Ground State Energy of the Low Density Hubbard Model

We derive a lower bound on the ground state energy of the Hubbard model for given value of the total spin. In combination with the upper bound derived previously by Giuliani (J. Math. Phys. 48:023302, [2007]), our result proves that in the low density limit the leading order correction compared to the ground state energy of a non-interacting lattice Fermi gas is given by 8π a ? _u ? _d , where ? _u(d) denotes the density of the spin-up (down) particles, and a is the scattering length of the contact interaction potential. This result extends previous work on the corresponding continuum model to the lattice case.     

A low-lying resonance in the spectrum of H

It was proved by Pekeris⁽¹⁾ that the singly excited states of H^- lie exactly at, or slightly above, the ground state of hydrogen. Using a theory of Fano,⁽²⁾ these fictitious states will have a configuration interaction with the H^- continuum. The strength of this configuration interaction is computed for the mixing of a 1s2p¹P⁰ state with the H^- continuum for different values of the fictitious binding energy of the 2p valence electron. In every case, the effect of the configuration interaction is to induce a rapid change of the phase shift of the continuum wave function by a quantity of π/2 over an energy range of a few times 0.01 eV, at an energy somewhat above the hydrogen ground state. The variation from π/2 to π is much slower. Such a swift change of the phase shift may be identified with the occurrence of a low-lying shape resonance.     

Coupling effects of resonant and discretized non-resonant continuum states in4He +6Li scattering at 10 MeV/A

Alpha- particle scattering from the resonant (3 ₁ ⁺ ) and non-resonant continuum states of⁶Li is studied at incident energy 10 MeV/A. Theα+d breakup continuum part within the excitation energyE _ex=1.475–2.475 MeV is discretized in two energy bins. Unlike the results at higher incident energies, here the coupled-channel calculations show significant breakup continuum coupling effects on the elastic and inelastic scattering. It is shown that even when the continuum-continuum coupling effects are strong, the experimental data of the ground state and the resonant as well as discretized non-resonant continuum states impose stringent constraint on the coupling strengths of the non-resonant continuum states.     

Time spectroscopy in theA 1 ∑ u + state of Li2. Perturbations by thea 3Π u state

We have employed time-resolved LIF spectroscopy in order to investigate perturbations in theA ¹ ∑ _u ⁺ state of the three isotopic Li₂ molecules. After a systematic check of more than 2000 individual rotation-vibration levels, 46 levels were found whose anomalous lifetimes can be interpreted by perturbations with thea ³ Π _u state. As almost all perturbed levels possess shortened lifetimes the predissociating nature of thea ³ Π _u state, caused by interaction with thex ³ ∑ _u ⁺ continuum, is revealed. On the basis of the Kovács-Budo theory of accidental predissociation we have fitted the molecular constants of thea ³ Π _u state, thex ³ ∑ _u ⁺ potential curve and the electronic parts of the perturbation matrix elements do that the observed lifetimes of all levels in the 78 investigatedA ¹ ∑ _u ⁺ ?a³ Π _u term-crossing regions can be understood.     

Volumenänderung durch Gitterverzerrung um ein F-Zentrum in Alkalihalogenidkristallen

The lattice-distortions in the vicinity of anF-centre in alkalihalide crystals and the volume change arising from the lattice distortions around this defect are being calculated. Only theF-centre ground state is considered and the effect of lattice vibrations is neglected. The interaction of theF-electron with the ions is described in terms of effective potentials, and a vacancy-centered wave function is calculated for theF-electron. In calculating the lattice distortions, an approximative procedure is adopted in which only the ions in the vicinity of anF-centre receive an atomistic treatment whereas the remainder of the crystal is treated as an elastic continuum. The volume change caused by the lattice distortions around anF-centre is calculated, using a method ofFischer andHahn which does not require an exact knowledge of the asymptotic strainfield around the point defect. The ions of the first, second and third shell around theF-centre-vacancy are found to be displaced in an outward direction. For the volume-change perF-centre the following values were obtained: 0.26a ³ in NaCl, 0.31a ³ in KCl and 0.35a ³ in KBr,a being the interionic distance. In order to check the validity of some of the approximations employed in the calculations, the volume changes caused by substitution of alien alkali- or halideions are computed and are found to be in good agreement with experimental data.     

Relativistic New Yukawa-Like Potential and Tensor Coupling

We approximately solve the Dirac equation for a new suggested generalized inversely quadratic Yukawa potential including a Coulomb-like tensor interaction with arbitrary spin-orbit coupling quantum number ${\kappa}$ . In the framework of the spin and pseudospin (p-spin) symmetry, we obtain the energy eigenvalue equation and the corresponding eigenfunctions, in closed form, by using the parametric Nikiforov–Uvarov method. The numerical results show that the Coulomb-like tensor interaction, ?T/r, removes degeneracies between spin and p-spin state doublets. The Dirac solutions in the presence of exact spin symmetry are reduced to Schr?dinger solutions for Yukawa and inversely quadratic Yukawa potentials.     

Anapole moment of an exotic nucleus

We consider the anapole moment of ¹¹Be and demonstrate that the contribution to it of the 1p_1/2 level, which is anomalously close to the ground state, is essentially compensated for by the contribution of the continuum. Our estimate for this anapole moment is κ(¹¹Be) ? (0.07–0.08)g _n .     

On the Interplay of Magnetic and Molecular Forces in Curie–Weiss Ferrofluid Models

We consider a mean-field continuum model of classical particles in R ^d with Ising or Heisenberg spins. The interaction has two ingredients, a ferromagnetic spin coupling and a spin-independent molecular force. We show that a feedback between these forces gives rise to a first-order phase transition with simultaneous jumps of particle density and magnetization per particle, either at the threshold of ferromagnetic order or within the ferromagnetic region. If the direct particle interaction alone already implies a phase transition, then the additional spin coupling leads to an even richer phase diagram containing triple (or higher order) points.     

Treatment of pairing in small systems by Green functions

A finite system of fermions with pairing interaction is treated by the Green function method. It is shown that a finite number of “bound pairs” must be assumed to get the correct properties of the system in that region of the interaction strength where the BCS-solution is incorrect. Also the difference betweenE ₀(N+2)?E ₀(N) andE ₀(N)?E ₀(N?2),E ₀(N) being the ground state energy of theN-particle system, has to be considered. The formulae derived give an interpolation between the region where perturbation theory applies and the region of validity of the BCS-equations.     

Continuum RPA correlations in quasielastic electron scattering from 12C decay on (e,e'p) and (e,e'n) reaction channels

We investigate the rôle of RPA correlations in longitudinal and transverse response functions for inelastic electron scattering from ¹²C at momentum transfers ranging between 200 MeV/c and 550 MeV/c. We refer to a continuum self-consistent RPA theory with a SK3 interaction. Electromagnetic operators are taken for uncorrelated nucléons. The partial response on (e, e'p) and (e, e'n) reaction channels is also calculated. Since energy-weighted sum rules are conserved, we can control the effect of the Hartree-Fock non-locality expressed by the SK3 nucleon effective mass as well as the action of creation and descruction of 1p 1h pairs on the true ground state induced by the RPA residual interaction.     

A Total Measure of Multi-Particle Quantum Correlations in Atomic Schrödinger Cat States

We propose a total measure of multi-particle quantum correlation in a system of N two-level atoms (N qubits). We construct a parameter that encompasses all possible quantum correlations among N two-level atoms in arbitrary symmetric pure states and define its numerical value to be the total measure of the net atom-atom correlations. We use that parameter to quantify the total quantum correlations in atomic Schrödinger cat states, which are generated by the dispersive interaction in a cavity. We study the variation of the net amount of quantum correlation as we vary the number of atoms from N=2 to N=100 and obtain some interesting results. We also study the variation of the net correlation, for fixed interaction time, as we increase the number of atoms in the excited state of the initial system, and notice some interesting features. We also observe the behaviour of the net quantum correlation as we continuously increase the interaction time, for the general state of N two-level atoms in a dispersive cavity.     

Coupling effects of resonant and discretized non-resonant continuum states in 4He + 6Li scattering at 10 MeV/A

Alpha-particle scattering from the resonant (3 ₁ ⁺ ) and non-resonant continuum states of ⁶Li is studied at incident energy 10 MeV/A. The α + d breakup continuum part within the excitation energy E _ex = 1.475–2.475 MeV is discretized in two energy bins. Unlike the results at higher incident energies, here the coupled-channel calculations show significant breakup continuum coupling effects on the elastic and inelastic scattering. It is shown that even when the continuum-continuum coupling effects are strong, the experimental data of the ground state and the resonant as well as discretized non-resonant continuum states impose stringent constraint on the coupling strengths of the non-resonant continuum states.     

Anisotropic intermolecular potential from nuclear spin-lattice relaxation in hexafluoride gases

The data on fluorine spin-lattice relaxation times per unit densityT _jσ in pure SF₆ and UF₆ gases can be analyzed to obtain information on the anisotropic part of the intermolecular potential in these systems. A new and more performant potential, Morse-Morse-Spline-van der Waals potential (J. Chem. Phys.94, 1034 (1991)) was used for the isotropic part of the intermolecular interaction. The analysis was made using the Bloom-Oppenheim theory, assuming, that the correlation time of the spin-rotation interaction can be approximated by the average lifetime of a molecule in a givenJ state. We have obtained the strengths of the repulsive and attractive terms in the anisotropic potential. From the strength of the attractive term, the hexadecapole moment of SF6 and UF6 were also obtained, being in good agreement with the values reported earlier, based on other potentials and techniques.     

Variation of potential energy surface height and bound state depth induced by laser phase along the reaction path in atom-molecule reactions: Application to Li + CH<Subscript>4</Subscript> → LiH + CH<Subscript>3</Subscript>

Laser atom-molecule reaction interaction through polarizability and dipole moment contribution leads to potential energy surface barrier reshaping and bound states along the reaction path. The polarizability is maximum in the transition state. We will show here by using gauge representation (electric field gauge) for wave length λ = 20.6 μm, intensity I = 1 × 10¹² W/cm², I = 5 × 10¹² W/cm², I = 1 × 10¹³ W/cm², I = 3 × 10¹³ W/cm², that we can create laser induced potential energy surface barrier reshaping in the transition state region (–1–0.5 a. u.). We illustrate such effects for the LiH + CH₃ ? Li + CH₄ reaction with a barrier using ab-initio methods for calculating the reaction path, polarizability and dipole moment contribution of the atom-molecule reaction.     

The pseudogap and superconducting gap in the ab-plane electronic Raman continuum of YBa2Cu4O8

We report plane-polarised Raman spectra from YBa₂Cu₄O₈ single crystals between 300 and 10 K. In the normal state we observe a gap-like depletion of intensity from the electronic continuum extending to around 1200 cm⁻¹ with an onset temperature of around 225 K. We remove the phonons and pseudogap depletion from the spectra using a simple model and recover a characteristic high-T_c superconductor continuum. In the superconducting state, intensity returns to the continuum in the form of a very broad pair-breaking peak.     

Bound states of three and four resonantly interacting particles

We present an exact diagrammatic approach for the problem of dimer-dimer scattering in 3D for dimers being a resonance bound state of two fermions in a spin-singlet state, with corresponding scattering length a _F . Applying this approach to the calculation of the dimmer-dimer scattering length a _B , we recover exactly the already known result a _B = 0.6 a _F . We use the developed approach to obtain new results in 2D for fermions and bosons. Namely, we calculate bound state energies for three bbb and four bbbb resonantly interacting bosons in 2D. For the case of resonance interaction between fermions and bosons, we exactly calculate bound state energies of the following complexes: two bosons plus one fermion bbf, two bosons plus two fermions bf↑bf↓, and three bosons plus one fermion bbbf.     

The absorption spectrum of beryllium

Energy terms, dipole oscillator strengths and photoionization cross-sections from the ground state are calculated. Autoionizing state transition energies and line widths for the ¹P⁰ resonances in the continuum are also obtained. The configuration interaction method for initial and final states is used, and atomic orbitals are generated through angular-momentum-dependent, scaled Thomas-Fermi-Dirac potentials.     

Three-body model of deuteron breakup and stripping

For a three-body model Hamiltonian, the scattering eigenfunction that corresponds to an incident deuteron is expanded in terms of eigenfunctions of the neutron-proton relative Hamiltonian, as suggested by Johnson and Soper. In this expansion, breakup is represented by an integral over the continuum of neutron-proton scattering states. Only states of zero relative angular momentum are included; the validity and advantages of this approximation are discussed. The continuum is divided into five discrete channels, whose coupling to each other and to the deuteron channel is treated by solving coupled differential equations with appropriate boundary conditions. It is found necessary to use a simple WKB method to take account of the long-range coupling among breakup channels; this method introduces potential matrices W and S that describe local and derivative coupling of the channels. The reaction of breakup on the elastic channel is neglected.The properties of W and S and the breakup wavefunction are examined for the case of 22.9 MeV deuterons incident on a target of mass number A ≈ 40. The Coulomb interaction is ignored, and a local Gaussian shape is used for both the real and imaginary parts of the nucleon-nucleus optical potential.It is found that a rather broad spectrum of n-p continuum states is excited, especially for low center-of-mass angular momentum. This result weakens the justification for the Johnson-Soper adiabatic theory, which emphasizes breakup into states of low relative energy.The breakup part of the wavefunction at zero n-p separation is comparable with the elastic part, but is important only over a surprisingly short range in the center-of-mass coordinate, with the result that breakup cross sections are quite small. Nevertheless, breakup produces major modifications of (d, p) cross sections. These modifications can to some extent be simulated by the Johnson-Soper method. The breakup wavefunctions show several interesting effects in their dependence on angular momentum and radius.