Four-body Yakubovsky differential equations for identical particles

The differential equations for Yakubovsky components of the four-body wave functions are derived. An asymptotic form of these components is described. A symmetrized form of the Yakubovsky differential equations for four identical particles is given and its angular analysis is performed. Bound-state calculations are presented for various potentials.     

Investigation of low-energy scattering in the nnpp system on the basis of differential equations for Yakubovsky components in configuration space

The s-wave differential equations for the Yakubovsky components characterizing the nnpp system have been solved by the method of cluster reduction. Two-cluster scattering at energies below the three-particle threshold in the singlet and triplet spin states has been considered. The MT I–III potential model has been used to simulate nucleon-nucleon interaction, and the Coulomb interaction between the protons has been taken into account. The singlet and triplet scattering lengths have been calculated for proton interaction with the triton (³H) and for neutron interaction with the ³He nucleus, and the deuteron-deuteron scattering length has also been determined. The low-energy behavior of the phase shifts and inelasticity factors in the corresponding scattering channels has been investigated. The features of the 0⁺ resonance in the ⁴He nucleus have been determined.     

Solving systems of fractional differential equations by homotopy-perturbation method

In this Letter, approximate analytical solutions of systems of Fractional Differential Equations (FDEs) are derived by the Homotopy-Perturbation Method (HPM). The fractional derivatives are described in the Caputo sense. The solutions are obtained in the form of rapidly convergent infinite series with easily computable terms. Numerical results reveal that HPM is very effective and simple for obtaining approximate solutions of nonlinear systems of FDEs.     

Progress in methods to solve the Faddeev and Yakubovsky differential equations

We shortly recall the derivation of the Faddeev-Yakubovsky differential equations and point out their main advantages. Then we give a review of the numerical approaches used to solve the bound-state and scattering problems for the three- and four-body systems based on these equations. A particular attention is payed to the latest developments.     

Microscopic calculation of low-energy deuteron-deuteron scattering on the basis of the cluster-reduction method

The cluster-reduction method is used to solve numerically the differential equations for the s-wave Yakubovsky components characterizing the nnpp system in the S=2 spin state. Elastic deuteron-deuteron scattering is analyzed for the case where nucleon-nucleon interaction is simulated by the MT I–III potentials. Effective equations describing the relative motion of clusters is derived. The scattering length and phase shifts for low-energy deuteron-deuteron scattering are calculated.     

Solving of problems of electromagnetic waves scattering by complex-shaped dielectric bodies via the pattern equations method

An efficient method is proposed for solving the problem of diffraction on complex-shaped dielectric bodies with the use of their replacement by a group of bodies with more simple form (fragments of complex objects). The initial problem is reduced to a system of algebraic equations by expanding the scattering patterns in vector angular spherical harmonics. It is shown that the method offers a high rate of convergence that weakly depends on the distances between the bodies. Examples of modeling the scattering characteristics of complex-shaped bodies are considered.     

利用转移矩阵方法求解一维散射问题

利用转移矩阵方法,求解粒子通过任意势垒的透射系数及反射系数,并给出粒子的概率密度分布曲线.     

求解微分方程的Hojman方法

首先，将Hojman用于求解二阶微分方程组守恒量的方法推广并应用于一阶微分方程组，特别是奇数维微分方程组的积分问题.然后，证明 Hojman定理是本文定理的特殊情形.最后，举例说明结果的应用. 关键词： 微分方程 Hojman定理 守恒量 积分     

Linear differential equations for the one‐dimensional scattering problem

The transmission and reflection amplitudes of an electron moving in a one dimensional potential of arbitrary form are obtained using the transfer matrix method. It is shown that the one‐dimensional scattering problem, in its most general form, can be reduced to Cauchy problem for a set of two linear differential equations.     

Solving the 3D MHD equilibrium equations in toroidal geometry by Newton’s method

We describe a novel form of Newton’s method for computing 3D MHD equilibria. The method has been implemented as an extension to the hybrid spectral/finite-difference Princeton Iterative Equilibrium Solver (PIES) which normally uses Picard iteration on the full nonlinear MHD equilibrium equations. Computing the Newton functional derivative numerically is not feasible in a code of this type but we are able to do the calculation analytically in magnetic coordinates by considering the response of the plasma’s Pfirsch–Schlüter currents to small changes in the magnetic field. Results demonstrate a significant advantage over Picard iteration in many cases, including simple finite-β stellarator equilibria. The method shows promise in cases that are difficult for Picard iteration, although it is sensitive to resolution and imperfections in the magnetic coordinates, and further work is required to adapt it to the presence of magnetic islands and stochastic regions.     

Multiple scattering effect for quasifree scattering in the 3He(p,pp)2H reaction at 64.8 MeV

For the ³He(p, pp)²H reaction at 64.8 MeV, angular correlations have been measured in the quasifree scattering region. Angular dependence of the ratio of the cross sections measured to those calculated in the plane-wave impulse approximation is well reproduced by a calculation taking account of the double-scattering effect.     

Hamilton--Jacobi method for solving ordinary differential equations

The Hamilton--Jacobi method for solving ordinary differential equations is presented in this paper. A system of ordinary differential equations of first order or second order can be expressed as a Hamilton system under certain conditions. Then the Hamilton--Jacobi method is used in the integration of the Hamilton system and the solution of the original ordinary differential equations can be found. Finally, an example is given to illustrate the application of the result.     

Lagrange--Noether method for solving second-order differential equations

The purpose of this paper is to provide a new method called the Lagrange--Noether method for solving second-order differential equations. The method is, firstly, to write the second-order differential equations completely or partially in the form of Lagrange equations, and secondly, to obtain the integrals of the equations by using the Noether theory of the Lagrange system. An example is given to illustrate the application of the result.     

3He electron scattering sum rules

Electron scattering sum rules for³He are derived with a realistic ground-state wave function. The theoretical results are compared with the experimentally measured integrated cross sections.This work was supported in part by the U.S. National Science foundation. Submitted to the symposium Mesons and Light Nuclei, Liblice, Czechoslovakia, June 1981.     

Analytical approach for the fractional differential equations by using the extended tanh method

In this study, we consider analytical solutions of space–time fractional derivative foam drainage equation, the nonlinear Korteweg–de Vries equation with time and space-fractional derivatives and time-fractional reaction–diffusion equation by using the extended tanh method. The fractional derivatives are defined in the modified Riemann–Liouville context. As a result, various exact analytical solutions consisting of trigonometric function solutions, kink-shaped soliton solutions and new exact solitary wave solutions are obtained.     

Non-energy weighted electron scattering sum rules for 3He

Electron scattering sum rules for ³He are derived with a realistic ground-state wave function. The theoretical results are compared with the experimentally measured integrated cross sections.     

Microscopic spin-orbit potentials for polarized 3He elastic scattering

The M3Y double folding model is used to calculate real central and spin-orbit potentials for ³He elastic scattering. These potentials are used to fit cross sections and analysing powers at 33 MeV for targets ranging from ¹⁶O to ⁵⁸Ni. The real central potential needs a normalization factor of about 0.85, but no change in the strength of the spin-orbit potential is necessary. Comparison is made with phenomenological and other microscopic studies of ³He elastic scattering.     

Unitarity and the inhomogeneous equations method for identical particle scattering

A K-matrix solution to the coupled, inhomogeneous equations describing the scattering of a particle by a system of identical particles is developed. It is shown that K is a sum of two terms, one arising from the homogeneous solution and one from the particular integral. The former is a direct contribution, i.e., with no exchange, while the latter is a pure exchange contribution. Thus, as in the previously studied case of the T matrix arising from this system of equations, the direct and exchange portions of K are additive, and can be computed separately. A unitary S matrix is obtained from K in the usual way: S = (1 + iK)(1 − iK)⁻¹. The problem of how to calculate K when an apparent two-channel problem is actually a two-particle problem with the channels referring to the identical particle labels is also solved.     

Solving the atmospheric scattering optical transfer function using the multi-coupled single scattering method

The atmospheric scattering optical transfer function （OTF） is solved by applying the multi-coupled single scattering （MCSS） method to the three-dimensional radiative transfer equation （RTE） under the periodic ground condition. This approach is a direct hit to the atmospheric scattering OTF using the same original context of modulation transfer function （MTF） measurement, i.e., images of sinusoidal grating at different spatial frequencies. Both the amplitude and phase shift of the OTF at various zenith and azimuth angles can be obtained at an arbitrary spatial frequency.