Spline algorithms for the hartree-fock equation for the helium ground state

Spline algorithms are evaluated for the non-linear, integro-differential equation describing the Hartree-Fock approximation for the He 1s²¹S ground state. The error in the energy decreases as h^2K−2, where h is a grid parameter and K is the order of the spline. It is shown that for higher order splines, the method is fast and accurate, and contrary to the conclusion reached by Altenberger-Siczek and Gilbert, that spline methods are suitable for SCF atomic structure calculations. Accuracy and timing studies are presented as well as comparisons with other accurate procedures.     

Ground-state properties of crystalline ice from periodic hartree-fock calculations and a coupled-cluster-based many-body decomposition of the correlation energy

Ground state properties of crystalline ice Ih are investigated by combining periodic Hartree-Fock calculations with a many-body expansion for the electron correlation energy using second-order many-body perturbation theory and coupled-cluster techniques. Very good agreement with experimental data can already be achieved by considering two-body correlation contributions up to the third coordination shell in crystalline ice. This hints at the possibility to accurately simulate ab initio water by using periodic Hartree-Fock calculations together with a parametrized two-body correlation potential.     

A variational method from the variance of energy

A variational method is studied based on the minimum of energy variance. The method is tested on exactly soluble problems in quantum mechanics, and is shown to be a useful tool whenever the properties of states are more relevant than the eigenvalues. In quantum field theory the method provides a consistent second-order extension to the Gaussian effective potential. PACS. 03.65.-w, 11.10.-z, 05.30.-d Received: 28 June 2005, Published online: 13 September 2005     

RPA calculation of the effective charge in a hartree-fock basis

Using a Hartree-Fock basis the diagrams of the Tamm-Dancoff and random-phase approximations have been summed to calculate the effective charge in the (1s0d) shell. The enhancement of the effective charge found by this summation is much less than in an oscillator basis, in fact in most cases the HF RPA result is smaller than the value obtained from the lowest order core polarization diagram in an oscillator basis. The HF neutron effective charges are thus too small. For protons the enhancement of the bare effective charge in a HF basis must also be taken into account, but for cases involving the 0d_5/2 orbital the final result appears rather small.     

On a simple formula for the energy of the lowest octupole state

A recently introduced way of parameterizing the energies of 3 states in many even-even nuclei, based on the microscopic structure of the low-energy octupole mode, is slightly modified so it now includes all (non-doubly magic) nuclei with A ? 30.     

He原子非相对论基态能量的变分计算

本文指出了一种现象:当忽略原子核的运动时,He原子非相对论基态变分能量的计算值将会低于实验值.考虑对原子核运动的修正后,通过使用一个带松弛坐标参数k的变分波函数对He原子的非相对论基态能量进行了变分计算,得到比较满意的结果.此计算与变分原理一致.     

The negative energy density for a three-single-electron state in the Dirac field

We examine the energy density produced by a state vector which is the superposition of three single electron states in the Dirac field in the four-dimensional Minkowski spacetime. We derive the conditions on which the energy density can be negative. We then show that the energy density satisfies two quantum inequalities in the ultrarelativistic limit.     

Ground state energy for a model gas in one dimension

Ground state energies of many-body systems in one dimension in the thermodynamic limit are calculated. We use relations between the ground state energy and the scattering phase, which are exact for a delta-function potential, and are fulfilled approximately for other interactions. This will be applied to a model of quantum field theory, for which theS-matrix can be calculated exactly by means of a property which is called factorization.     

Dissociation energy for the ground state of AlO from true potential energy curve

The true potential energy curve for the ground state of AlO has been extended up to the observed vibrational levels v = 22 using revised vibrational constants. The dissociation energy for the ground state of AlO has been estimated to be 4.15 ± 0.05 eV by the method of curve fitting. The Lippincott potential function has been used for fitting with the RKRV curve.     

Ground state energy of a polaron in a superlattice

The ground state energy of a polaron in a superlattice was calculated using the double-time Green functions. The effective mass of the polaron along the planes perpendicular to the superlattice axis was also calculated. The dependence of the ground state energy and the effective mass along the planes perpendicular to the superlattice axis on the electron–phonon coupling constant α and on the superlattice parameters (i.e. the superlattice periodd and the bandwidth Δ) were studied. It was observed that if an infinite square-well potential is assumed, the ground state energy of the polaron decreases (i.e. becomes more negative) with increasing α and d, but increases with increasing Δ. For small values of α, the polaron ground state energy varies slowly with Δ, becoming approximately constant for large Δ. The effective mass along the planes perpendicular to the superlattice axis was found to be approximately equal to the mass of an electron for all typical values ofα , d and Δ.     

On the ground state energy of a two-dimensional electron fluid

A new theory of the ground state energy of a two-dimensional electron fluid is presented. It is shown that the ring diagram contribution changes its analytical behavior atr _s =2^1/2, wherer _s is the usual density parameter defined by r_S = 1/a ₀( n)^1/2,a ₀ being the Bohr radius andn is the electron density. For smallr _s , a high density series is obtained in agreement with the previous calculation. For larger _s , a hitherto unknown low density series is obtained. In the low density region, the first order exchange energy is completely cancelled out by a term from the ring contribution so that the ground state energy decreases in proportion tor _s ^–2/3 , followed byr _s ^/–4/3 and higher order terms. The energy is found to be minimum atr _s=1.4757, the minimum value being –0.481915 Rydbergs.     

On the ground state energy of a two-dimensional electron fluid

A new theory of the ground state energy of a two-dimensional electron fluid is presented. It is shown that the ring diagram contribution changes its analytical behavior atr _s =2^1/2, wherer _s is the usual density parameter defined by r_S = 1/a ₀(π n)^1/2,a ₀ being the Bohr radius andn is the electron density. For smallr _s , a high density series is obtained in agreement with the previous calculation. For larger _s , a hitherto unknown low density series is obtained. In the low density region, the first order exchange energy is completely cancelled out by a term from the ring contribution so that the ground state energy decreases in proportion tor _s ^?2/3 , followed byr _s ^/?4/3 and higher order terms. The energy is found to be minimum atr _s=1.4757, the minimum value being ?0.481915 Rydbergs.     

The ground state energy of a classical gas

In this paper we study the ground state energy of a classical gas. Our interest centers mainly on Coulomb systems. We obtain some new lower bounds for the energy of a Coulomb gas. As a corollary of our results we can show that a fermionic system with relativistic kinetic energy and Coulomb interaction is stable. More precisely, letH _N (α) be theN particle Hamiltonian $$H_N (\alpha ) = \alpha \sum\limits_{i = 1}^N {( - \Delta _i )^{1/2} + } \sum\limits_{i< j} {\left| {x_i - x_j } \right|^{ - 1} } - \sum\limits_{i,j} {\left| {x_i - R_j } \right|^{ - 1} } + \sum\limits_{i< j} {\left| {R_i - R_j } \right|^{ - 1} } $$ where Δ _i is the Laplacian in the variablex _i ∈?³ andR ₁, ...,R _N are fixed points in ?³. We show that for sufficiently large α, independent ofN, the HamiltonianH _N (α) is nonnegative on the space of square integrable functions ψ(x ₁, ...,x _N ), antisymmetric in the variablesx _i , 1≦i≦N.     

HD as a probe for detecting mass variation on a cosmological time scale

The strong electronic absorption systems of the B1 Sigma u+-X1 Sigma g+ Lyman and the C1Pi u-X1 Sigma g+ Werner bands can be used to probe possible mass-variation effects on a cosmological time scale from spectra observed at high redshift, not only in H2 but also in the second most abundant hydrogen isotopomer HD. High resolution laboratory determination of the most prominent HD lines at extreme ultraviolet wavelengths is performed at an accuracy of delta lambda/lambda approximately 5 x 10(-8), forming a database for comparison with astrophysical data. Sensitivity coefficients Ki = d ln lambda i/d ln mu are determined for HD from quantum ab initio calculations as a function of the proton-electron mass ratio mu. Strategies to deduce possible effects beyond first-order baryon/lepton mass ratio deviations are discussed.     

Ground state energy of a many-particle boson system

A trial expression for the ground state energy of a system of many bosons interacting with strong forces is studied. Using an approximate expression for the pair-distribution function and applying the variational principle in an appropriate way, we obtain a non-linear integrodifferential equation for the correlation functionf(r). This equation is subsequently linearised and its behaviour for large separations is studied. It is also shown that for large separations an effective reduced mass of the pair can be defined. This is given by ^*=2, where=m/2 is the reduced mass of the pair.     

Ground state energy of a bound piezoelectric polaron

The ground state energy of a piezoelectric polaron bound in a Coulomb potential is calculated analytically in the weak coupling limit.     

Ultrasoft X-ray spectroscopy with variation of the electron excitation energy as a method for analyzing thin films and solid/solid interfaces

The application of ultrasoft X-ray spectroscopy with variation of the electron excitation energy for phase analysis of thin films and phase reactions at solid/solid interfaces is considered. CN _x nanocondensatess obtained by pulsed arc sputtering of graphite in the presence of nitrogen, silicon implanted with hydrogen ions, and Fe-Co silicides fabricated by ion-beam synthesis have been studied.     

Minimization of the free energy of large continuous quantum systems over product states

The asymptotic form of the necessary condition for the minimum of free energy of large interacting n-fermion and n-boson systems, over all product states, is derived.     

Response variance prediction in the statistical energy analysis of built-up systems

In the statistical energy analysis (SEA) of high frequency noise and vibration, a complex engineering structure is represented as an assembly of subsystems. The response of the system to external excitation is expressed in terms of the vibrational energy of each subsystem, and these energies are found by employing the principle of power balance. Strictly the computed energy is an average taken over an ensemble of random structures, and for many years there has been interest in extending the SEA prediction to the variance of the energy. A variance prediction method for a general built-up structure is presented here. Closed form expressions for the variance are obtained in terms of the standard SEA parameters and an additional set of parameters alpha(k) that describe the nature of the power input to each subsystem k, and alpha(ks) that describe the nature of the coupling between subsystems k and s. The theory is validated by comparison with Monte Carlo simulations of plate networks and structural-acoustic systems.     

类铍离子激发态的能量计算

采用多组态相互作用方法及Rayleigh- Ritz变分法,计算了类铍O4+离子1s22s2p3Po态的非相对论能量,并详细分析了如何选择质量最好的变分波函数.运用截断变分方法进一步饱和函数空间得到能量的改进量,并考虑相对论修正、质量极化效应等获得了相对论能量计算值.计算结果表明,此理论计算方法可得到高精度的能量计算值.