Algebraic connectivity analysis in molecular electronic structure theory II: total exponential formulation of second-quantised correlated methods

The fundamentality of the exponential representation of a second-quantised correlated wave function is emphasised with an accent on the physical sense of cluster amplitudes as cumulants of the correlated ansatz. Three main wave function formalisms, namely, the configuration-interaction theory, the coupled-cluster approach, and the many-body perturbation theory (as well as their extensions, e.g. the equation-of-motion coupled-cluster method, multireference schemes, etc.), are represented in an exponential form, leading to a formulation of the working equations in terms of cluster amplitudes. By expressing the corresponding many-body tensor equations in terms of cluster amplitudes, we could unambiguously check connectivity types and the asymptotic behaviour of all tensors/scalars involved (in the formal limit of an infinite number of correlated particles). In particular, the appearance of disconnected cluster amplitudes corresponds to unphysical correlations. Besides, we demonstrate that the equation-of-motion coupled-cluster approach, as well as certain excited-state configuration-interaction methods, can be recast in a fully connected (exponential) form, thus breaking the common belief that all truncated configuration-interaction methods violate connectivity. Our work is based on the recently developed algebraic framework which can be viewed as a complement to the classical diagrammatic analysis.     

On the hierarchy equations of the wave-operator for open-shell systems

Starting with the open-shell analogue of the Gell Mann-Low theorem of many-body perturbation theory, a non-perturbative linear operator equation is derived for the linked part of the wave-operatorW for open-shell systems. It is shown that, for a proper treatment of the linked nature of the wave-operator, a separation into its connected and disconnected components has to be made, and this leads to a hierarchy of equations for the various connected components. It is proved that the set of equations can be cast into a form equivalent to the non-perturbative equations of the wave-operator recently derived by Mukherjee and others in a coupled-cluster or exp(T) type formalism if a consistent use is made of a ‘core-valence separability’ condition introduced earlier. A comparison of the coupled-cluster representation ofW with the perturbative representation reveals that various alternative forms ofW in the coupled-cluster representation are possible and these reflect alternative ways of realising the core-valence expansion of the wave-operator. In particular it is emphasised how the use of Mandelstam block-ordering simplifies the coupled-cluster theories to a considerable extent and a comparison is made with coupled-cluster methods for open-shells put forward very recently by Ey and Lindgren. Finally, it is shown how difference energies of interest may be derived in a compact manner using the Mandelstam block-ordering of the wave-operator.     

Strangeness enhancement in Cu-Cu and Au-Au collisions at √S(NN)=200 GeV

We report new STAR measurements of midrapidity yields for the Λ, Λ[over ˉ], K(S)(0), Ξ(-), Ξ[over ˉ](+), Ω(-), Ω[over ˉ](+) particles in Cu+Cu collisions at √S(NN)==200 GeV, and midrapidity yields for the Λ, Λ[over ˉ], K(S)(0) particles in Au+Au at √S(NN)==200 GeV. We show that, at a given number of participating nucleons, the production of strange hadrons is higher in Cu+Cu collisions than in Au+Au collisions at the same center-of-mass energy. We find that aspects of the enhancement factors for all particles can be described by a parametrization based on the fraction of participants that undergo multiple collisions.     

Coherent population trapping with a train of pulses via a continuum and its application to the suppression of excited-state absorption

We discuss the coherent population trapping (CPT) effect induced in a three-level Λ-type system by a train of short pulses. Specifically, we consider a modified Λ system with the upper level replaced by a continuum of states. We show that CPT with a train of pulses can be applied to the suppression of excited-state absorption of pump radiation in crystalline laser materials. The utility of the technique for pumping a promising yellow-orange solid-state medium Ti:YAlO₃ and overcoming excited-state pump absorption is analyzed.     

Efficient electronic structure theory via hierarchical scale-adaptive coupled-cluster formalism: I. Theory and computational complexity analysis

ABSTRACT

A novel reduced-scaling, general-order coupled-cluster approach is formulated by exploiting hierarchical representations of many-body tensors, combined with the recently suggested formalism of scale-adaptive tensor algebra. Inspired by the hierarchical techniques from the renormalisation group approach, H/H²-matrix algebra and fast multipole method, the computational scaling reduction in our formalism is achieved via coarsening of quantum many-body interactions at larger interaction scales, thus imposing a hierarchical structure on many-body tensors of coupled-cluster theory. In our approach, the interaction scale can be defined on any appropriate Euclidean domain (spatial domain, momentum-space domain, energy domain, etc.). We show that the hierarchically resolved many-body tensors can reduce the storage requirements to O(N), where N is the number of simulated quantum particles. Subsequently, we prove that any connected many-body diagram consisting of a finite number of arbitrary-order tensors, e.g. an arbitrary coupled-cluster diagram, can be evaluated in O(NlogN) floating-point operations. On top of that, we suggest an additional approximation to further reduce the computational complexity of higher order coupled-cluster equations, i.e. equations involving higher than double excitations, which otherwise would introduce a large prefactor into formal O(NlogN) scaling.     

Ab initio calculations of energy transfer and non-additivity in the He-Ne laser system

Ab initio calculations were performed for several suggested mechanisms of energy transfer between helium metastable particles and neon. Optimized geometries and excited-state energies were calculated for neon excited-state complexes and the convergence properties of the non-additive contributions to the interaction energies were examined. The most probable excitation-transfer mechanism was found to be based on an energy difference of 0.0674 eV between the triplet excited state of and the singlet excited state of . No theoretical evidence was found for the production of neon singlet excited-state complexes other than 20.0858 to 20.4875 eV by the considered two-, three- and four-body models of energy transfer processes. The energy curves of the reactions involving the excited-state complexes and are provided and compared with the previously reported experimental results on the reaction . The relation between the probability of energy transfer and laser activity is discussed. The non-additive contribution to the total interaction energy of the nominated intermediate complex was found to be negligible, pointing to the possibility of constructing model potentials and simulation of larger systems. Received: 15 December 1998 / Received in final form: 20 March 1999     

An alternative definition of the electron propagator in the superoperator form and its relation to linear response theory in a coupled-cluster framework

In this paper it is shown that (i) there exists an alternative definition of the superoperator resolvent for calculation of difference energy satisfying linked cluster theorem for a coupled-cluster choice of the ground-state function which may even be approximate; (ii) the pole-structure of this propagator-like function in superoperator form is shown to contain information similar to that contained in the conventional propagator. (iii) It is demonstrated that suitable “Killer conditions” and completeness of the “operator manifold”—essential for understanding the pole-structure of the propagator—can be established both for an exact and an approximate ground state function in a coupled-cluster form. (iv) It is also demonstrated that difference energies calculated with these propagator-like functions are identical to those obtained from a linear response theory in a coupled-cluster form put forward recently by Mukherjeeet al and Monkhorst.     

Interacting Dark Energy in the Dark <Emphasis Type="Italic">S</Emphasis><Emphasis Type="Italic">U</Emphasis>(2)<Subscript><Emphasis Type="Italic">R</Emphasis></Subscript> Model

We explore the cosmological implications of the interactions among the dark particles in the dark SU(2) _R model. It turns out that the relevant interaction is between dark energy and dark matter, through a decay process. With respect to the standard ΛCDM model, it changes only the background equations. We note that the observational aspects of the model are dominated by degeneracies between the parameters that describe the process. Thus, only the usual Λ CDM parameters such as the Hubble expansion rate and the dark energy density parameter (interpreted as the combination of the densities of the dark energy doublet) could be constrained by observations at this moment.     

On the effect of ΛΣ conversion on the Λ particle binding energy in nuclear matter

The Λ particle binding energy in nuclear matter is calculated with a phenomenological separable ΛN-ΣN potential matrix and with a separable NN potential. The calculation includes the three-body ΛNN cluster energy and the rearrangement energy, both of which give only relatively small contributions to the calculated substantial Σ suppression.     

On enhancement of Λ0 production in the proton-nucleus collisions and multiproduction models

Production of Λ⁰ in the particlenucleus interactions is shown to be a particularily clean signature of reabsorption of the produced particles inside a nucleus. We find a significant enhancement of a relative fraction ofp A collisions with two and three wounded constituent quarks of the projectile proton in the Λ⁰-containing events and predict resulting enhancement of the central rapidity density and mean multiplicity of charged particles and grey tracks in the Λ⁰ and Λ⁰Λ⁰-containingp Xe andp Ar collisions, studied by the NA5 collaboration. We predict multiplicities in the minimal bias and Λ⁰-containing deep-inelastic μXe collisions under study by E665 at FNAL.     

Average Λ-nucleus potentials

A few model Λ-nucleus potentials are proposed which explain the ground state binding energy data of⁵He and thep-shell hypernuclei satisfactorily. Potential-II is capable of distinguishing the hypernuclei of the same mass number but of differentN andZ values. The dependence of this potential on (N ? Z) term indicates that there is a charge symmetry breaking component in ΛN force. Alongwith the earlier density dependent effective Λ-nucleus interaction, these potentials may be used to determine approximately the density distributions of light nuclei. From these potentials an estimate ofD _Λ is also made. It is found to be in conformity with the earlier estimates.     

Two examples of in-flight spin flippers

In precise experiments with polarized beam it’s very often appear a necessity to change beam polarization on opposite. If such operation does not change other beam parameters, it helps to avoid or minimize some systematic errors. It is especially important in experiments, where spin dependent effect is small enough. This paper describes two set of equipments, that make spin flip for extracted beams. In both cases, these devices are absolutely distinct, because they are appropriate for different particles and at different energy range. The first of them is intended for future muon (g-2) experiment, which is under preparation now at JPARC. Here, the muon spin flip will be done by chain of electrostatic and magnetic bends at the kinetic energy 340 keV. A beam matching is provided by a number of short solenoids. The other flipper (or Siberian snake) will rotate spin of protons or antiprotons, which come from Λ-meson decay with the energy up to 40 GeV. This experiment (no. 24) is planed at IHEP, Protvino. In this case, two superconducting helical magnets with opposite helicities and magnetic field 4.5 T will be used. To correct beam trajectory, additional dipole correctors are required.     

He-HF体系各向异性势及分波散射截面的研究

用BFW势函数拟合在CCSD(T)/aug-cc-pVQZ理论水平下计算的He-HF相互作用能数据,获得了He原子与HF分子相互作用的各向异性势,并与已知的势模型进行比较,验证了拟合势的可靠性;然后采用密耦方法计算了He-HF体系在不同碰撞能量下的分波散射截面,总结了分波散射截面的变化趋势.研究表明:①拟合势不但表达形式简洁,而且较好地描述了He-HF系统相互作用的各向异性特征.②入射粒子的能量越高,得到收敛的分波截面所需的分波数越多,量子效应越不显著,尾部效应也越弱;尾部效应仅在低激发态中产生,高激发态不产生尾部效应.     

Accelerating Universe with spacetime torsion but without dark matter and dark energy

It is shown that cosmological equations for homogeneous isotropic models deduced in the framework of the Poincaré gauge theory of gravity by certain restrictions on indefinite parameters of gravitational Lagrangian take at asymptotics the same form as cosmological equations of general relativity theory for ΛCDM-model. Terms related to dark matter and dark energy in cosmological equations of standard theory for ΛCDM-model are connected in considered theory with the change of gravitational interaction provoked by spacetime torsion.     

Das Konsistenzproblem der Greenfunktion eines A-Hyperons in Kernmaterie

An iteration procedure is derived for determining a self-consistent approximation for the one-particle Green's function in any order, starting from perturbation theory. This method is used to calculate the second Born approximation of the self energy of a Λ-particle in nuclear matter. After one iteration the approximation is nearly self-consistent. The value of the binding energy of the Λ-paiticle is only slightly decreased from the value of perturbation theory. Because of the vanishing particle density of the Λ-hyperon the quasiparticle energy depends on the square of the momentumk, the width of the spectral function is proportional tok ⁴ and the imaginary part of the self energy operator is proportional to (Ω-μ)^5/2 for Ω approaching the chemical potential μ.     

有机材料反饱和吸收特性分析

从能级角度出发,结合入射激光脉宽对粒子吸收方面的影响,用速率方程模拟了各能级粒子数的瞬时变化关系,给出了激光脉宽与能级寿命可比拟时反饱和吸收的动态解,表明粒子在能级上的分布情况。用C60和HITCI(1,1′,3,3,3′,3′hexa methyl lindo tricarbocyanine Iodide)的实验参数理论模拟了激发态吸收截面大于基态吸收截面时透射率随光强的变化关系,用以说明大的上能级吸收截面可以抑制光强过大时引起的饱和吸收,增强材料的非线性光限幅特性。     

Microscopic calculation of the restoring force for scissor isovector vibrations

The restoring force for scissor isovector vibrations is calculated microscopically with the wave functions of an axially symmetric Woods-Saxon potential from a density-dependent symmetry energy. The experimental energies of the low-lying magnetic dipole states in rare-earth nuclei are well reproduced. It is found that only outer particles, which contribute to the nuclear moment of inertia, take part in this collective vibration. They are about half of the total number of nucleons.     

Excited-state forces within a first-principles Green's function formalism

We present a new first-principles formalism for calculating forces for optically excited electronic states using the interacting Green's function approach with the GW Bethe-Salpeter-equation method. This advance allows for efficient computation of gradients of the excited-state Born-Oppenheimer energy, allowing for the study of relaxation, molecular dynamics, and photoluminescence of excited states. The approach is tested on photoexcited carbon dioxide and ammonia molecules, and the calculations accurately describe the excitation energies and photoinduced structural deformations.     

The (p,n) reaction on cadmium isotopes leading to the ground- and excited-state analogs

The (p, n) reactions to ground- and excited-state analogs on ^110,114,116Cd have been studied at a bombarding energy of 25 MeV. Angular distributions of emitted neutrons leading to ground-state analogs, and 2⁺, 3^? and 4⁺ excited-state analogs were obtained for each target. Angular distributions of differential cross sections to the ground-state analog agree with the predictions obtained from macroscopic DWBA calculations in which a Lane potential is employed. Coupled-channel calculations indicate the importance of two-step processes in the (p, n) transition to an excited-state analog. Further, the calculation using a larger value for the deformation parameter of the isovector part than of the isoscalar one fairly well describes the 2⁺ excited-state analog.     

Self-consistent calculation of the optical potential and ground-state properties of nuclear matter

On the basis of the Green-function formalism, we performed a self-consistent calculation of the self-energy ∑(k, ω) of a particle interacting with the infinite nuclear medium. The function ∑(k, ω) was mapped out in the energy-momentum plane, and the single-particle energy ω(k), momentum distribution ?(k) and the “on-shell” part of the self-energy, ∑(k, ω(k)), were defined, from which all physical properties followed. In particular we investigated the ground-state properties of nuclear matter in two Λ-approximations of the T-matrix. In one, the intermediate two-particle propagator, Λ₀₀, represented free-particle propagation; in the other, called Λ₁₁, intermediate states included both interacting particles and holes. Pauli principle effects were included in both approximations. The second approximation was expected to be conserving because it included a large part of the rearrangement effects which, we found, contributed ～6 MeV per particle to the average energy and ～28 MeV to the singleparticle energy at zero momentum. The Hugenholtz-van Hove theorem was nearly satisfied, with only 1 MeV separating the chemical potential from the average energy. We also studied, in the Λ₀₀-approximation, the optical potential for the scattering of a particle by a large nucleus; it was directly related to the “on-shell” part of the self-energy. It was found that, below 100 MeV, the real part varied as (?90 + 0.584E) [MeV], and the imaginary part as (2.4 + 0.009 E) [MeV].