Analysis of the two-photon absorption spectrum of benzonitrile based on the direct quantum-mechanical calculation of the intensity distribution

A direct quantum-mechanical calculation of the intensity distribution in the two-photon absorption spectrum of benzonitrile is performed taking into account the Herzberg-Teller effect. The excitation mechanism of all the observed lines, including lines corresponding to the excitation of single-quantum nontotally symmetric vibrations and their combinations with totally symmetric modes, is analyzed. The results of the calculation, performed taking into account the frequency effect and the Duschinsky effect, agree satisfactorily with experimental data. This indicates that it is worthwhile to apply the quantum-mechanical method in calculations of the intensity distribution in the two-photon absorption spectra of cyclic molecules.     

Quantum-mechanical calculation of the van der Waals interaction between small metallic spheres

We give the first microscopic calculation of the leading terms in the van der Waals interaction energy between two very small metallic particles, treating their electronic excitations in the quantum-mechanical Infinite Barrier Model and the Random Phase Approximation. The results are very close to those obtained for the corresponding classical spheres, provided that we describe them by their effective radii calculated to satisfy the electrostatic zero-force sum-rule. We examine the higher order terms and the exact results at short distances in the plasmon-pole approximation, and discuss the convergence of the multipole expansions.     

Angular Anisotropy of the Fission Fragments in the Dinuclear System Mo del

A theoretical evaluation of the collective excitation spectra of nucleus at large deformations is possible within the framework of the dinuclear system (DNS) model, which treats the wave function of the fissioning nucleus as a superposition of a mononucleus configuration and two-cluster configurations in a dynamical way, permitting exchange of nucleons between clusters. In this work the method of calculation of the potential energy and the collective spectrum of fissioning nucleus at scission point is presented. Combining the DNS model calculations and the statistical model of fission we calculate the angular distribution of fission fragments for the neutron–induced fission of 239Pu.     

Algorithm for solving the inverse vibronic problem on the basis of SVL fluorescence spectra

Computer methods whereby the inverse vibronic problem is solved on the basis of resonance fluorescence spectra with the use of modern quantum-mechanical methods for constructing structuraldynamic models of polyatomic molecules are discussed. An algorithm is proposed for solving the inverse vibronic problem according to resonance fluorescence spectra under laser excitation, and the corresponding calculation programs are constructed. The initial program data are acquired by means of an original software package which implements the scaling of quantum-mechanical force fields in two electronic states. The Duschinsky matrix and the initial matrix of shifts in normal coordinates caused by electron excitation are calculated in the Cartesian and natural vibrational coordinates. The program data are taken from quantum-molecular models based on calculations performed via ab initio modern quantum-mechanical methods and density functional theory. The algorithm is tested through the calculation of a model molecular system.     

The impact of vibrational wave function on low energy electron vibrational scattering from nitrogen molecule

The vibrational wave function of the target theoretically plays an important role in the calculation of vibrational excitation cross sections. By a careful study of the differential cross sections resulting from different vibrational wave functions we find that cross sections are susceptible to vibrational wave functions. Minor changes in the vibration wave function may cause a significant change in the cross section. Even more surprising is that by selecting a few numbers of potential models(which determine the vibrational wave functions) we can often calculate the differential scattering cross section in much closer agreement with experiment in the framework of body-frame vibrational close-coupling theory, which suggest that an accurate potential energy may play a more important role in scattering than we thought before.     

Mass dependence of the ground state of charged particles in a silicon crystal

We report a quantum-mechanical study of the ground state of a positively charged particle in an otherwise perfect Si crystal. Particles with intermediate masses between the positron and the deuteron are considered. We find that there are two substantially different limit behaviours, depending on the mass value, ranging from the extreme localization in the high-electronic-density region of the deuteron wave function to the almost uniform extension of the positron one, which on the contrary attributes the maximum of probability to the interstitial region. Moreover, we underline the behaviour of the intermediate mass particles, μ⁺ and π⁺, which exhibit a significant degree of delocalization of their wave functions.     

Ground-state correlations and finite temperature properties of the transverse Ising model

We present a semi-analytic study of Ising spins on a simple square or cubic lattice coupled to a transverse magnetic field of variable strength. The formal analysis employs correlated basis functions (CBF) theory to investigate the properties of the corresponding N-body ground and excited states. For these states we discuss two different ansaetze of correlated trial wave functions and associated longitudinal and transverse excitation modes. The formalism is then generalized to describe the spin system at nonzero temperatures with the help of a suitable functional approximating the Helmholtz free energy. To test the quality of the functional in a first step we perform numerical calculations within the extended formalism but ignore spatial correlations. Numerical results are reported on the energies of the longitudinal and the transverse excitation modes at zero temperature, on critical data at finite temperatures, and on the optimized spontaneous magnetization as a function of temperature and external field strength.     

A method for constructing radial wave packets with application to target distortion in electron-atom collisions

It has been shown that an analysis of radial stationary state wave functions of a particle in terms of their loops leads to such continuous, single-valued and finite functions which represent a practically convenient form of the radial wave packets of that particle at various positions. The radial wave packets have been used to investigate target distortion in electron-atom collisions. The distortion of the target is defined in terms of quantum-mechanical probabilities given by the wave packets. A closed expression which depends upon the position of the colliding electron, is obtained for the potential energy of the target in the field of the colliding electron.     

Vacancy excitation spectrum in solid 4He and longitudinal phonons

The first microscopic ab initio calculation of the excitation spectrum of a vacancy in solid 4He is reported. The energy-wave vector dispersion relation has been obtained at melting density within a development of the shadow wave function variational technique. The calculation of the excitation spectrum of a vacancy gives a bandwidth which ranges from 6 to 10 K in the hcp solid 4He, depending on the particular direction of the wave vector of the excitation. The effective mass of the vacancy turns out to be about 0.35 4He masses. We have also computed the spectrum of longitudinal phonons and we find rather good agreement with recent experimental results.     

Unified Analysis of the Structures of Three-Boson and Three-Fermion Systems

A model system of three identical particles was examined to understand the features of its structure. The low-lying states having different sets of quantum numbers and obeying different permutation symmetries were studied in a unified way, though only qualitatively. It was found that the constraints imposed by quantum-mechanical symmetry on the wave functions are embodied in inherent nodal surfaces, which affect the structures and the ways of excitation decisively. The origin of a number of rotational bands has been clarified. Features in the low-lying spectrum have been revealed. Received April 10, 1996; revised September 27, 1996; accepted for publication November 27, 1996     

Time-dependent density-functional theory with a self-interaction correction

We discuss an implementation of the self-interaction correction for the local-density approximation to time-dependent density-functional theory. A variational formulation is given, taking care of the necessary constraints. A manageable and transparent propagation scheme using two sets of wave functions is proposed and applied to laser excitation with subsequent ionization of a dimer molecule.     

One-dimensional plasmon in an atomic-scale metal wire

We have measured one-dimensional (1D) plasmons in an atom wire array on the Si(557)-Au surface by inelastic scattering of a highly collimated slow electron beam. The angular dependence of the excitation energy clearly indicates the strong 1D confinement and free propagation of the plasma wave along the wire. The observed plasmon dispersion is explained very well by a quantum-mechanical scheme which takes into account dynamic exchange-correlation effects, interwire interactions, and spin-orbit splitting of the 1D bands. Although the qualitative feature of the plasmon dispersion is reminiscent of that of a high-density free-electron gas, we detected the substantial influence of electron correlation due to strong 1D confinement.     

Finite-mode regularization of the fermion functional integral

We present a regularization of the fermion functional integral in the presence of a gauge field, obtained by projecting the fermion fields on a finite subspace of the fermion wave functions. We find the basis that ensures manifest gauge covariance. We are able, in this way, to develop a non-perturbative method of calculation and test it by calculating the triangle anomalies in different models. All the calculations are carried out on a finite-size momentum space lattice. Finally we briefly discuss the zero-mode problem.     

Theory of internal photoemission in sandwich structures

The internal photoemission in sandwich structures is treated as a multi-step process. The excitation functions for electrons in the electrodes are obtained as a result of a rigorous optical analysis of the light propagation and absorption. The electron-electron and electron-phonon interactions are described in terms of energy-dependent mean free paths. The calculation of the quantum. yield and photocurrent includes the electrons which escape without scattering, after one scattering, and after two scattering processes. In calculating the probability for electrons to escape over the inner potential barrier within the structure account has been taken of both their being scattered within the barrier region and their quantum-mechanical character.The present calculations can convenietly be used for theoretical investigations of the photoemission in its dependence on various parameters of the structure. The formulae also retain their validity for the photoemission of holes when the quantities due to electrons are correspondingly replaced. An adaptation of the theory to the vacuum photoemission from thick as well as very thin samples is possible without difficulties.     

Equivalence between local Fermi gas and shell models in inclusive muon capture from nuclei

Motivated by recent studies of inclusive neutrino nucleus processes and muon capture within a correlated local Fermi gas model (LFG), we discuss the relevance of nuclear finite-size effects in these reactions at low energy, in particular for muon capture. To disentangle these effects from others coming from the reaction dynamics we employ here a simple uncorrelated shell model that embodies the typical finite-size content of the problem. The integrated decay widths of muon atoms calculated with this shell model are then compared for several nuclei with those obtained within the uncorrelated LFG, using in both models exactly the same theoretical ingredients and parameters. We find that the two predictions are in quite good agreement, within 1-7%, when the shell model density and the correct energy balance is used as input in the LFG calculation. The present study indicates that, despite the low excitation energies involved in the reaction, integrated inclusive observables, like the total muon capture width, are quite independent of the fine details of the nuclear wave functions. An erratum to this article is available at .     

Optomechanical control of atoms and molecules

We briefly review some of our recent and ongoing work on nanoscale optomechanics, an emerging area at the confluence of atomic, condensed matter and gravitational wave physics. A central tenet of optomechanics is the laser cooling of a moving mirror, typically an end mirror of a Fabry-Perot resonator, to a point near its quantum-mechanical ground state of vibration. Following a general introduction we discuss how the motion of such a macroscopic quantum oscillator can be squeezed, and then show how the placement of a ferroelectric tip on the oscillator allows the coherent manipulation and control of the center-of-mass motion of ultracold polar molecules.     

Fractals and quantum mechanics

A new application of a fractal concept to quantum physics has been developed. The fractional path integrals over the paths of the Levy flights are defined. It is shown that if fractality of the Brownian trajectories leads to standard quantum mechanics, then the fractality of the Levy paths leads to fractional quantum mechanics. The fractional quantum mechanics has been developed via the new fractional path integrals approach. A fractional generalization of the Schrodinger equation has been discovered. The new relationship between the energy and the momentum of the nonrelativistic fractional quantum-mechanical particle has been established, and the Levy wave packet has been introduced into quantum mechanics. The equation for the fractional plane wave function has been found. We have derived a free particle quantum-mechanical kernel using Fox's H-function. A fractional generalization of the Heisenberg uncertainty relation has been found. As physical applications of the fractional quantum mechanics we have studied a free particle in a square infinite potential well, the fractional "Bohr atom" and have developed a new fractional approach to the QCD problem of quarkonium. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum mechanics. (c) 2000 American Institute of Physics.