Sensitivity of the electronic-interaction parameters used in molecular calculations to correlation effects

The correlation corrections to the one-center Coulomb integrals are calculated for the⁵S(1s²2s2p³) state of carbon, the⁴P(1s²2s2p⁴) state of nitrogen and the³P(1s²2s²2p⁴) state of oxygen. The calculated results are compared with semiempirical values. A satisfactory agreement is found for all three atoms.Translated from Izvestiya VUZ. Fizika, No. 3, pp. 119–122, March, 1970In conclusion the author thanks his colleagues in the Theoretical Physics Laboratory and the Optics and Spectroscopy Laboratory, Siberian Physicotechnical Institute, for many fruitful discussions of these topics.     

Variational calculations on the three-body scattering problem

An extended resonating-group method is used to calculate the elastic scattering amplitudes (up to L = 2 for a system of three identical bosons interacting through local Yukawa potentials. The results are compared to approximate solutions of the Faddeev equations.     

Continuum-discretized coupled-channels calculations for three-body models of deuteron-nucleus reactions

The formalism and results of truncated coupled channels evaluations of three-body models of deutron-induced nuclear reactions are reviewed. Emphasis is placed on breakup, elastic scattering and stripping. The relations of the coupled channels method to the Faddeev method, the adiabatic approximation and the distorted wave Born approximation are discussed extensively. Although the adiabatic approximation is seen to be excellent for the wavefunction in the elastic channel, it significantly underestimates the contributions of breakup states in stripping. Significant effects are associated with coupling to relative l = 2 breakup states.     

Helium trimer calculations with a public quantum three-body code

We present an illustration of using a quantumthree-body code being prepared for public release. The code is based on iterative solving of the three-dimensional Faddeev equations. The code is easy to use and allows users to perform highly-accurate calculations of quantum three-body systems. The previously known results for He₃ ground state are well reproduced by the code.     

Bound-state calculations of the three-dimensional Yakubovsky equations with the inclusion of three-body forces

The four-body Yakubovsky equations in a three-dimensional approach with the inclusion of the three-body forces are proposed. The four-body bound state with two- and three-body interactions is formulated in the three-dimensional approach for identical particles as a function of vector Jacobi momenta, specifically, the magnitudes of the momenta and the angles between them. The modified three-dimensional Yakubovsky integral equations are successfully solved with the scalar two-meson exchange three-body force, where the Malfliet-Tjon-type two-body force is implemented. The three-body force effects on the energy eigenvalue and the four-body wave function, as well as accuracy of our numerical calculations are presented.     

Water pair and three-body potential of spectroscopic quality from Ab initio calculations

We present the first pair plus three-body potential of water from ab initio calculations that quantitatively reproduces the experimental far-infrared spectra of the water dimer and trimer. The dimer spectrum was obtained from the pair potential through rigorous six-dimensional quantum calculations of the vibration-rotation-tunneling levels. The three-body interactions, together with the pair potential, produce an accurate representation of the hydrogen bond torsional levels of the water trimer.     

Ab initio shell model calculations with three-body effective interactions for p-shell nuclei

We present a qualitative improvement of the ab initio no-core shell model (NCSM) approach by implementing three-body interaction capability for p-shell nuclei. We report the first calculations using three-body effective interactions derived from realistic nucleon-nucleon potentials for 6Li, 8Be, and 10B and demonstrate that the use of three-body effective interactions speeds up the convergence of the NCSM approach. For 10B, we predict JpiT = 1(+)0 ground state, contrary to the experimental observation of 3(+)0, when the AV8(') potential is used, indicating the need for true three-body forces.     

Choreographic solution to the general-relativistic three-body problem

We reexamine the three-body problem in the framework of general relativity. The Newtonian N-body problem admits choreographic solutions, where a solution is called choreographic if every massive particle moves periodically in a single closed orbit. One is a stable figure-eight orbit for a three-body system, which was found first by Moore (1993) and rediscovered with its existence proof by Chenciner and Montgomery (2000). In general relativity, however, the periastron shift prohibits a binary system from orbiting in a single closed curve. Therefore, it is unclear whether general-relativistic effects admit choreography such as the figure eight. We examine general-relativistic corrections to initial conditions so that an orbit for a three-body system can be choreographic and a figure eight. This illustration suggests that the general-relativistic N-body problem also may admit a certain class of choreographic solutions.     

Semiclassical approach to the three-body muon-transfer collisions

Muon-transfer rates in collisions of hydrogen-like atoms or with light nuclei t, ³He, ⁴He, ⁶Li or ⁷Li, are calculated in a semiclassical approximation to the Faddeev-Hahn equations. The two nuclei involved are treated classically, while the motion of the muon in their Coulomb field is considered from the quantum mechanical point of view. The experimentally observed strong dependence on the charge of the nuclei is reproduced. Received: 1st November 1997 / Revised: 26 March 1998 / Accepted: 18 August 1998     

J-matrix method for calculations of three-body Coulomb wave functions and cross sections of physical processes

The review is devoted to a widely known method of numerical solution to the three-body Coulomb problem, namely, the J-matrix method. Special attention is paid to ways of solving the Lippmann-Schwinger integral equation without attraction of pseudostates. Difficulties related to the formulation of the integral equation in spherical coordinates, leading to the divergence of its integral part if the wave function is calculated with two asymptotically free electrons, are demonstrated. In addition, the relation between exact and approximate solutions turns out to be unclear if the matrix of a residual potential is restricted to a finite number of basis functions, with the latter being increased. It is shown that, in principle, these problems can be avoided by reformulating a problem in parabolic coordinates.     

Approach to studying three-body processes

An approach to studying three-body reactions that takes consistently into account the single-collision mechanism is discussed. Specific calculations are performed for elastic and quasielastic nucleon scattering by a deuteron. The ability of the proposed simple approach to account for a wide range of experimental data suggests that it can be applied to more complicated nuclear reactions.     

Numerical experiments of the planar equal-mass three-body problem: the effects of rotation

The planar three-body problem with angular momentum is numerically and systematically studied as a generalization of the free-fall problem (i.e., the three-body problem with zero initial velocities). The initial conditions in the configuration space exhaust all possible forms of a triangle, whereas the initial conditions in the momentum space are chosen so that position vectors and momentum vectors are orthogonal. Numerical results are organized according to the value of virial ratio k defined as the ratio of the total kinetic energy to the total potential energy. Final motions are mapped in the initial value space. Several interesting features are found. Among others, binary collision curves seem to spiral into the Lagrange point, and for large k, binary collision curves connect the Lagrange point and the Euler point. The existence of a lunar periodic orbit and a periodic orbit of petal-type is suggested. The number of escape orbits as a function of the escape time is analyzed for different k. The behavior of this number for different time and k shows most remarkably the effects of rotation of triple systems. The number of escape orbits increases exponentially for k相似文献   

A method to estimate the self-consistency effects on electronic structure calculations

A simple method to estimate the effects of the self- -consistency on the calculation of the electronic structure of molecule and crystals is proposed. This procedure is based on the charge transfer between the constituent atoms and is intended to avoid much computational effort. Numerical results are presented for GaAs.     

Application of the method of moments to three-body scattering

The method of moments is investigated as a possible iterative method of solution of the Faddeev equations. The method is shown to converge rapidly to the three-body wave function for the case of zero energy neutrons scattering off deuterium. It is suggested that the method should be appropriate for the treatment of three-body break-up with separable or local potentials.     

A three-body calculation for polarization effects in neutron-deuteron scattering

The Faddeev equations with separable two-particle interactions have been solved for the 2n + p system at energies 14.1 MeV and 22.7 MeV respectively. The simultaneous and individual effect of the S- and P-wave interactions and the tensor force on the differential cross section and polarizations has been studied. The experimental data have not been reproduced satisfactorily. A method different from the contour-deformation method has been suggested to treat the singularities of the kernels of the Faddeev integral equations.     

A three-body approach to the effective nucleon-nucleon interaction

The problem of the effective nucleon-nucleon interaction is formulated in a three-body model. The interaction of two nucleons and a heavy core having internal excitations is described by means of Faddeev-type coupled equations. The elimination of the excited states of the core leads to a set of coupled equations with an effective kernel which incorporates the effect of the eliminated degrees of freedom. An exactly soluble model is constructed and solved. The exact and an approximate solution are compared. The comparison demonstrates the applicability of the model for the investigation of problems connected with the effective nucleon-nucleon interaction.