Cross sections for the elastic scattering of low-energy electrons by molecular fluorine: an approximate theoretical treatment using discrete basis functions

Phaseshifts and total cross sections for the elastic scattering of low-energy (0-13.6 eV) electrons by molecular fluorine are presented. The phaseshifts are obtained by an approximate technique based on the weak asymptotic coupling of orbital angular momenta and are calculated solely from the results of a discrete basis set diagonalization of the molecular Hamiltonian. Correlation and polarization effects are not treated. The elastic cross section is dominated by a Sigma u+ shape resonance at about 2.2 eV in the static-exchange model

Probability Density in the Complex Plane

The correspondence principle asserts that quantum mechanics resembles classical mechanics in the high-quantum-number limit. In the past few years many papers have been published on the extension of both quantum mechanics and classical mechanics into the complex domain. However, the question of whether complex quantum mechanics resembles complex classical mechanics at high energy has not yet been studied. This paper introduces the concept of a local quantum probability density $\rho(z)$ in the complex plane. It is shown that there exist infinitely many complex contours $C$ of infinite length on which $\rho(z) dz$ is real and positive. Furthermore, the probability integral $\int_C\rho(z) dz$ is finite. Demonstrating the existence of such contours is the essential element in establishing the correspondence between complex quantum and classical mechanics. The mathematics needed to analyze these contours is subtle and involves the use of asymptotics beyond all orders.Comment: 38 pages, 17figure

On Multilingual Training of Neural Dependency Parsers

We show that a recently proposed neural dependency parser can be improved by joint training on multiple languages from the same family. The parser is implemented as a deep neural network whose only input is orthographic representations of words. In order to successfully parse, the network has to discover how linguistically relevant concepts can be inferred from word spellings. We analyze the representations of characters and words that are learned by the network to establish which properties of languages were accounted for. In particular we show that the parser has approximately learned to associate Latin characters with their Cyrillic counterparts and that it can group Polish and Russian words that have a similar grammatical function. Finally, we evaluate the parser on selected languages from the Universal Dependencies dataset and show that it is competitive with other recently proposed state-of-the art methods, while having a simple structure.Comment: preprint accepted into the TSD201

Complex Correspondence Principle

Quantum mechanics and classical mechanics are two very different theories, but the correspondence principle states that quantum particles behave classically in the limit of high quantum number. In recent years much research has been done on extending both quantum mechanics and classical mechanics into the complex domain. This letter shows that these complex extensions continue to exhibit a correspondence, and that this correspondence becomes more pronounced in the complex domain. The association between complex quantum mechanics and complex classical mechanics is subtle and demonstrating this relationship prequires the use of asymptotics beyond all orders.Comment: 4 pages, 6 figure

Asymptotics of Expansion of the Evolution Operator Kernel in Powers of Time Interval Δt\Delta t

The upper bound for asymptotic behavior of the coefficients of expansion of the evolution operator kernel in powers of the time interval \Dt was obtained. It is found that for the nonpolynomial potentials the coefficients may increase as $n!$. But increasing may be more slow if the contributions with opposite signs cancel each other. Particularly, it is not excluded that for number of the potentials the expansion is convergent. For the polynomial potentials \Dt-expansion is certainly asymptotic one. The coefficients increase in this case as $\Gamma(n \frac{L-2}{L+2})$, where $L$ is the order of the polynom. It means that the point \Dt=0 is singular point of the kernel.Comment: 12 pp., LaTe

The role of Mie scattering in the seeding of matter-wave superradiance

Matter-wave superradiance is based on the interplay between ultracold atoms coherently organized in momentum space and a backscattered wave. Here, we show that this mechanism may be triggered by Mie scattering from the atomic cloud. We show how the laser light populates the modes of the cloud, and thus imprints a phase gradient on the excited atomic dipoles. The interference with the atoms in the ground state results in a grating, that in turn generates coherent emission, contributing to the backward light wave onset. The atomic recoil 'halos' created by the scattered light exhibit a strong anisotropy, in contrast to single-atom scattering

Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. III: Role of particle-number projection

Starting from HFB-6, we have constructed a new mass table, referred to as HFB-8, including all the 9200 nuclei lying between the two drip lines over the range of Z and N > 6 and Z < 122. It differs from HFB-6 in that the wave function is projected on the exact particle number. Like HFB-6, the isoscalar effective mass is constrained to the value 0.80 M and the pairing is density independent. The rms errors of the mass-data fit is 0.635 MeV, i.e. better than almost all our previous HFB mass formulas. The extrapolations of this new mass formula out to the drip lines do not differ significantly from the previous HFB-6 mass formula.Comment: 9 pages, 7 figures, accepted for publication in Phys. Rev.

Quantum gravitational optics: the induced phase

The geometrical approximation of the extended Maxwell equation in curved spacetime incorporating interactions induced by the vacuum polarization effects is considered. Taking into account these QED interactions and employing the analogy between eikonal equation in geometrical optics and Hamilton-Jacobi equation for the particle motion, we study the phase structure of the modified theory. There is a complicated, local induced phase which is believed to be responsible for the modification of the classical picture of light ray. The main features of QGO could be obtained through the study of this induced phase. We discuss initial principles in conventional and modified geometrical optics and compare the results.Comment: 10 pages, REVTex forma

Theoretical studies of photoexcitation and ionization in H_2O

Theoretical studies are reported of the complete dipole excitation and ionization spectrum in H_2O employing Franck–Condon and static‐exchange approximations. Large Cartesian Gaussian basis sets are used to represent the required discrete and continuum electronic eigenfunctions at the ground‐state equilibrium geometry, and previously devised moment‐theory techniques are employed in constructing the continuum oscillator‐strength densities from the calculated spectra. Detailed comparisons are made of the calculated excitation and ionization profiles with recent experimental photoabsorption studies and corresponding spectral assignments, electron impact–excitation cross sections, and dipole (e, 2e)/(e, e+ion) and synchrotron‐radiation studies of partial‐channel photoionization cross sections. The various calculated excitation series in the outer‐valence (1b(^−1)_1, 3a(^−1)_1, 1b(^−1)_2) region are found to include contributions from valence‐like 2b_2 (σ*) and 4a_1(γ*) virtual orbitals, as well as appropriate nsa_1, npa_1, nda_1, npb_1, npb_2, ndb_1, ndb_2, and nda_2 Rydberg states. Transition energies and intensities in the ∼7 to 19 eV interval obtained from the present studies are seen to be in excellent agreement with the measured photoabsorption cross section, and to provide a basis for detailed spectral assignments. The calculated (1b(^−1)_1)X(^ 2)B_1, (3a_1(^−1))^2A_1, and (1b_2(^−1))(^2)B_2 partial‐channel cross sections are found to be largely atomic‐like and dominated by 2p→kd components, although the 2b_2(σ*) orbital gives rise to resonance‐like contributions just above threshold in the 3a_1→kb_2 and 1b_2→kb_2 channels. It is suggested that the latter transition couples with the underlying 1b_1→kb_1 channel, accounting for a prominent feature in the recent high‐resolution synchrotron‐radiation measurements. When this feature is taken into account, the calculations of the three outer‐valence channels are in excellent accord with recent synchrotron‐radiation and dipole (e, 2e) photoionization cross‐sectional measurements. The calculated inner‐valence (2a_1(^−1)) cross section is also in excellent agreement with corresponding measured values, although proper account must be taken of the appropriate final‐state configuration‐mixing effects that give rise to a modest failure of the Koopmans approximation, and to the observed broad PES band, in this case. Finally, the origins of the various spectral features present in the measured 1a_1 oxygen K‐edge electron energy‐loss profile in H_2O are seen to be clarified fully by the present calculations

Gravitational Stability of Circumnuclear Disks in Elliptical Galaxies

A significant fraction of nearby elliptical galaxies are known to have high density gas disks in their circumnuclear (CN) region (0.1 to a few kpc). Yet, ellipticals, especially luminous ones, show little signs of recent star formation (SF). To investigate the possible cause of the dearth of SF in these systems, we study the gravitational stability of CN gas disks embedded within the potentials of both the stellar bulge and the central massive black hole (BH) in ellipticals. We find that CN disks in higher mass galaxies are generally more stable than those in lower mass galaxies, because higher mass galaxies tend to have more massive BHs and more centrally concentrated stellar density profiles. We also consider the case in which the central stellar density profile has a core, which is often observed for ellipticals whose total stellar mass is higher than about 10^11 Msun. Such a cored stellar density profile leads to more unstable CN disks than the power-law density profile characteristic of less massive galaxies. However, the more massive BHs in high-mass galaxies act to stabilize the CN disk. Our results demonstrate that the gravitational potentials of both the central BH and the stellar component should be taken into account when studying the properties of CN disks, as their stability is sensitive to both the BH mass and the stellar density profile. Our results could explain the observed trend that less luminous ellipticals have a greater tendency to exhibit ongoing SF than giant ellipticals.Comment: 8 pages, 5 figures, accepted for publication in Ap