Adiabatic Jacobi corrections for H2+-like systems

The Coulomb three-body problem in Jacobi coordinates was solved by treating the distance of the particles having equal charge as a parameter. This method allows computation of electronic energies with finite nuclear masses while maintaining the notion of a potential energy curve. The rotationless ground-state electronic and the so-called adiabatic Jacobi correction (AJC) energies are presented for H2+, D2+, and HD+ at fixed internuclear separations. The AJCs are defined as the difference between the results obtained from calculations using proper finite and infinite nuclear masses. Except at the united atom limit, the AJCs are smaller than the traditional first-order diagonal Born-Oppenheimer corrections. Expectation values of proton-electron, p-e, and deuteron-electron, d-e, distances for HD+ have been computed as a function of internuclear separation. Similarly to the fully nonadiabatic approach, the present method is able to follow the symmetry breaking in HD+. Exact and approximate analytical and numerical results are given for counterfactual systems as well. In these cases changes are allowed for the values of the electron rest mass or the elementary charge, as well as for the mass or charge of the unique particle (electron).     

Efficient computation of potential energy first and second derivatives for molecular dynamics,normal coordinate analysis,and molecular mechanics calculations

By using two- and three-body internal coordinates and their derivatives as intermediates, it is possible to enormously simplify formulas for three- and four-body internal coordinates and their derivatives. Using this approach, simple formulas are presented for stretch (two-body), two types of bend (three-body), and wag and two types of torsion (four-body) internal coordinates and their first and second derivatives. The formulas are eminently suitable for economizing molecular dynamics and molecular mechanics calculations and normal coordinate analysis of complicated potential energy surfaces. Efficient methods for computing derivatives of entire potential energy terms, and in particular cross terms with switching functions, are presented.     

Dalitz plot analysis of Coulomb exploding O3 in ultrashort intense laser fields

The three-body Coulomb explosion of O3, O3(3+)-->O++O++O+, in ultrashort intense laser fields (2x10(15) W/cm2) is studied with two different pulse durations (9 and 40 fs) by the coincidence momentum imaging method. In addition to a decrease in the total kinetic energy release, a broadening in the Dalitz plot distribution [Philos. Mag. 44, 1068 (1953)] is observed when the pulse duration is increased from 9 to 40 fs. The analysis based on a simple Coulomb explosion model shows that the geometrical structure of O3 remains almost unchanged during the interaction with the few-cycle intense laser fields, while a significant structural deformation along all the three vibrational coordinates, including the antisymmetric stretching coordinate, is identified in the 40 fs intense laser fields. The observed nuclear dynamics are discussed in terms of the population transfer to the excited states of O3.     

A second-quantization representation of the Epstein-Nesbet partitioning of the full hamiltonian

A second-quantization representation of the Epstein-Nesbet partitioning of the total electronic hamiltonian is suggested. In this approach, the unperturbed hamiltonian contains not only the one-particle orbital energies but also the Coulomb and corresponding exchange two-particle terms. Such a hamiltonian can advantageously be used in all branches of the many-body diagrammatic perturbation theory for simple and correct inclusion of the diagonal ladder and ring diagrams in all orders of perturbation theory.     

Non-Born-Oppenheimer electronic and nuclear densities for a Hooke-Calogero three-particle model: non-uniqueness of density-derived molecular structure

We consider the calculation of non-Born-Oppenheimer, nBO, one-particle densities for both electrons and nuclei. We show that the nBO one-particle densities evaluated in terms of translationally invariant coordinates are independent of the wavefunction describing the motion of center of mass of the whole system. We show that they depend, however, on an arbitrary reference point from which the positions of the vectors labeling the particles are determined. We examine the effect that this arbitrary choice has on the topology of the one-particle density by selecting the Hooke-Calogero model of a three-body system for which expressions for the one-particle densities can be readily obtained in analytic form. We extend this analysis to the one-particle densities obtained from full Coulomb interaction wavefunctions for three-body systems. We conclude, in view of the fact that there is a close link between the choice of the reference point and the topology of one-particle densities that the molecular structure inferred from the topology of these densities is not unique. We analyze the behavior of one-particle densities for the Hooke-Calogero Born-Oppenheimer, BO, wavefunction and show that topological transitions are also present in this case for a particular mass value of the light particles even though in the BO regime the nuclear masses are infinite. In this vein, we argue that the change in topology caused by variation of the mass ratio between light and heavy particles does not constitute a true indication in the nBO regime of the emergence of molecular structure.     

Electrostatic interaction between two spherical colloidal particles

Explicit exact analytic expressions are obtained in the form of infinite series for the potential distribution and the potential energy of the electrostatic interaction for the system of two dissimilar spheres in an electrolyte solution on the basis of the linearized Poisson—Boltzmann equation without recourse to Derjaguin's approximation. The leading term of the expression for the interaction energy (the zeroth order approximation) corresponds to the interaction energy that would be obtained if both spheres were ion-penetrable spheres (“soft” spheres). This term is a screened Coulomb interaction due to a simple linear superposition of the unperturbed potentials of the respective spheres, which is proportional to the product of their unperturbed surface potentials. The first-order approximation corresponds to the interaction energy that would be obtained if either sphere were a soft particle (the other being hard). The first-order correction term consists of two sub-terms, each of which is proportional to the square of the unperturbed surface potential of either sphere and does not depend on the unperturbed surface potential of the other sphere, can be interpreted as the interaction between the soft sphere and its image with respect to the hard sphere. This image interaction is attractive if the surface potential of the hard sphere is constant and repulsive if the surface charge density of the sphere is constant. It is shown that Derjaguin's method as well as its extension to the interaction of unequal spheres by Hogg, Healy and Fuerstenau (HHF) is quite a good approximation.     

Representation of cusps in a hyperspherical basis set

The wave functions of Coulomb systems have cusps at points corresponding to two particle coelescences. In this paper, we derive series representing the cusps in terms of hyperspherical harmonics multiplied by functions of the hyperradius. When the hyperspherical method is applied to Coulomb systems, the harmonics which appear in these series should be included in the hyperangular basis set.     

A chainlike relative coordinate system for few-particle problems

Jacobi coordinates have often been used to treat few-particle quantum systems. In this paper, we propose an alternative coordinate system which is very easily generalized as the number of particles becomes larger. We make use of forms of the Laplace–Beltrami operator that are invariant under general coordinate transformations, and use Coulomb Sturmian basis sets to solve the N-body wave equation.     

Non relativistic continuum wave functions for two coulomb centres

We give the continuum wave function solutions to the Schrödinger equation for an electron moving field of two point nuclei, as an expansion in terms of one centre Coulomb wave functions in a prolate elliptical coordinate system. These solutions may be chosen to have a convenient asymptotic behaviour, and tend to the conventional solutions of the Helmholtz equation in the limit that the nuclear charge goes to zero. In symmetric systems, where both nuclei have the same charge the angular wave functions are found to be identical with those occurring in the free case, and the expansion coefficients for the corresponding radial solutions are given for selected values of electron energy and nuclear separation.[/p]     

A practical treatment for the three-body interactions in the transcorrelated variational Monte Carlo method: application to atoms from lithium to neon

We suggest a practical solution to dealing with the three-body interactions in the transcorrelated variational Monte Carlo method (TC-VMC). In the TC-VMC method, which was suggested in our previous paper [N. Umezawa and S. Tsuneyuki, J. Chem. Phys. 119, 10015 (2003)], the Jastrow-Slater-type wave function is efficiently optimized through a self-consistent procedure by minimizing the variance of the local energy. The three-body terms in the transcorrelated self-consistent-field equation, which have been simply ignored in our previous works, are efficiently calculated by the Monte Carlo numerical integration. We found that our treatment for the three-body interactions is successful for atoms from Li to Ne.     

Coordinate measurements and operators

Relativistic quantum-field theory provides the machinery for calculating wave functions or probability amplitudes depending upon space-time coordinates. The currently accepted theory, however, fails to provide position operators and a means of measuring particle coordinates that are consistent with Dirac's properties of physical observables. This is because it calls for a space position probability distribution at a specified time. This paper shows, however, that space-time event coordinate operators, together with a corresponding measurement procedure, can be found that are consistent with Dirac's requirements. This is done through a reinterpretation of the amplitudes computed by field theory and does not involve any change in that mathematical formalism. The measurement of the space-time coordinates of an event is accomplished by detecting the absorption of a photon by a particle from each of two light pulses designed to overlap at a given point at a given time. If a final emitted photon has an energy whose sum with the final particle energy approximately equals the sum of the mean energies of the pulses, then the absorption of the two pulse photons must certainly have taken place within a distance the order of a Compton wavelength of the small space-time region of overlapping pulses. This is clear from the fact that the high energy required to confine the pulses to very small volumes must throw a particle absorbing them far off the mass shell. Thus the absorption of the two photons throws the particle into a narrowly confined spatial wave function that must decay extremely rapidly—to within a Compton wavelength, a delta function in space-time. This delta function is the eigenfunction of space-time coordinate operators X^μ and is the scalar product of vectors in a Hilbert space spanned by spin–space-time kets large enough to contain the operators of the Poincaré group. These event operators transform properly under the action of Poincaré operators but do not commute with the mass. If the Compton wavelength is not negligible compared to the accuracy desired in the coordinate measurements, individual coordinate measurements are no longer possible. Nevertheless, a large number of repeated coordinate measurements can be carried out to produce a coordinate probability distribution. This distribution can be unfolded to find a true coordinate probability distribution if the charge form factor is known from basic theory. An analysis of laboratory particle detection techniques shows that they actually determine space coordinates and energy rather than spatial coordinates at a given time. When this fact is included, the Klein–Nishina formula can be derived using the electromagnetic four-vector potential as the photon probability amplitude wave. To clarify the meaning of the observables, a mass-momentum measurement is described.     

球胶体颗粒之间相互作用能的求解

根据线性迭加近似方法,定义了一个修正电位项,较详细地推导出用于中等电位条件下球形胶体颗粒相互作用能和力的公式,该公式较为简单、实用,然而,对其所做的改进主要是针对相互作用能而不是力,对其原因也作了简单的讨论.     

Review of theories on ionization in fast ion-atom collisions with prospects for applications to hadron therapy

This work reviews quantum-mechanical four-body distorted wave theories for double electron capture in collisions between fast heavy multiply charged ions and heliumlike atomic systems. The widely used distorted wave methods of the first- and second-order in the pertinent perturbation series expansions are compared with each other. This tests the presumed importance of double continuum intermediate states of two electrons. Further, the relative performance is evaluated of the second-order theories with and without the eikonalization of the two-electron Coulomb wave functions for double continuum intermediate states. This checks the correctness and usefulness of the eikonalized Coulomb waves when two electrons participate actively to the transition from the initial to the final state of the entire system. We also analyze the significance of the contributions from excited heliumlike states especially in comparison between theory and measurement. The overall goal of the present study is to determine how much of the unprecedented experience gained over several decades in studying high-energy theories of pure three-body charge exchange could be exported directly to four-body double-electron capture without much of additional and essential eleaborations, besides the naturally increased computational demand. In particular, we address the unexpected breakdown of the continuum distorted wave eikonal initial state approximation and the anticipated success of continuum distorted wave theory for double charge exchange in ion-atom collisions at high impact energies.     

Charging effects in a CdSe nanotetrapod

The charging effects in a CdSe nanotetrapod have been theoretically investigated by using an atomistic pseudopotential method. We showed that the simple quasiparticle equation based on classical electrostatic consideration can be derived from the many-body GW equation under proper approximations. We found that the surface polarization potential can significantly change the electron wave functions, and there is an incomplete cancellation for this potential between the single particle energies and the electron-hole Coulomb interaction. Thus, it is necessary to include this potential in the calculation for complex unconvex systems. We also calculated the electron addition energies for a tetrapod. Unlike a simple spherical quantum dot, in which the addition energies are almost a constant, there is a large variation in the calculated addition energies for different numbers of electrons in a tetrapod.     

Review of theories on double electron capture in fast ion-atom collisions

This work reviews quantum-mechanical four-body distorted wave theories for double electron capture in collisions between fast heavy multiply charged ions and heliumlike atomic systems. The widely used distorted wave methods of the first- and second-order in the pertinent perturbation series expansions are compared with each other. This tests the presumed importance of double continuum intermediate states of two electrons. Further, the relative performance is evaluated of the second-order theories with and without the eikonalization of the two-electron Coulomb wave functions for double continuum intermediate states. This checks the correctness and usefulness of the eikonalized Coulomb waves when two electrons participate actively to the transition from the initial to the final state of the entire system. We also analyze the significance of the contributions from excited heliumlike states especially in comparison between theory and measurement. The overall goal of the present study is to determine how much of the unprecedented experience gained over several decades in studying high-energy theories of pure three-body charge exchange could be exported directly to four-body double-electron capture without much of additional and essential eleaborations, besides the naturally increased computational demand. In particular, we address the unexpected breakdown of the continuum distorted wave eikonal initial state approximation and the anticipated success of continuum distorted wave theory for double charge exchange in ion-atom collisions at high impact energies.     

Centrifugation equilibrium for spheres and spherocylinders

The centrifugation equilibrium problem is formulated and solved using a new procedure in which the specified variables are the temperature, system volume, particle dimensions and concentrations, angular speed, cell length, and cell distance from the rotation axis. As a result, we obtain the concentration profiles for all types of particles present in the system, which are considered to be immersed in a fluid. The particles are modeled as hard nonattractive spherocylinders using an equation of state, but the procedure is not restricted to any geometrical shape, and can be used with any equation of state available. The fluid is treated as a continuous medium, responsible for centrifugal buoyancy. We make calculations for colloidal suspensions of silica, often used for separations in biotechnology. Results are in good agreement with experiments and show excellent agreement in comparison with Monte Carlo simulations. Our calculations also predict focusing and shifting phenomena that have been experimentally observed in separations of fine particles.     

Response function theory of electron correlation

The full perturbation expansion for the response (or density—density correlation) function is examined in order to provide a useful general theory of excitation energies, oscillator strengths, dynamic polarizabilities, etc., that is more accurate than the random phase approximation. It is first shown how the formal partition of the diagrammatic version of the perturbation expansion into reducible and irreducible diagrams is generally useless as the latter category contains all the difficult terms which have heretofore resisted analysis in all but a haphazard form. It is then shown how the diagram for the response function can be partitioned into “correlated” and “uncorrelated” subsets. Restricting attention to the particle—hole blocks of the full response function, the “uncorrelated” diagrams desecribe the propagation of a particle—hole pair in an N-electron system where the particle and hole are each interacting with the remaining electrons but they are not interacting with each other. The “correlated” diagrams are those containing the hole—particle interactions, and, by defining a new class of reducible and irreducible diagrams, these are all summed to provide a perturbation expansion of the effective two-body hole—particle interaction that appears in the inverse of the response function. The “uncorrelated” diagrams are further partitioned into two sets, one of which is summed to all orders, while the other set is inverted in an order by order fashion. The final result presents a perturbation expansion for the inverse of the response function that is analogous to the Dyson equation for one-electron Green functions. Maintaining the perturbation expansion through first order for the inverse of the response function yields the eigenvalue equation of the familiar random phase approximation, while truncation at second order provides the most advanced theories that have been generated by the equations-of-motion method.     

Vibrational spectra of molecules in the Hartree–Fock dielectric screening approach

Traditionally, the calculation of the vibrational spectra of molecules involves at one point or another a numerical differentiation procedure. Such a method has some serious drawbacks both in efficiency and in accuracy. In this paper, an alternative method based on linear response theory is presented. The second derivative of the ground-state energy is expressed in terms of the electron density response matrix by means of perturbation theory. The unperturbed wave functions are obtained from the Hartree–Fock equation. First-order perturbation theory applied to this equation leads to the Hartree–Fock linear response. As an illustration of this method the vibrational frequency of a H₂ molecule is calculated. The result is 1.348 × 10¹⁴ Hz as compared to the experimental value of 1.319 × 10¹⁴ Hz. This method is also applicable in the calculation of the phonon dispersion curves of solids.     

Bound Energy for the Exponential-Cosine-Screened Coulomb Potential

An alternative approximation scheme has been used in solving the Schrödinger equation for the exponential-cosine-screened Coulomb potential. The bound state energ?es for various eigenstates and the corresponding wave functions are obtained analytically up to the second perturbation term.