One-body Terms Research Articles

Inhomogeneous random-phase approximation and many-electron trial wave functions

The long-range electronic correlations in a uniform electron gas may be deduced from the random-phase approximation (RPA) of Bohm and Pines [Phys. Rev. 92, 609 (1953)]. Here we generalize the RPA to nonuniform systems and use it to derive many-electron Slater-Jastrow trial wave functions for quantum Monte Carlo simulations. The RPA theory fixes the long-range behavior of the inhomogeneous two-body terms in the Jastrow factor and provides an accurate analytic expression for the one-body terms. It also explains the success of Slater-Jastrow trial functions containing determinants of Hartree-Fock or density-functional orbitals, even though these theories do not include Jastrow factors. After adjusting the RPA Jastrow factor to incorporate the known short-range behavior, we test it using variational Monte Carlo simulations. In the small inhomogeneous electron gas system we consider, the analytic RPA-based Jastrow factor slightly outperforms the standard numerically optimized form. The inhomogeneous RPA theory therefore enables us to reduce or even avoid the costly numerical optimization process.

Poincaré covariant current operator and elastic electron-deuteron scattering in the front-form Hamiltonian dynamics

The deuteron electromagnetic form factors, $A(Q^2)$ and $B(Q^2)$, and the tensor polarization $T_{20}(Q^2)$, are unambiguously calculated within the front-form relativistic Hamiltonian dynamics, by using a novel current, built up from one-body terms, which fulfills Poincar\'e, parity and time reversal covariance, together with Hermiticity and the continuity equation. A simultaneous description of the experimental data for the three deuteron form factors is achieved up to $Q^2 < 0.4 (GeV/c)^2$. At higher momentum transfer, different nucleon-nucleon interactions strongly affect $A(Q^2)$, $B(Q^2)$, and $T_{20}(Q^2)$ and the effects of the interactions can be related to $S$-state kinetic energy in the deuteron. Different nucleon form factor models have huge effects on $A(Q^2)$, smaller effects on $B(Q^2)$ and essentially none on $T_{20}(Q^2)$.

Effective Collision Strengths of Fine‐Structure Transitions in Fex, Fexi, and Fexiii

Electron excitation collision strengths for fine-structure transitions in Fe X, Fe XI, and Fe XIII are calculated using full Breit-Pauli R-matrix approach. We included 49 fine-structure levels of Fe X, 38 fine-structure levels of Fe XI, and 26 fine-structure levels of Fe XIII in our scattering calculations. These levels are represented by configuration-interaction wave functions. The relativistic effects are included in the Breit-Pauli approximation via one-body mass correction, Darwin, and spin-orbit interaction terms in the scattering equations. Rydberg series of resonances converging to the excited state thresholds are explicitly included in the calculations. The effective collision strengths are determined by integrating collision strengths and assuming a Maxwellian distribution of electron energies.

Calculation of rotational states of methane molecules in a square lattice

Methane molecules in a square lattice perform hindered rotation due to the molecular interaction. First, the one-body term in the interaction gives the new pattern of rotational energy level scheme. In the case of strong interaction, this scheme becomes similar to tunneling levels calculated from the pocket state formalism. Secondly, the two-body term produces a potential with lower symmetry. We investigate the case of a ferro-orientational phase. Four levels remain in the lowest part of rotational energy spectrum under the field strength estimated from the sum of atom–atom pair potentials. This small number of levels approaches to more realistic systems.

Electron Impact Excitation of Fine‐Structure Levels in Sulfur‐like Fe xi

Collision strengths for electron impact excitation of fine-structure levels in sulfur-like Fe XI are calculated in a semirelativistic R-matrix approach. The 38 fine-structure levels arising from the 20 LS states 3s23p43P,1D,1S; 3s3p53Po,1Po; 3s23p3(4So)3d3Do, 3s23p3(2Po)3d1,3Po,1,3Do,1,3Fo, 3s23p3(2Do)3d1,3So,1,3Po,1,3Do,1,3Fo are included in our calculation. The target levels are represented by configuration interaction wave functions. The relativistic effects are considered in the Breit-Pauli approximation by including one-body mass correction, Darwin term, and spin-orbit terms in the scattering equations. Collision strengths for transitions from the 3s23p43P2,1,0 levels to the fine-structure levels of the 3s23p33d configuration are compared with the distorted-wave results of Bhatia & Doschek at 8.0, 16.0, 24.0 ryd. There are some significant discrepancies between the two calculations, mostly caused by the difference in target wave functions. The collision strengths are integrated over a Maxwellian distribution of electron energies to obtain effective collision strengths over the temperature range from 5 × 105 to 5 × 106 K.

Effective Collision Strengths for Electron Impact Excitation of Fine‐Structure Levels in Fexi

Collision strengths for transitions between the 3s23p4 P2, 1, 03, 1D2, and 1S0 levels and from these levels to the 3s3p5 P02, 1, 03 and 1P01 levels of Fe XI are calculated using a semirelativistic R-matrix approach. The 38 fine-structure levels arising from the 20 LS 3s23p4 P3, 1D, 1S, 3s3p5 P03, 1P0, 3s23p3(4S0)3d D03, 3s23p3(2P0)3d P01,3, 1, 3D0, 1, 3F0, 3s23p3(2D0)3d S01,3, 1, 3P0, 1, 3D0, 1, 3F0 states are included in our calculation. These target levels are represented by configuration-interaction wave functions. The relativistic effects are considered in the Breit-Pauli approximation by including one-body mass correction, Darwin term, and spin-orbit terms in the scattering equations. Complicated resonance structures are found to enhance the collision strengths significantly for many transitions in the threshold energy regions. Our collision strengths are compared with the available results of Bhatia & Doschek at 8.0, 16.0, and 24.0 ryd. The collision strengths are integrated over a Maxwellian distribution of electron energies to give effective collision strengths over a wide temperature range.

Collision Strengths for Electron Impact Excitation of Fine‐Structure Levels in Fexiii

Electron collisional excitation strengths for transitions among the fine-structure levels of the ground 3s23p2 configuration and from the levels of 3s23p2 configuration to the levels of the excited 3s3p3 and 3s23p3d configurations in Fe XIII are calculated using a semirelativistic R-matrix approach. We considered 14 LS 3s23p23P,1D,1S, 3s3p33Do,3Po,1Do,3So,1Po, 3s23p3d3Po,1Do,3Do,3Fo,1Fo, and 1Po states of Fe XIII in the present calculation. The 14 LS states give rise to 26 fine-structure levels that are represented by configuration-interaction wave functions. The relativistic effects are included in the Breit-Pauli approximation via one-body mass correction, Darwin, and spin-orbit interaction terms in the scattering equations. Complicated resonance structures are explicitly included in the collision strengths. The collision strengths are integrated over a Maxwellian distribution of electron energies to give effective collision strengths over a wide temperature range from 5 × 105 to 5 × 106 K.

Variational quantum Monte Carlo calculation of the cohesive properties of cubic boron nitride

The cohesive properties of cubic boron nitride are calculated using the variational quantum Monte Carlo approach. The calculated properties are found to be in good agreement with experiment and demonstrate the effectiveness of the variational forms of wave functions previously used in $\mathrm{sp}$-bonded systems involving only one chemical species when applied to solids with more than one type of atom. The formulation of variance minimization for the one-body term in solids without inversion symmetry is presented, and a particularly simple form of one-body term based on a charge-fluctuation picture of electron correlation is shown to obtain excellent results for ground-state energies of B, C, and N atoms, and for the cubic boron nitride solid.

SURFACE ROTATIONAL DISORDERING IN CRYSTALLINE C60

We present a theory of surface rotational disordering of crystalline fullerene. Realistic intermolecular interactions are implemented, in a layer-by-layer mean field theory. The crucial new ingredient turns out to be a one-body potential energy term, or "crystal field," is totally different at the surface, therefore locally frustrating bulk order. This frustration causes a severe surface order parameter reduction, and a first order surface rotational disordering transition, well below the corresponding bulk one. Preliminary results are in agreement with recent experiments, confirming a first order surface rotational transition of C 60(111) at a transition temperature lower than the bulk one.

Chiral perturbation theory and thepp→ppπ0reaction near threshold

A chiral-perturbative consideration of the near-threshold $\mathrm{pp}\ensuremath{\rightarrow}\mathrm{pp}{\ensuremath{\pi}}^{0}$ reaction indicates that the pion-rescattering term has a substantial energy and momentum dependence. The existing calculations that incorporate this dependence give pion rescattering contributions significantly larger than those of the conventional treatment, and this enhanced rescattering term interferes destructively with the one-body impulse term, leading to theoretical cross sections that are much smaller than the observed values. However, since the existing calculations are based on coordinate-space representation, they involve a number of simplifying assumptions about the energy-momentum flow in the rescattering diagram, even though the delicate interplay between the one-body and two-body terms makes it desirable to avoid these kinematical assumptions. We carry out here a momentum-space calculation that retains the energy-momentum dependence of the vertices as predicted by chiral perturbation theory. Our improved treatment increases the rescattering amplitude by a factor of $\ensuremath{\sim}$3 over the value obtained in the $r$-space calculations. The $\mathrm{pp}\ensuremath{\rightarrow}\mathrm{pp}{\ensuremath{\pi}}^{0}$ transition amplitude, which is now dominated by the rescattering term, leads to the cross section much larger than what was reported in the approximate $r$-space calculations. Thus, the extremely small cross sections obtained in the previous chiral perturbative treatments of this reaction should be considered as an accidental consequence of the approximations employed rather than a general feature.

A global H2O potential energy surface for the reaction O(1D)+H2→OH+H

A global, single-valued ground-state H2O potential surface for the reaction O(1D)+H2→OH+H has been constructed from a new set of accurate ab initio data using a general multidimensional interpolation method. The ab initio calculations are of the multireference, configuration interaction variety and were carried out using augmented polarized triple zeta basis sets. The multidimensional method is formulated within the framework of the reproducing kernel Hilbert space theory. The H2O potential is expressed as a many-body sum of a single one-body term, three two-body terms, and a single three-body term. The one-body term is the dissociation energy to the three-atom limit 2H(2S)+O(3P). The two-body terms are two O–H and one H–H adiabatic diatomic potentials of lowest energy. Each diatomic term is obtained by interpolating a discrete set of ab initio data using a one-dimensional, second-order, distancelike reproducing kernel. The three-body term is obtained by interpolating the difference of the H2O ab initio data and the one- and two-body sum by means of a direct product of three one-dimensional reproducing kernels on an optimized regular three-dimensional grid. The H2O potential energy surface is accurate, globally smooth, easy to evaluate, and asymptotically correct. Extensive quasiclassical trajectory calculations based on this new potential energy surface have been performed and compared with the results based on the potential energy surface of Murrell and Carter (MC) and that of Schinke and Lester (SL). Comparisons with recent experimental measurements on total cross sections, isotope effects, rate constants, vibrational, rotational, and angular distributions of the O(1D)+H2/HD reaction show that the new potential energy surface is a significant improvement over the MC and SL surfaces.

Diffusion Monte Carlo study of jellium surfaces: Electronic densities and pair correlation functions.

We present the results of fixed-node diffusion Monte Carlo calculations of jellium surfaces for metallic densities. We used a trial wave function of the Slater-Jastrow type, with the long-range part of the two-body term modified to account for the anisotropy of the system. The one-body term is optimized so that the electronic density from variational and diffusion Monte Carlo calculations agree with each other. The final densities are close to the densities obtained from density-functional calculations in the local-density approximation and the surface energies to the results obtained using the Langreth-Mehl and Perdew-Wang generalized gradient approximation at high densities ( r s 3.25) they agree with the results of the Fermi-hypernetted-chain calculations. The pair-correlation functions at regions near the surface are tabulated, showing the anisotropy of the exchange-correlation hole in regions of fast-varying densities. @S0163-1829~96!06848-8#

Metal-insulator transition in the presence of excitonic correlation

We study the possibility of an excitonic transition in a two-band model and show that a true phase transition does not occur in the presence of hybridization since the one-body mixing term acts as a conjugate field to the order parameter of the excitonic phase. We suggest an alternative interpretation for recent experiments on rare earth semiconductors based on a metal-insulator transition associated with the opening or closing of a hybridization gap at a critical pressure.

Role of heavy-meson exchange in pion production near threshold.

Recent calculations of s-wave pion production have severely underestimated the accurately known pp\ensuremath{\rightarrow}pp${\mathrm{\ensuremath{\pi}}}^{0}$ total cross section near threshold. In these calculations, only the single-nucleon axial-charge operator is considered. We have calculated, in addition to the one-body term, the two-body contributions to this reaction that arise from the exchange of mesons. We find that the inclusion of the scalar \ensuremath{\sigma}-meson exchange current (and lesser ocntributions from other mesons) increases the cross section by about a factor of 5 and leads to excellent agreement with the data. The results are sensitive neither to changes in the distorting potential that generates the NN wave functions nor to different choices for the meson-nucleon form factors.

Coulomb effect in operator expansion method for two-neutrino double beta decay.

The operator expansion method for the evaluation of the 2[nu] [beta][beta] decay nuclear matrix element is extended to include the Coulomb interaction and nuclear central and tensor interactions. It is shown that the Coulomb interaction, which represents a part of one-body terms of Hamiltonian, plays a decisive role in taking into account effects of ground-state correlations, and a significant improvement is achieved in simulating the exact'' calculation based on the quasiparticle RPA. However, this method does not reproduce the strong suppression of the nuclear matrix element, probably because of the two-body approximation.

Coulomb sum and proton-proton correlations in few-body nuclei.

For simple models of the nuclear charge operator, measurements of the Coulomb sum and the charge form factor of a nucleus directly determine the proton-proton correlations. We examine experimental results obtained for few-body nuclei at Bates and Saclay using models of the charge operator that include both one- and two-body terms. Previous analyses using one-body terms only have failed to reproduce the experimental results. However, we find that the same operators which have been used to successfully describe the charge form factors also produce substantial agreement with measurements of the Coulomb sum.

Smallness of gluon coupling to constituent quarks in baryons and validity of nonrelativistic quark model.

A study of the parametrization of baryon masses and other quantities leads to a ratio \ensuremath{\cong} ⅕ for two-gluon-exchange versus one-gluon-exchange terms between two constituent quarks in a baryon. This fact (plus the factor 3 reduction from each additional order in flavor breaking) explains the success, to a part per thousand, of a new baryon mass formula [Phys. Rev. Lett. 68, 139 (1992)]. It also explains why the results of SU(3) that neglect second-order flavor breaking (such as the Gell-Mann-Okubo baryon mass formula) work much better than expected. Finally the general parametrization, plus the above reduction factors, clarify why the naive nonrelativistic quark model (NRQM) is quantitatively fairly good. The reasons are twofold: (a) The structure of the general parametrization (an exact consequence of any QCD-like relativistic field theory) is similar to that of the NRQM; (b) the smallness of the gluon coupling and the reduction factor due to flavor imply that the additive (one-body) terms in the parametrization prevail on the two-body terms and the latter on the three-body ones, the typical feature of the naive NRQM.

Mean-field treatment of the hybridization influence on narrow-band superconductivity.

We study the effect of hybridization on superconductivity within a two-band model, in the framework of an extended BCS theory. We describe interband effects through a one-body mixing term differently from the standard many-body approach. We use a Green's-function method to obtain the energies of the quasiparticles, the critical temperature, and the order parameter as functions of hybridization. We show that, in general, one should distinguish between the BCS order parameter and the gap in the quasiparticle spectrum. Finally, we discuss the application of our results for transition metals and high-${\mathit{T}}_{\mathit{c}}$ superconductors.

Superconductivity in two-band systems: application to transition metals and high Tc materials

We study the effect of hybridization on superconductivity within a two band model, in the framework of an extended BCS theory. We describe interband effects through a one-body mixing term differently from the standard many body approach. Using homothetic relations for tje bands and the hybridization we obtain the energies of the quasiparticles, the critical temperature and the order parameter. We discuss the application of our results for transition metals and high T c superconductors.

The 2νββ decay rate within a boson expansion formalism

A microscopic hamiltonian consisting of a one-body term and a realistic two-body interaction, corresponding to the G-matrix of the Bonn potential, is treated within the QRPA formalism including both particle-hole (ph) and particle-particle (pp) channels. The β ± transition operators are expanded up to the first order in terms of the dipole and quadrupole RPA bosons. The influence of the higher RPA terms on the ββ matrix elements M GT (00) and M GT (02), associated with the transitions 0 i + → 0 i + → 0 i + → 2 f + respectively, is studied as a function of the strength of the dipole pp interactions g pp (1). The HRPA terms shift the zero ( g pp (1) = 1) of the RPA function M GT (00) to the region where QRPA collapses. The M GT (02) value is an increasing function of g pp (1).