Ground-state properties of a dilute homogeneous Bose gas of hard disks in two dimensions

The energy and structure of a dilute hard-disks Bose gas are studied in the framework of a variational many-body approach based on a Jastrow correlated ground-state wave function. The asymptotic behaviors of the radial distribution function and the one-body density matrix are analyzed after solving the Euler equation obtained by a free minimization of the hypernetted chain energy functional. Our results show important deviations from those of the available low density expansions, already at gas parameter values x~0.001 . The condensate fraction in 2D is also computed and found generally lower than the 3D one at the same x.

Experimental deuteron momentum distributions with reduced final state interactions

This dissertation presents a study of the D( e, e′p)n reaction carried out at the Thomas Jefferson National Accelerator Facility (Jefferson Lab) for a set of fixed values of four-momentum transfer Q 2 = 2.1 and 0.8 (GeV/c)2 and for missing momenta pm ranging from pm = 0.03 to pm = 0.65 GeV/c. The analysis resulted in the determination of absolute D(e,e′ p)n cross sections as a function of the recoiling neutron momentum and it's scattering angle with respect to the momentum transfer [vector] q. The angular distribution was compared to various modern theoretical predictions that also included final state interactions. The data confirmed the theoretical prediction of a strong anisotropy of final state interaction contributions at Q2 of 2.1 (GeV/c)2 while at the lower Q2 value, the anisotropy was much less pronounced. At Q2 of 0.8 (GeV/c)2, theories show a large disagreement with the experimental results. The experimental momentum distribution of the bound proton inside the deuteron has been determined for the first time at a set of fixed neutron recoil angles. The momentum distribution is directly related to the ground state wave function of the deuteron in momentum space. The high momentum part of this wave function plays a crucial role in understanding the short-range part of the nucleon-nucleon force. At Q2 = 2.1 (GeV/c)2, the momentum distribution determined at small neutron recoil angles is much less affected by FSI compared to a recoil angle of 75°. In contrast, at Q2 = 0.8 (GeV/c)2 there seems to be no region with reduced FSI for larger missing momenta. Besides the statistical errors, systematic errors of about 5–6 % were included in the final results in order to account for normalization uncertainties and uncertainties in the determi- nation of kinematic veriables. The measurements were carried out using an electron beam energy of 2.8 and 4.7 GeV with beam currents between 10 to 100 &mgr; A. The scattered electrons and the ejected protons originated from a 15cm long liquid deuterium target, and were detected in conicidence with the two high resolution spectrometers of Hall A at Jefferson Lab.^

Classes of exact Klein-Gordon equations with spatially dependent masses: Regularizing the one-dimensional inversely linear potential

In this work we consider the effect of a spatially dependent mass over the solution of the Klein-Gordon equation in 1 + 1 dimensions, particularly the case of inversely linear scalar potential, which usually presents problems of divergence of the ground-state wave function at the origin, and possible nonexistence of the even-parity wave functions. Here we study this problem, showing that for a certain dependence of the mass with respect to the coordinate, this problem disappears. (c) 2006 Elsevier B.V. All rights reserved.

Numerical study of the spherically symmetric Gross-Pitaevskii equation in two space dimensions

The Gross-Pitaevskii equation for Bose-Einstein condensation (BEC) in two space dimensions under the action of a harmonic oscillator trap potential for bosonic atoms with attractive and repulsive interparticle interactions was numerically studied by using time-dependent and time-independent approaches. In both cases, numerical difficulty appeared for large nonlinearity. Nonetheless, the solution of the time-dependent approach exhibited intrinsic oscillation with time iteration which is independent of space and time steps used in discretization.

GROUND-STATE-ENERGY OF SINGULAR POTENTIALS

It is shown that for singular potentials of the form lambda/r(alpha),the asymptotic form of the wave function both at r --> infinity and r --> 0 plays an important role. Using a wave function having the correct asymptotic behavior for the potential lambda/r(4), it is, shown that it gives the exact ground-state energy for this potential when lambda --> 0, as given earlier by Harrell [Ann. Phys. (NY) 105, 379 (1977)]. For other values of the coupling parameter X, a trial basis;set of wave functions which also satisfy the correct boundary conditions at r --> infinity and r --> 0 are used to find the ground-state energy of the singular potential lambda/r(4) It is shown that the obtained eigenvalues are in excellent agreement with their exact ones for a very large range of lambda values.

Site Specific Spin Dynamics In Bafe2as2: Tuning The Ground State By Orbital Differentiation.

The role of orbital differentiation on the emergence of superconductivity in the Fe-based superconductors remains an open question to the scientific community. In this investigation, we employ a suitable microscopic spin probe technique, namely Electron Spin Resonance (ESR), to investigate this issue on selected chemically substituted BaFe2As2 single crystals. As the spin-density wave (SDW) phase is suppressed, we observe a clear increase of the Fe 3d bands anisotropy along with their localization at the FeAs plane. Such an increase of the planar orbital content is interestingly independent of the chemical substitution responsible for suppressing the SDW phase. As a consequence, the magnetic fluctuations in combination with this particular symmetry of the Fe 3d bands are propitious ingredients for the emergence of superconductivity in this class of materials.

Full-dimensional analytical ab initio potential energy surface of the ground state of HOI

Extensive ab initio calculations using a complete active space second-order perturbation theory wavefunction, including scalar and spin-orbit relativistic effects with a quadruple-zeta quality basis set were used to construct an analytical potential energy surface (PES) of the ground state of the [H, O, I] system. A total of 5344 points were fit to a three-dimensional function of the internuclear distances, with a global root-mean-square error of 1.26 kcal mol(-1). The resulting PES describes accurately the main features of this system: the HOI and HIO isomers, the transition state between them, and all dissociation asymptotes. After a small adjustment, using a scaling factor on the internal coordinates of HOI, the frequencies calculated in this work agree with the experimental data available within 10 cm(-1). (C) 2011 American Institute of Physics. [doi: 10.1063/1.3615545]

Excitation energies from ground-state density-functionals by means of generator coordinates

The generator-coordinate method is a flexible and powerful reformulation of the variational principle. Here we show that by introducing a generator coordinate in the Kohn-Sham equation of density-functional theory, excitation energies can be obtained from ground-state density functionals. As a viability test, the method is applied to ground-state energies and various types of excited-state energies of atoms and ions from the He and the Li isoelectronic series. Results are compared to a variety of alternative DFT-based approaches to excited states, in particular time-dependent density-functional theory with exact and approximate potentials.

Delta(1232) isobar excitations and the ground state of nuclei

The influence of Delta isobar components on the ground-state properties of nuclear systems is investigated for nuclear matter as well as finite nuclei. Many-body wave functions, including isobar configurations and binding energies, are evaluated employing the framework of the coupled-cluster theory. It is demonstrated that the effect of isobar configurations depends in a rather sensitive way on the model used for the baryon-baryon interaction. As examples for realistic baryon-baryon interactions with explicit inclusion of isobar channels we use the local (V28) and nonlocal meson-exchange potentials (Bonn2000) but also a model recently developed by the Salamanca group, which is based on a quark picture. The differences obtained for the nuclear observables are related to the treatment of the interaction, the pi-exchange contributions in particular, at high momentum transfers.

Studying Avalanches in the ground-state of the two-dimensional random field Ising model driven by an external field

We study the exact ground state of the two-dimensional random-field Ising model as a function of both the external applied field B and the standard deviation ¿ of the Gaussian random-field distribution. The equilibrium evolution of the magnetization consists in a sequence of discrete jumps. These are very similar to the avalanche behavior found in the out-of-equilibrium version of the same model with local relaxation dynamics. We compare the statistical distributions of magnetization jumps and find that both exhibit power-law behavior for the same value of ¿. The corresponding exponents are compared.

Delta(1232) isobar excitations and the ground state of nuclei

The influence of Delta isobar components on the ground-state properties of nuclear systems is investigated for nuclear matter as well as finite nuclei. Many-body wave functions, including isobar configurations and binding energies, are evaluated employing the framework of the coupled-cluster theory. It is demonstrated that the effect of isobar configurations depends in a rather sensitive way on the model used for the baryon-baryon interaction. As examples for realistic baryon-baryon interactions with explicit inclusion of isobar channels we use the local (V28) and nonlocal meson-exchange potentials (Bonn2000) but also a model recently developed by the Salamanca group, which is based on a quark picture. The differences obtained for the nuclear observables are related to the treatment of the interaction, the pi-exchange contributions in particular, at high momentum transfers.

A potential energy surface for the ground state of acetylene, C2H2

A potential energy function has been derived for the ground state surface of C2H2 as a many-body expansion. The 2- and 3-body terms have been obtained by preliminary investigation of the ground state surfaces of CH2( 3B1) and C2H( 2Σ+). A 4-body term has been derived which reproduces the energy, geometry and harmonic force field of C2H2. The potential has a secondary minimum corresponding to the vinylidene structure and the geometry and energy of this are in close agreement with predictions from ab initio calculations. The saddle point for the HCCH-H2CC rearrangement is predicted to lie 2•530 eV above the acetylene minimum.

A potential energy surface for the ground state of formaldehyde, H2CO(1A1)

A model potential energy function for the ground state of H2CO has been derived which covers the whole space of the six internal coordinates. This potential reproduces the experimental energy, geometry and quadratic force field of formaldehyde, and dissociates correctly to all possible atom, diatom and triatom fragments. Thus there are good reasons for believing it to be close to the true potential energy surface except in regions where both hydrogen atoms are close to the oxygen. It leads to the prediction that there should be a metastable singlet hydroxycarbene HCOH which has a planar trans structure and an energy of 2•31 eV above that of equilibrium formaldehyde. The reaction path for dissociation into H2 + CO is predicted to pass through a low symmetry transition state with an activation energy of 4•8 eV. Both of these predictions are in good agreement with recently published ab initio calculations.

Theoretical rovibrational line intensities in the electronic ground state of ozone

First-principles calculations of absolute line intensities and rovibrational energies of ozone (O-16(3)) are reported using potential energy and electric dipole moment functions calculated by the internally contracted MRCI approach. The rovibrational energies and eigenfunctions (up to about 8500 cm(-1) and J = 64) were obtained variationally with an exact Hamiltonian in internal valence coordinates. More than 4.8 x 10(6) electric dipole transition matrix elements were calculated for the absolute rovibrational line intensities. They are compared with the values of the HITRAN database. The purely rotational absolute line intensities in the (000) state and the rovibrational intensities for the (001)-(000) band agree to within about 0.3 to 1% for the (0 10)-(000) band to within about 3 to 4%. Excellent agreement with experiment is also achieved for low-lying overtone and combination bands. Inconsistencies are found for the (100)-(000) band overlapping with the antisymmetric stretching fundamental and also for the (002)-(000) antisymmetric stretching overtone. The generated dipole moment function can be used for predicting the absorption intensities in any of the heavier isotopomers, hot bands or the rates of spontaneous emission.

Ground-state energy of a classical artificial molecule

We study the ground-state energy of a classical artificial molecule formed by two-dimensional clusters (artificial atoms) of N/2 charged particles separated by a distance d. For the small molecules of N = 2 and 4, we obtain analytical expressions for this energy. For the larger ones, we calculate the ground-state energy using molecular dynamics simulation for N up to 128. From our numerical results, we are able to find out a function to approximate the ground-state energy of the molecules covering the range from atoms to molecules for any inter-atom distance d and for particle number from N = 8 to 128 within a difference less than one percent from the MD data.