Quadrupole-quadrupole Interaction Research Articles

An ab Initio Study of van der Waals Potential Energy Parameters for Silver Clusters

We employ ab initio calculations of van der Waals complexes to study the potential energy parameters (C(6) coefficients) of van der Waals interactions for modeling of the adsorption of silver clusters on the graphite surface. Electronic structure calculations of the (Ag(2))(2), Ag(2)-H(2), and Ag(2)-C(6)H(6) complexes are performed using a coupled-cluster approach that includes single, double, and perturbative triple excitations (CCSD(T)), Møller-Plesset second-order perturbation theory (MP2), and spin-component-scaled MP2 (SCS-MP2) methods. Using the atom pair approximation, the C(6) coefficients for silver-silver, silver-hydrogen, and silver-carbon atom systems are obtained after subtracting the energies of quadrupole-quadrupole interactions from the total electronic energy.

Anisotropy in the interaction of ultracold dysprosium

The nature of the interaction between ultracold atoms with a large orbital and spin angular momentum has attracted considerable attention. It was suggested that such interactions can lead to the realization of exotic states of highly correlated matter. Here, we report on a theoretical study of the competing anisotropic dispersion, magnetic dipole-dipole, and electric quadrupole-quadrupole forces between two dysprosium atoms. Each dysprosium atom has an orbital angular momentum of L = 6 and a magnetic moment of μ = 10 μ(B). We show that the dispersion coefficients of the ground state adiabatic potentials lie between 1865 a.u. and 1890 a.u., creating a non-negligible anisotropy with a spread of 25 a.u. and that the electric quadrupole-quadrupole interaction is weak compared to the other interactions. We also find that for interatomic separations R < 50a(0) both the anisotropic dispersion and magnetic dipole-dipole potential are larger than the atomic Zeeman splittings for external magnetic fields of order 10 G to 100 G. At these separations the atomic angular momentum can be reoriented. We finish by describing two scattering models for these inelastic m-changing collisions. A universal scattering theory is used to model loss due to the anisotropy in the dispersion and a Born approximation is used to model losses from the magnetic dipole-dipole interaction for the (164)Dy isotope. These models find loss rates that are of the same order of magnitude as the experimental value.

Photoassociation of a cold-atom–molecule pair: Long-range quadrupole-quadrupole interactions

The general formalism of the multipolar expansion of electrostatic interactions is applied to the calculation the potential energy between an excited atom (without fine structure) and a ground state diatomic molecule at large separations. Both partners exhibit a permanent quadrupole moment, so that their mutual quadrupole-quadrupole long-range interaction is attractive enough to bind trimers. Numerical results are given for an excited Cs(6P) atom and a ground state Cs2 molecule. The prospects for achieving photoassociation of a cold atom/dimer pair is thus discussed and found promising. The formalism can be easily generalized to the long-range interaction between molecules to investigate the formation of cold tetramers.

Highly Selective Carbon Dioxide Sorption in an Organic Molecular Porous Material

The organic molecular porous material 1 obtained by recrystallization of cucurbit[6]uril (CB[6]) from HCl shows a high CO(2) sorption capacity at 298 K, 1 bar. Most interestingly, 1 showed the highest selectivity of CO(2) over CO among the known porous materials so far. The remarkable selectivity of CO(2) may be attributed to the exceptionally high enthalpy of adsorption (33.0 kJ/mol). X-ray crystal structure analysis of CO(2) adsorbed 1 revealed three independent CO(2) sorption sites: two in the 1D channels (A and B) and one in the molecular cavities (C). The CO(2) molecules adsorbed at sorption site A near the wall of the 1D channels interact with 1 through hydrogen bonding and at the same time interact with those at site B mainly through quadrupole-quadrupole interaction in a T-shaped arrangement. Interestingly, two CO(2) molecules are included in the CB[6] cavity (site C), interacting not only with the carbonyl groups of CB[6] but also with each other in a slipped-parallel geometry. The exceptionally selective CO(2) sorption properties of 1 may find useful applications in the pressure swing adsorption (PSA) process for CO(2) separation not only in the steel industry but also in other industries such as natural gas mining.

Investigations of proton-neutron correlations close to the drip line

Proton-neutron correlations in nuclei above the $Z=50$ shell closure are investigated with the aim of understanding the behavior of the $2$${}^{+}$ and $4$${}^{+}$ states in Te and Xe isotopes, which remain at a rather constant energy as one approaches the shell closure at $N=50$. Our calculations reveal that standard quasiparticle random phase approximation calculations, involving a quadrupole-quadrupole (QQ) interaction with constant strengths, cannot explain this feature. It is found that to reproduce the experimental data within this model one has to include a variable proton-neutron interaction. It turns out that an increased proton-neutron QQ interaction increases the collectivity (i.e., $B(E2)$ values) when approaching the $N=50$ region, whereas an increased proton-neutron pairing interaction decreases the collectivity. We thus conclude that the ratio between the $B(E2)$ value and ${2}^{+}$ energy is a ``fingerprint'' of proton-neutron collectivity and it should be determined in future experiments concerning light Te isotopes. Based on this criterion, we conclude that the available experimental data indicate an enhanced proton-neutron pairing interaction by approaching doubly magic $Z=N=20$ and $Z=N=28$ regions.

Transfer strengths to the0+states excited by (p,t) reactions inBa130,132,134

The aim of this work is to calculate the transfer strengths to the excited ${0}^{+}$ states in $^{130,132,134}\mathrm{Ba}$ which have been identified in ($p,t$) reactions and to investigate their related properties. For this purpose, we have used a model Hamiltonian which includes monopole pairing, quadrupole-quadrupole, and spin-quadrupole interactions. The model Hamiltonian has been diagonalized with the random phase approximation (RPA). To investigate the general trend of the transfer strengths to the excited ${0}^{+}$ states, two-nucleon transition intensities relative to the transition to the ground state and their cumulative values have been calculated versus energy and compared with the data. The comparisons revealed that fairly good results for the distribution of the energies and the transfer strengths have been obtained. For almost all nuclei, the cumulative values of the transfer strengths were nicely predicted. Moreover, qualitatively, a parallel result that agrees with the data and the prediction of the O(6) limit of the IBM model which is a weak excitation for the first ${0}^{+}$ state and a strong one for the second ${0}^{+}$ state has been obtained for $^{130}\mathrm{Ba}$ and $^{132}\mathrm{Ba}$.

Phase transitions in algebraic cluster models

Two algebraic cluster models are studied from the point of view of phase transitions: one in which the Pauli exclusion principle is taken into account and one in which it isn't. A third-order interaction is introduced to avoid instabilities in the model spectra, which is generally not taken into account. It is shown that both first- and second-order phase transitions occur. The 20Ne→16O+α system is considered as an example. Without taking into account the Pauli exclusion principle the transition from the SU(3) to the SO(4) dynamical symmetry is of first or second order, depending on the strength of the quadrupole-quadrupole interaction. It is shown that the inclusion of the Pauli-principle can be simulated by higher-order interactions when the model space is not truncated.

EFFECTS OF VIBRATIONAL AND PAIRING CORRELATIONS ON ISOSPIN MIXING IN THE HIGHER TAMM-DANCOFF APPROXIMATION

In the framework of the Higher Tamm-Dancoff Approximation which allows for a consistent treatment of pairing and quadrupole vibrational correlations preserving the particle-number symmetry and the Pauli principle, we compare the isospin content of ground and excited Kπ = 0+ states including either type of the above mentioned correlations using an approximate projection-after-variation technique for isospin. The pairing correlations are described with a delta interaction using the same strength in the T = 0 and T = 1 channels, whereas the vibrational correlations are treated with an isoscalar quadrupole-quadrupole interaction. As a first study, we apply this approach in the N = Z, even-even 16 O nucleus. For the same amount of correlations measured by the diffusivity of Fermi surface or depletion of particle-hole vacuum in the ground-state solution, we find very similar isospin mixing in the ground state for both types of correlations, but different patterns for the distribution in the calculated solutions of the expectation value of the square of the isospin operator.

Quadrupolar contact fields: Theory and applications

Contact terms for the electric dipole and magnetic dipole fields are well known. We give a simple derivation of the contact term of the electric quadrupole field. We then consider applications to the surface potential across a vapor/liquid interface of a nonpolar fluid, an extension of Jackson’s theorems for the mean electric fields for spherical regions of space with and without a fixed system of charges, and hyperfine interactions due to the electric quadrupole-monopole and quadrupole-quadrupole interactions of two bound particles of spin one or greater.

Nuclear scissors with pairing and continuity equation

The coupled dynamics of the isovector and isoscalar giant quadrupole resonances and low lying modes (including scissors) are studied with the help of the Wigner Function Moments (WFM) method generalized to take into account pair correlations. Equations of motion for collective variables are derived on the basis of the Time Dependent Hartree-Fock-Bogoliubov (TDHFB) equations in the harmonic oscillator model with quadrupole-quadrupole (QQ) residual interaction and a Gaussian pairing force. Special care is taken of the continuity equation.

Low-lying states of heavy nuclei within the nucleon pair approximation

In this article we perform systematic calculations on low-lying states of 33 nuclei with A=202-212, using the nucleon pair approximation of the shell model. We use a phenomenological shell-model Hamiltonian that includes single-particle energies, monopole and quadrupole pairing interactions, and quadrupole-quadrupole interactions. The building blocks of our model space include one J=4 valence neutron pair, and one J=4,6,8 valence proton pair, in addition to the usual S and D pairs. We calculate binding energies, excitation energies, electric quadrupole and magnetic dipole moments of low-lying states, and E2 transition rates between low-lying states. Our calculated results are reasonably consistent with available experimental data. The calculated quadrupole moments and magnetic moments, many of which have not yet been measured for these nuclei, are useful for future experimental measurements.

The quenching of excited F(2 P 1/2) and Cl(2 P 1/2) atoms by N2(X 1Σ g + ) molecules

The rate constant for the quenching of excited F(2P1/2) and Cl(2P1/2) atoms in collisions with N2 molecules were calculated. The electron interaction matrix between N2(X1Σg+) and F and Cl atoms in the 2Pj state calculated asymptotically taking into account quadrupole-quadrupole, dispersion, and exchange interactions was used. The dynamic problem of electronic transitions was solved using the modified wave number approximation, the exactly solvable semiclassical exponential nonadiabatic bond model, and the method of phase functions.

Zero-phonon emission bands of solid hydrogen at 6–12μm wavelength. An astrophysical phenomenon

Infrared emission bands in the wavelength range of 6–12μm observed in the ISO-SWS mission are assigned to rotational zero-phonon bands of solid parahydrogen by using Van Kranendonk’s approximate rigid-lattice method. This method is based on superposed electric quadrupole pair interactions and superposed quadrupole induced dipole moments of pairs in the hcp crystal. Accordingly, the approximate formalism uses zero-order H2 pair wave functions. Symmetry effects of the hcp crystal require preference of rotational pair transitions. The interaction potential of the pairs is confined to the electric quadrupole-quadrupole interaction. Zero-phonon emission bands of H2 pair transitions fitted to the spectrum contain at least one delocalized j=2 state initially and/or finally because of their significantly enhanced emission rates. They also yield the characteristic bandwidths which fit nicely to the widths of the observed features. The frequency positions of the seven pure parahydrogen pair transitions used, obtained from experimentally determined rotational solid hydrogen energy levels, are in perfect agreement with the observed features, whereas the three mixed ortho-parapair transitions need a presently unknown frequency correction, caused by the migration of the ortho-H2 molecules into the parahydrogen crystal prior to emission, the so-called initial excess binding energies. The astrophysical setup of the observed source is discussed in the end of the paper.

STM Imagingortho-andpara-Fluorothiophenol Self-Assembled Monolayers on Au(111)

Self-assembled monolayers (SAMs) of para- and ortho-fluorothiophenol (p- and o-FTP) spontaneously formed on Au(111) substrate have been contrasted through investigation by a scanning tunneling microscope (STM) at room temperature. High-resolution STM imaging reveals that p-FTP adopts a 6 x radical3R30 degrees molecule arrangement containing six molecules. Two different kinds of p-FTP molecule dimer line structures have been formed on Au(111) by intermolecular pi-pi stacking along 112 substrate directions, besides a single p-FTP molecule line. In contrast, o-FTP molecules self-assemble into a much looser wave-like SAM, which can be described as a 5 x 3 radical3R30 degrees structure containing two molecules. Periodic density functional theory (DFT) calculations for the two systems suggest that these kinds of FTP molecules preferentially take the asymmetrical positions between 3-fold face-centered cubic (fcc) hollow and bridge sites on Au(111), tilting from the substrate surface. Theoretical simulation gives apparent average tilted angles of 58 degrees and 68 degrees for p-FTP and o-FTP with respect to the surface normal, respectively. This simulation shows that o-FTP is more inclined to lie down toward the Au(111) surface compared to p-FTP. The difference between p-FTP and o-FTP SAM structures can be qualitatively understood in terms of the variation of intermolecular dipole-dipole orientation. This suggests that, besides well-known Au-S and pi-pi interactions, electrostatic interactions including dipole-dipole, quadrupole-quadrupole, and dipole-quadrupole interactions might also play an important role in influencing the SAM structures formed by aromatic thiols with a permanent dipole moment.

Coarse-grained models for fluids and their mixtures: Comparison of Monte Carlo studies of their phase behavior with perturbation theory and experiment

The prediction of the equation of state and the phase behavior of simple fluids (noble gases, carbon dioxide, benzene, methane, and short alkane chains) and their mixtures by Monte Carlo computer simulation and analytic approximations based on thermodynamic perturbation theory is discussed. Molecules are described by coarse grained models, where either the whole molecule (carbon dioxide, benzene, and methane) or a group of a few successive CH(2) groups (in the case of alkanes) are lumped into an effective point particle. Interactions among these point particles are fitted by Lennard-Jones (LJ) potentials such that the vapor-liquid critical point of the fluid is reproduced in agreement with experiment; in the case of quadrupolar molecules a quadrupole-quadrupole interaction is included. These models are shown to provide a satisfactory description of the liquid-vapor phase diagram of these pure fluids. Investigations of mixtures, using the Lorentz-Berthelot (LB) combining rule, also produce satisfactory results if compared with experiment, while in some previous attempts (in which polar solvents were modeled without explicitly taking into account quadrupolar interaction), strong violations of the LB rules were required. For this reason, the present investigation is a step towards predictive modeling of polar mixtures at low computational cost. In many cases Monte Carlo simulations of such models (employing the grand-canonical ensemble together with reweighting techniques, successive umbrella sampling, and finite size scaling) yield accurate results in very good agreement with experimental data. Simulation results are quantitatively compared to an analytical approximation for the equation of state of the same model, which is computationally much more efficient, and some systematic discrepancies are discussed. These very simple coarse-grained models of small molecules developed here should be useful, e.g., for simulations of polymer solutions with such molecules as solvent.

Hyperfine energy levels of alkali-metal dimers: Ground-state homonuclear molecules in magnetic fields

We investigate the hyperfine energy levels and Zeeman splittings for homonuclear alkali-metal dimers in low-lying rotational and vibrational states, which are important for experiments designed to produce quantum gases of deeply bound molecules. We carry out density-functional theory (DFT) calculations of the nuclear hyperfine coupling constants. For nonrotating states, the zero-field splittings are determined almost entirely by the scalar nuclear spin-spin coupling constant. By contrast with the heteronuclear case, the total nuclear spin remains a good quantum number in a magnetic field. We also investigate levels with rotational quantum number N = 1, which have long-range anisotropic quadrupole-quadrupole interactions and may be collisionally stable. For these states the splitting is dominated by nuclear quadrupole coupling for most of the alkali-metal dimers and the Zeeman splittings are considerably more complicated.

PROTON-NEUTRON INTERACTING BOSON-FERMION-FERMION MODEL AND THE EXCHANGE INTERACTIONS

The exchange interactions proper to the proton-neutron version of the interacting boson-fermion-fermion model are derived from the proton-neutron quadrupole-quadrupole interaction. The influence of the exchange interactions on the F-spin content of wave functions is analysed for a typical odd-odd nucleus.

Collective motion from various aspects

Three methods to describe collective motion, the Random Phase Approximation (RPA), Wigner Function Moments (WFM), and Green’s Function (GF) methods, are compared in detail and their physical content analyzed in the example of a simple model, a harmonic oscillator with quadrupole-quadrupole residual interaction. It is shown that they give identical formulae for eigenfrequencies and transition probabilities of all collective excitations of the model. The exact relation between the RPA and WFM variables and the respective dynamical equations is established. The transformation of the RPA spectrum into one of WFM is explained. The very close connection of the WFM method with the GF method is demonstrated. A differential equation describing the current lines of RPA modes is established and the current lines of the scissors mode are analyzed as a superposition of rotational and irrotational components. The orthogonality of the spurious state to all physical states is proved rigorously.

Effective shell model Hamiltonians from density functional theory: Quadrupolar and pairing correlations

We describe a procedure for mapping a self-consistent mean-field theory (also known as density functional theory) onto a shell-model Hamiltonian that includes quadrupole-quadrupole and monopole pairing interactions in a truncated space. We test our method in the deformed $N=Z \mathit{sd}$-shell nuclei $^{20}\mathrm{Ne}$, $^{24}\mathrm{Mg}$, and $^{36}\mathrm{Ar}$, starting from the Hartree-Fock plus Bardeen-Cooper-Schrieffer (BCS) approximation of the universal $\mathit{sd}$ shell-model interaction. A similar method is then followed using the SLy4 Skyrme energy density functional in the particle-hole channel plus a zero-range density-dependent force in the pairing channel. Based on the ground-state solution of this density functional theory at the Hartree-Fock plus BCS level, an effective shell-model Hamiltonian is constructed. We apply this mapped Hamiltonian to extract quadrupolar and pairing correlation energies beyond the mean-field approximation. The rescaling of the mass quadrupole operator in the truncated shell-model space is found to be almost independent of the coupling strength used in the pairing channel of the underlying mean-field theory.

High-temperature spin relaxation process inDy2Ti2O7probed byT47i-NQR

We have performed nuclear quadrupole resonance (NQR) experiments on $^{47}\text{T}\text{i}$ nuclei in ${\text{Dy}}_{2}{\text{Ti}}_{2}{\text{O}}_{7}$ in the temperature range of 70--300 K in order to investigate the dynamics of $4f$ electrons with strong Ising anisotropy. A significant change in the NQR frequency with temperature was attributed to the variation of the quadrupole moment of $\text{Dy}\text{ }4f$ electrons. A quantitative account was given by the mean-field analysis of the quadrupole-quadrupole (Q-Q) interaction in the presence of the crystalline-electric-field splitting. The magnitude and the temperature dependence of the nuclear spin-lattice relaxation rate were analyzed, including both the spin-spin and the Q-Q interactions. The results indicate that these two types of interaction contribute almost equally to the fluctuation of Dy magnetic moments.