Three-particle Effects Research Articles

Comment on the magnetic dipole hyperfine interaction in the gold atom ground state

The multiconfiguration Dirac–Hartree–Fock (MCDHF) model has been employed to calculate the magnetic dipole hyperfine constant A of the 5d106s 2S1/2 ground state of atomic gold. Electron correlation effects contribute more than 20% to the total value of A. We investigated the effects of single, double, and a subset of triple substitutions. The calculations reveal strong cancellations between one-, two- and three-particle correlation effects. It is demonstrated that in the case of the ground state of atomic gold the three-particle effects are comparable in size to the one- and two-particle ones.

Green's-function approach to atomic many-body calculations with application to the ground state in alkali-metal atoms

In this paper we apply the single-particle Green's-function method to the atomic many-body perturbation theory. We present an all-order evaluation scheme for the proper self-energy operator based on the systematic use of Dyson's integral equations. The method is complete to third order in perturbation theory and, in addition, large classes of higher-order effects are included by solving the Dyson equations. Certain classes of many-body correlation effects beyond the pair-correlation approximation are included. The proposed method is tested by calculating the ground-state valence-electron binding energy for the alkali-metal atoms Li, Na, and K. Agreement with experimental results corresponds to an error in the correlation energy contribution of 3--4%. If certain three-particle effects, not evaluated in this work, are added, the agreement with experiments is, for sodium and potassium, approximately within 1% of the correlation energy.

Large-scale multiconfiguration Hartree-Fock and configuration-interaction calculations of the transition probability and hyperfine structures in the sodium resonance transition

Results from large-scale multiconfiguration Hartree-Fock (MCHF) and configuration-interaction (CI) calculations of the transition probability and hyperfine structures in the sodium 3s${\mathrm{}}^{2}$S-3p${\mathrm{}}^{2}$P resonance transition are presented. In the calculations the orbital sets of the initial and final state wave functions were not restricted to be the same, but were optimized independently. The evaluation of the transition matrix elements was done using a technique where the two orbital sets are transformed so as to become biorthonormal, in which case standard Racah algebra can be used. Three-particle effects were taken into account in the CI calculations and were found to be important for the hyperfine structures, but less important for the transition probability. The calculated transition probability is in perfect agreement with the most recent experimental values, thus resolving the long-standing disagreement between theory and experiment. Also the 3s${\mathrm{}}^{2}$${\mathit{S}}_{1/2}$ and 3p${\mathrm{}}^{2}$${\mathit{P}}_{1/2,3/2}$ hyperfine interaction constants are in very good agreement with available experimental values. \textcopyright{} 1996 The American Physical Society.

Analysis of certain binary collision approximation closures of the BBGKY hierarchy

The closure of the BBGKY hierarchy to obtain the Boltzmann equation requires, in particular, restricting particle interactions to include only isolated binary collisions. Boercker and Dufty accomplish this by approximating the three-particle reduced density operator in a particular manner that favours correlation between two of the particles, while ignoring the correlation with the third. The tradition of most other closures has more closely followed Boltzmann's original thinking to completely neglect any reference to three-particle effects while assuming a generalized form of molecular chaos for the pair density operator. The two closures are compared in two ways: (a) by finding iterated series solutions of the BBGKY hierarchy and of the Boltzmann equation; (b) by computing an exact correction to the quantum Boltzmann equation. A consequence of the comparison of the iterated series shows that an important, but little emphasized, difference between the BBGKY and Boltzmann hierarchies is the effective instantaneousness of binary collisions in the latter. The form for the correction found is shown to vanish for either closure provided the instantaneousness of the binary collisions is imposed. It is shown moreover that the correction is closely related to the three-body collision integral arising in the standard theory of the density corrections to the Boltzmann equation. We also comment on the related work of Klimontovich, who introduces an approximation analogous to that of Boercker and Dufty.

Large-scale multiconfiguration Hartree-Fock calculations of hyperfine-interaction constants for low-lying states in beryllium, boron, and carbon.

Multiconfiguration Hartree-Fock (MCHF) calculations of hyperfine constants for the 2s2p $^{3}$P states of beryllium and the ground states of boron and carbon are reported. The capacity of a recently developed configuration-interaction program [Froese Fischer and Tong (unpublished); Stathopoulos and Froese Fischer (unpublished)], allowing for large configuration expansions, is explored. Using a systematic active-space MCHF approach, combined with large multireference configuration-interaction calculations, it is shown that hyperfine constants can be calculated very accurately. To reliably account for spin-polarization of the 1s and 2s shells in boron and carbon, three-particle effects had to be included in a systematic way. The relativistic, finite-nuclear-size- and finite-nuclear-mass-corrected values of the hyperfine constants are compared with experimental values and with the most accurate theoretical values obtained with other methods.

Differential cross section of the 2H(n, nnp)-reaction at En = 13 MeV

The differential cross section of the nD break-up reaction was investigated at E n = 13 MeV using the Erlangen multidetector neutron facility. Twenty-two different configurations including np final-state interaction, collinearity, coplanar- and space star were measured in a kinematically complete experiment. The results are compared with rigorous Faddeev calculations based on the Paris potential. The discrepancies between data and calculations indicate imperfections in the potential and may be caused by three-particle effects such as wrong off-shell behavior of the potential or an additional three-body force.

Many-particle effects in nearly integrable systems

For the sine-Gordon and nonlinear Schrödinger equations with conservative perturbations three-particle effects in collision of a fast soliton with two more slow ones are considered in the first order of the perturbation theory. The momentum and energy exchanged between the fast soliton and slow ones are calculated. For the latter system the three-particle contribution to the perturbation-induced phase shift of the fast soliton is calculated too. The effects vanish when the overlapping between the slow solitons is absent at the collision moment. In the former system inelastic interaction between the fast kink and a weakly bound breather is considered. The threshold value of the breather's binding energy admitting breaking the breather into a kink-antikink pair is calculated. Analogously, the inelastic collision of two bound breathers is considered. For the collision of two “relativistic” sine-Gordon kinks the energy radiated under the action of the conservative perturbation is found and is demonstrated to be asymptotically independent on the relative polarity of the kinks.

Three-particle and inelastic effects in the interaction of conservatively perturbed sine-Gordon equation kinks

Three-particle effects in the collision of a fast kink with two more slow ones described by the conservatively perturbed sine-Gordon equation are considered. The collision of a fast kink with a more slow one in the presence of a localized inhomogeneity, and radiative effects accompanying the reflection of a kink from the edge in a problem on a half-line are considered too.

Three-particle and inelastic effects in the interaction of conservatively perturbed nonlinear Schrödinger equation solitons

For the conservatively perturbed nonlinear Schrödinger equation three-particle effects in the collision of a fast soliton with a pair of more slow ones are considered in the first order of perturbation theory. The changes of the solitions' velocities and amplitudes, and the perturbation-induced three-particle contribution to the phase shift of the fast soliton are calculated. The total energy emitted during collision of two fast solitons is calculated too.

Three-particle effects observed in two-particle correlation measurements

Correlations between coincident alpha particles and protons were measured for 40Ar induced reactions on 197Au at E/A = 60 MeV. The correlation function exhibits features not expected from free α-p interactions. These include a pronounced maximum at low relative momenta, q ≈ 15 MeV / c , and a dependence of the 5Li ground state peak on the total 5Li energy and decay kinematics. These anomalies are explained by considering the contribution of the decay of 9B, and the effects of the Coulomb field, due to the reaction residue, on the decay of 5Li.

Nuclear quadrupolar relaxation by translational diffusion in solids: I. Mean field theory

The theory of nuclear quadrupolar relaxation due to translational diffusion in crystalline solids is investigated. Unlike the case of dipolar relaxation, it is often necessary to take into account three-particle, as well as two-particle, probability functions in the expression for the spectral densities of the quadrupolar interaction. In particular, the nuclear relaxation of a particle diffusing on a cubic lattice, due to the relative translational motion of other identical particles on the same lattice, is evaluated according to the mean field theory which includes, in an average way, the effects of spatial correlations between the motions of particles. Formal expressions are obtained for the three-particle probability function for nearest-neighbour jumps on SC, FCC and BCC lattices. Analytical formulae are derived for the spectral density functions in the low-temperature limit and demonstrate the greater importance of three-particle effects as the concentration of particles increases. In a subsequent paper, the mean field theory is applied to the quadrupolar relaxation of deuterons in transition metal deuterides.

One-dimensional integral equations for a system of three identical particles in the boundary condition model and the possibility of changing the off-shell behaviour of the two-particle T-matrix

It is shown that in the framework of the boundary condition model (BCM) for the two-particle interaction the Schrödinger equation for the system of three identical bosons can be reduced to the one-dimensional integral equation in an exact way. The method used for obtaining such an equation is based on a special consideration of the two-particle off-shell wave functions. The binding energy of the simple three-particle system is calculated. It is indicated that by means of the equation obtained it is possible to change the off-shell behaviour of the two-particle (-matrix and therefore to simulate three-particle effects.

Atomic Bethe-Goldstone Calculations of Term Splittings, Ionization Potentials, and Electron Affinities for B, C, N, O, F, and Ne

The ionization potentials, electron affinities, and term splittings of the lowest electronic configurations for first-row atoms for $Z$ from 5 to 10 have been computed. The method used is that applied previously to ground-state correlation energies. Variational calculations equivalent to solution of one- and two-particle Bethe-Goldstone equations are carried out, following approximate Hartree-Fock calculations for each state of each atom or ion considered. Computed quantities are in reasonably good agreement with experiment. Bethe-Goldstone equations as used here are defined in terms of individual orbital excitations. Calculations of three-particle effects are included in some cases, computed with less relative accuracy than the other results. The three-particle terms are not negligible. In particular, they substantially reduce the magnitude of computed electron affinities.

Faddeev Equations for the Three-Pion Final-State Interaction inτ,τ′, andηDecays

The anisotropy in the pion energy spectra for the various three-pion decay modes are assumed capable of providing information concerning the $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ interaction parameters. Such determinations have so far yielded values that differ radically from those obtained from.the analysis of low-energy pion-nucleon elastic scattering as well as production phenomena. The problem is reconsidered in the light of the complete three-body scattering amplitude given according to the prescription of Faddeev. The assumptions made regarding the kernel of the integral equations include (i) a simple off-shell extension of the two-body scattering amplitude, separable in the initial and final momenta, (ii) a nonrelativistic framework except for the pion kinematics, and (iii) an attractive $s$-wave $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ interaction in the absence of bound states or resonances. Besides the pion scattering-length parameters, we have a momentum cutoff which, over a wide range of values, has an insignificant effect on the shape of the pion energy spectrum. The integral equations are solved numerically and the parameters that best fit the pion spectra for $\ensuremath{\tau}$, ${\ensuremath{\tau}}^{\ensuremath{'}}$, and $\ensuremath{\eta}$ decay are obtained. In each case the $s$-wave scattering length ${a}_{2}$ is found to be much larger than ${a}_{0}$. This confirms the conjecture that the inclusion of the three-particle effects does not significantly alter the general features of earlier work.