The intermolecular potential of HF

The functional form of separate contributions to the intermolecular potential between small dipolar molecules has been analysed using the HF intermolecular potential as an example. The SCF energy was partitioned into first order electrostatic and exchange terms and higher order terms, called the polarization energy, which can be obtained by iterating the wavefunction to self consistency. A comparison was made for each term between a bipolar expansion about a single centre in each molecule and spherically symmetric site-site models. The overlap dependent part of the electrostatic energy could be combined with the exchange energy to give a single term which we call the repulsion energy and this was most accurately represented by a six term bipolar expansion. The polarization energy has a long range (R ^-6) component and an overlap dependent component and both could be separately represented by a two-term bipolar expansion. A semiempirical estimate was made of the dispersion energy and the total potential predicts a geometry of the HF dimer in good agreement with experiment. The predicted binding energy of the dimer is 17 kJ mol^-1 which is slightly smaller than a previous empirical estimate (23 kJ mol^-1).     

The interaction between first excited state hydrogen atoms and a different non-degenerate atom: an example of second-order resonance forces

The interaction of a first excited state hydrogen atom with a different non-degenerate atom is considered in the R ^-1 multiple approximation. The interaction energies for the Π states arising from this interaction have the form usually associated with second-order dispersion energies while those for the Σ states behave quite differently as a function of R. Because of a second-order ‘resonance within one molecule effect’ the second-order Σ-state energies do not possess single R ^-1 expansions that are formally valid for all values of R consistent with the multipole treatment. The expansions of these Σ-state energies, that are valid for ‘small’ R, contain terms varying as both even and odd powers of R ^-1; the lead R ^-7 ‘odd’ term competes strongly with the usual R ^-6 dispersion energy. The expansions that are valid for ‘large’ R contain terms varying as even powers of R ^-1 only and usually have little physical meaning. The He(¹S)-H(n=2) interaction is considered as a specific example of these results and the interaction energies for this system are evaluated through O(R ^-8) by using one-centre pseudostate methods. The general significance of the results is also discussed briefly.     

Charge overlap effects dependence on the nature of the interaction

The He-He, He-H(1s), H(1s)-H(1s) and H(1s)-H(2s) interactions are considered as model systems for studying how charge overlap effects in second-order dispersion energies vary as a function of the nature of the interacting species. The non-expanded second-order energy and the corresponding multipole R ^-1 expansions, through all powers of R ^-1, are obtained for each interaction using Unsöld's average energy approximation. The results are used to discuss the limitations of the usefulness of the R ^-1 expansions.     

A simple route to the energy shift between an electrically polarizable molecule and a magnetically susceptible molecule via the electromagnetic energy density

The van der Waals dispersion interaction between a molecule that is electrically polarizable and one that is magnetically susceptible, is recalculated within the framework of non-relativistic quantum electrodynamics. The energy shift is obtained in a simple way by calculating the response of a test polarizable body to the electromagnetic energy density due to a second source molecule. It is confirmed that the near-zone asymptote of the potential between an electric dipole polarizable molecule and a paramagnetic one varies as R ^{? 4}. Inclusion of the often neglected diamagnetic coupling term, however, results in an R ^?5 dependent short-range behaviour, which is seen to dominate over the paramagnetic contribution in the near-zone. For larger intermolecular distances, the expected R ^?7 dependence on separation is found for both paramagnetic and diamagnetic susceptible molecules interacting with an electric dipole polarizable one.     

Statistical thermodynamics of isolated rigid rod-like molecules near a surface

The configurational behaviour and thermodynamic properties of a dilute gas of rigid rod-like molecules in the vicinity of a macroscopic planar adsorption surface are investigated using statistical mechanics. The interaction energy between the surface and a rod-like molecule is determined as a function of both its molecular centre of mass separation R and its orientation relative to the surface. In calculating this interaction energy, each rod segment and molecule comprising the surface is assumed to interact through a Lennard-Jones pair potential. The average molecular order parameter is then determined as a function of R. We find that an isolated rod-like molecule tends to align nearly parallel to the surface for small separations. However, as R increases the order parameter first passes through a maximum then decays to zero as R ^-5 for large R. The configurational behaviour of an isolated rod-like molecule located between two parallel adsorption surfaces is also considered briefly. The surface spreading pressure, excess surface energy and entropy are also obtained for a dilute gas of rod-like molecules near a surface. We find that the extent of surface binding increases nearly exponentially with molecular length at constant temperature and surface density, and that the excess surface energy and entropy are essentially proportional to the molecular length.     

The neutron/proton ratio of fast nucleon emission in antiproton annihilation on nuclei

The measurement of fast protons and neutrons emitted after antiproton annihilation at rest on²³⁸U and⁶³Cu reveals a large neutron/proton ratioR. Its value for⁶³Cu is larger than expected from the conventional model of intranuclear pion rescattering. A value ofR essentially constant over the whole range of mass number, from¹²C up to²³⁸U, is also announced by the experimentalists. It is shown that, on the contrary, the conventional scheme predicts a regular increase ofR with mass number. Alternative explanations of the effect are looked for. Within the usual scheme, an excess of negative pions, leading to more emitted neutrons, is not compatible with final pion multiplicities. The influence of meson resonances on the neutron/proton ratio is considered, as well as the possible occurrence of annihilations on two nucleons. They cannot warrant an increase ofR at low mass targets sufficient to explain a constant value over the whole range of target masses.     

Three‐Phonon and Four‐Phonon Interaction Processes in a Pair‐Condensed Fermi Gas

We study the interactions among phonons and the phonon lifetime in a pair‐condensed Fermi gas in the BEC‐BCS crossover in the collisionless regime. To compute the phonon‐phonon coupling amplitudes we use a microscopic model based on a generalized BCS Ansatz including moving pairs, which allows for a systematic expansion around the mean field BCS approximation of the ground state. We show that the quantum hydrodynamic expression of the amplitudes obtained by Landau and Khalatnikov apply only on the energy shell, that is for resonant processes that conserve energy. The microscopic model yields the same excitation spectrum as the Random Phase Approximation, with a linear (phononic) start and a concavity at low wave number that changes from upwards to downwards in the BEC‐BCS crossover. When the concavity of the dispersion relation is upwards at low wave number, the leading damping mechanism at low temperature is the Beliaev‐Landau process 2 phonons ? 1 phonon while, when the concavity is downwards, it is the Landau‐Khalatnikov process 2 phonons ? 2 phonons. In both cases, by rescaling the wave vectors to absorb the dependence on the interaction strength, we obtain a universal formula for the damping rate. This universal formula corrects and extends the original analytic results of Landau and Khalatnikov [ZhETF 19 , 637 (1949)] for the 2?2 processes in the downward concavity case. In the upward concavity case, for the Beliaev 1? 2 process for the unitary gas at zero temperature, we calculate the damping rate of an excitation with wave number q including the first correction proportional to q ⁷ to the q ⁵ hydrodynamic prediction, which was never done before in a systematic way.     

Generalizations of Quantum Mechanics Induced by Classical Statistical Field Theory

No Heading We show that the Dirac-von Neumann formalism for quantum mechanics can be obtained as an approximation of classical statistical field theory. This approximation is based on the Taylor expansion (up to terms of the second order) of classical physical variables – maps f : Ω → R, where Ω is the infinite-dimensional Hilbert space. The space of classical statistical states consists of Gaussian measures ρ on Ω having zero mean value and dispersion σ²(ρ) ≈ h. This viewpoint to the conventional quantum formalism gives the possibility to create generalized quantum formalisms based on expansions of classical physical variables in the Taylor series up to terms of nth order and considering statistical states ρ having dispersion σ²(ρ) = hⁿ (for n = 2 we obtain the conventional quantum formalism).     

Quark structure and weak decays of heavy mesons

We construct a cellular space which has as a continuous limit the Euclidean spaceR ^N . We consider quantum mechanics on this cellular space and we examine in particular an harmonic oscillator and a free particle on the cellularR ¹,R ² respectively. In both cases we find that the energy spectrum is bounded from above.Partially supported by CEC Science project No SC1-CT91-0729     

Accurately solving the electronic Schrödinger equation of atoms and molecules using explicitly correlated (r 12-)MR-CI IV. The helium dimer (He 2)

The helium dimer interaction potential is computed using the recently proposed (explicitly correlated) r ₁₂-MR-ACPF (averaged coupled-pair functional) method and a [11s8p6d5f4g] basis set. With an MR-ACPF ansatz that contains 121 references we obtain interaction energies that are close to full CI. In a smaller reference space containing 9 functions, however, even by successively adding [3h] and [2i] functions to the basis set mentioned above, the basis set limit could not be reached. While convergence to the basis set limit is slow, it nevertheless is monotonic and therefore allows for extrapolation to the limit. We obtain basis set corrections at R = 4 a ₀ and 5.6 a ₀ which we further extend to all distances and which we apply to the potential energy curve mentioned above. From our calculations, we conclude that a very recent potential which has been calculated using the SAPT (symmetry adapted perturbation theory) method, and which previously was assumed to be the most accurate available, is insufficiently repulsive at short distances. We correct our extrapolated potential for retardation and finally calculate the expectation value of the interatomic distance (?R?) and dissociation energy (D ₀) by solving the Schrödinger equation of the vibrating ⁴He₂. Our results (?R? = 41 ± 13 Å and D ₀ = 2.2 ± 1.0 mK) are in acceptable agreement with very recent calculations in the literature, but they disagree with a recent experiment.     

Modification of Dispersion Relations and Generalization of the Hartree-Fock Method for Hard-Core Interactions in Nuclear Matter

The influence of a hard-core part in the interaction on dispersion relations for the generalized optical potential (mass operator) and the T-matrix of nuclear matter is investigated in the frame-work of the A⁰⁰-approximation. The model is based on the two-nucleon scattering problem in vacuo, for which a hard-core generalization of the Low equation is derived. As a consequence, T-matrix and mass operator are shown to split into a polynomial of the first order in the energy variable and a dispersion integral generalized by a limiting process, so that dispersion relations of the twice subtracted type result. Restriction to a self-consistent calculation of the non-dispersive term of the mass operator leads to a close analogue of the Hartree-Fock equations for non-singular interactions. This simple approximation which avoids the full-nucleon problem is shown to yield a qualitatively correct density dependence of the ground-state energy possibly to be improved by more realistic interactions. A formulation as an eigenvalue problem for finite nuclei is also given.     

Effect of non‐extensivity parameter q on the damping rate of dust ion acoustic waves in non‐extensive dusty plasma

Kinetic theory has been applied to study the damping characteristics of dust ion acoustic waves (DIAWs) in a dusty plasma comprising q‐non‐extensive distributed electrons and ions, while the dust particles are considered extensive following the Maxwellian velocity distribution function. It is found that the results of the three‐dimensional velocity distribution function are more accurate compared to the results of the one‐dimensional velocity distribution function. The numerical solution of the dispersion relation is carried out to study the effect of the non‐extensivity parameter q on the dispersion, the damping rate, and the range of the values of the normalized wavenumber ( k λ_D) for which the DIAWs are weakly damped. It is found that the change in the value of the electron non‐extensivity parameter q_e has a minor effect on the dispersion, the damping rate, and the range of the values of the normalized wavenumber ( k λ_D) for which the DIAWs are weakly damped, while on the other hand, ion non‐extensivity parameter q_i has a strong effect on these arguments. The effect of other parameters, such as the ratio of electron to ion number density and ratio of electron to ion temperature, on the damping characteristics of DIAWs is also highlighted.     

Slow Motion of Charges¶Interacting Through the Maxwell Field

We study the Abraham model for N charges interacting with the Maxwell field. On the scale of the charge diameter, R _ϕ, the charges are a distance ɛ^-1 R _ϕ apart and have a velocity with ɛ a small dimensionless parameter. We follow the motion of the charges over times of the order ɛ^-3/2 R _ϕ/c and prove that on this time scale their motion is well approximated by the Darwin Lagrangian. The mass is renormalized. The interaction is dominated by the instantaneous Coulomb forces, which are of the order ɛ². The magnetic fields and first order retardation generate the Darwin correction of the order ɛ³. Radiation damping would be of the order ɛ^7/2. Received: 13 January 2000 / Accepted: 4 February 2000     

De Sitter solutions in higher order gravity

We consider de Sitter solutions, relevant for instance in studies of inflation, in cosmologies where the gravitational Lagrangian is a functionf(R),R being the scalar curvature. Previous investigations have mostly concentrated onf(R) = R+R² which always has a solution matching the conventional de Sitter one. We show that this circumstance is rather exceptional, and that one must go to higher terms to see signs of the generic behaviour, In general the de Sitter solutions are different from those of Einstein gravity. We present complete solutions for the general cubic Lagrangian. We also address the question of when the solutions to equations from truncated actions can be expected to well represent solutions of some full (and possibly unknown) theory. Such theories provide the possibility of weakening the bounds on the energy density of the inflaton, allowing an easier reconciliation of the inflationary universe with structure-forming topological defects.     

Modified Gravity with ln R Terms and Cosmic Acceleration

The modified gravity with ln R or R ^–n (ln R) ^m terms which grow at small curvature is discussed. It is shown that such a model which has a well-defined Newtonian limit may eliminate the need for dark energy and may provide the current cosmic acceleration. It is demonstrated that R ² terms are important not only for early time inflation but also to avoid the instabilities and the linear growth of the gravitational force. It is very interesting that the condition of no linear growth for gravitational force coincides with the one for scalar mass in the equivalent scalar-tensor theory to be very large. Thus, modified gravity with R ² term seems to be a viable classical theory.     

A theoretical perspective on the accuracy of rotational resonance (R 2)-based distance measurements in solid-state NMR

The application of solid-state NMR methodology for bio-molecular structure determination requires the measurement of constraints in the form of ¹³C–¹³C and ¹³C–¹⁵N distances, torsion angles and, in some cases, correlation of the anisotropic interactions. Since the availability of structurally important constraints in the solid state is limited due to lack of sufficient spectral resolution, the accuracy of the measured constraints become vital in studies relating the three-dimensional structure of proteins to its biological functions. Consequently, the theoretical methods employed to quantify the experimental data become important. To accentuate this aspect, we re-examine analytical two-spin models currently employed in the estimation of ¹³C–¹³C distances based on the rotational resonance (R ²) phenomenon. Although the error bars for the estimated distances tend to be in the range 0.5–1.0 Å, R ² experiments are routinely employed in a variety of systems ranging from simple peptides to more complex amyloidogenic proteins. In this article we address this aspect by highlighting the systematic errors introduced by analytical models employing phenomenological damping terms to describe multi-spin effects. Specifically, the spin dynamics in R ² experiments is described using Floquet theory employing two different operator formalisms. The systematic errors introduced by the phenomenological damping terms and their limitations are elucidated in two analytical models and analysed by comparing the results with rigorous numerical simulations.     

Role of equilibrium plasma flow on damping of slow MHD waves

In the solar corona waves and oscillatory activities are observed with modern imaging and spectral instruments. These oscillations are interpreted as slow magneto-acoustic waves excited impulsively in coronal loops. This study explores the effect of steady plasma flow on the dissipation of slow magneto-acoustic waves in the solar coronal loops permeated by uniform magnetic field. We have investigated the damping of slow waves in the coronal plasma taking into account viscosity and thermal conductivity as dissipative processes. On solving the dispersion relation it is found that the presence of plasma flow influences the characteristics of wave propagation and dissipation. We have shown that the time damping of slow waves exhibits varying behavior depending upon the physical parameters of the loop. The wave energy flux associated with slow magnetoacoustic waves turns out to be of the order of 10⁶ erg cm⁻² s⁻¹ which is high enough to replace the energy lost through optically thin coronal emission and the thermal conduction below to the transition region.     

新型矩形点阵光子晶体光纤的高双折射负色散效应

设计了一种新型矩形点阵光子晶体光纤,该光纤纤芯缺失一根空气柱,包层沿光纤长度方向在普通矩形点阵光子晶体光纤中每两列之间隔一行插入一列空气孔而形成正方形网孔结构.采用全矢量有限元法并结合各向异性完美匹配边界条件,对该光纤的色散、双折射和约束损耗进行了数值模拟.结果发现,该光纤具有高双折射负色散效应和较强的模约束能力,约束损耗小于10-2dB·m-1,通过改变光纤结构参数(即空气孔间隔Λ和相对孔间隔d/Λ),可以调节该光纤高双折射负色散工作波长.若调整光纤结构参数Λ=2.0μm,d/Λ=0.4,该光纤在C波段(1.53—1.565μm)呈现负色散并具有负色散斜率,双折射高达10-2,非线性系数接近55km-1W-1.该光纤将在保偏光通信、色散补偿以及基于四波混频的波长转换器设计等方面具有重要的应用.