes of these elements. We found the coherent scattering amplitudes of the bound atoms to be:a _H=?3.7409(1l)fm,a _c=6.6484(13)fm,a _c1=9.5792(8)fm,a _F=5.66(2)fm anda _Br=6.79(2)fm. The low energy (n, p)-parametersa _t anda _s were calculated with the presenta _H and a new value of the (n, p) scattering cross-sectionσ ₀. By comparing the measureda _C with values obtained from precise transmission experiments we could determine the gravitational accelerationg _f of the free neutron in terms of the local value g. We found the two values to be equal:g _f =0.9996(7)g.     

On-shell T-matrices in multiple scattering

The transition operator T for the scattering of a particle from N potentials V_j(x) can be expanded into a series featuring the transition operators t_j associated with the individual potentials. For V_j(x) both absolutely and square integrable in x, we show, using an analytic continuation argument, that if T is on-shell, i.e. in 〈k|T(k₀²±i0)|k′〉, |k| = |k′| = k₀, then each t_j is also on-shell.