Momentum Properties Research Articles

A very large Paul trap ion gun for delivering bunched low energy ion beams

Ions extracted from mass separators normally have energies in the range of tens of kilovolts and poor emittances, and are thereby not suited for soft landing, especially in ion deposition applications. In this article a system is described that has been developed for in-flight capture of continuous 60 keV ion beams and delivering them as low energy beam pulses of less than 1 μs duration and energies of less than 5 keV. They are also cooled so that their emittances and energy spreads are considerably reduced from those of the original beam. The basis of the system is a very large Paul trap as a collection system, together with a pulse-down cavity for modifying the energy of the delivered beam. The performance of the system has been analyzed using time-of-flight of the extracted ions. Experimental results are presented, together with numerical simulations of the results that lead to an understanding of the spatial and momentum properties of the ion collection in the trap. The results show how such collection systems can be designed for specific purposes, such as high-current implantation or precise implantation of smaller collections. Such a system can also be used where the ultimate destination is storage in an electromagnetic trap at ground potential.

Walking cavity solitons.

A family of walking solitons is obtained for the degenerate optical parametric oscillator below threshold. The loss-driven mechanism of velocity selection for these structures is described analytically and numerically. Our approach is based on understanding the role played by the field momentum and generic symmetry properties and, therefore, it can be easily generalized to other dissipative multicomponent models with walk off.

Conservation Properties of Unstructured Staggered Mesh Schemes

Classic Cartesian staggered mesh schemes have a number of attractive properties. They do not display spurious pressure modes and they have been shown to locally conserve, mass, momentum, kinetic energy, and circulation to machine precision. Recently, a number of generalizations of the staggered mesh approach have been proposed for unstructured (triangular or tetrahedral) meshes. These unstructured staggered mesh methods have been created to retain the attractive pressure aspects and mass conservation properties of the classic Cartesian mesh method. This work addresses the momentum, kinetic energy, and circulation conservation properties of unstructured staggered mesh methods. It is shown that with certain choices of the velocity interpolation, unstructured staggered mesh discretizations of the divergence form of the Navier?Stokes equations can conserve kinetic energy and momentum both locally and globally. In addition, it is shown that unstructured staggered mesh discretizations of the rotational form of the Navier?Stokes equations can conserve kinetic energy and circulation both locally and globally. The analysis includes viscous terms and a generalization of the concept of conservation in the presence of viscosity to include a negative definite dissipation term in the kinetic energy equation. These novel conserving unstructured staggered mesh schemes have not been previously analyzed. It is shown that they are first-order accurate on nonuniform two-dimensional unstructured meshes and second-order accurate on uniform unstructured meshes. Numerical confirmation of the conservation properties and the order of accuracy of these unstructured staggered mesh methods is presented.

Atomic motion in hollow submicron circular cylinders

The motion of atoms inside a long hollow cylindrical waveguide with a circular cross section is investigated. The guide is assumed to have subwavelength dimensions, in which case the spontaneous decay process is effected only by emission of a few possible cavity modes. The characteristics of the atomic motion in the guide are explored in the presence of an excited waveguide mode. We show that the atomic motion in this case is determined by an axial channelling force and a trapping dipole force, plus a quantized light torque associated with the orbital angular momentum property of excited waveguide modes of order $\mathcal{l}>0.$ It is predicted that in addition to its axial motion, an atom subject to such a mode should be trapped radially in a vibrational state and should exhibit interesting rotational features due to the light torque, including a rotational frequency shift.

Baryonic 3 P2 Superfluidity under Charged-Pion Condensation with Isobar

Baryonic 3P2 superfluidity under charged-pion (πc) condensation is studied by taking into account the Δ isobar degrees of freedom, in order to seek the possibility of the coexistence of the two hadronic condensates in the high density core of neutron stars. To treat such a coexistence problem, we develop a formulation of the pairing correlation due to the interaction between quasi-baryons under πc condensation. Quasi-baryons are described as a superposition of the quasi-neutron consisting of the neutron plus the isobar Δ− and the quasi-proton consisting of the proton plus the isobar Δ++. In this formulation, effects of Δ-mixing on the 3P2 pairing interaction can be expressed in a compact form as an additional 3P2 potential, which arises from the modification of the isospin and spin-isospin components of realistic nuclear forces due to Δ-mixing. The Δ-mixing brings about significant attractive contributions to the 3P2 pairing potential with moderate dependence on the density ρ. In the nucleon sector, repulsive effects on the pairing potential appear at short distance, growing with ρ. As a result of the competition between the two, the baryonic 3P2 superfluid critical temperature Tc under πc condensation is higher than the internal temperature of neutron stars, and the superfluid exists, up to about (3–5) times the nuclear density ρ0. for ρ≿ρ0, the persistence of the superfluid under πc condensation is regarded as model-dependent: Tc depends largely on the behavior of the condensed-πc momentum and short-range properties of nuclear forces.

Correlated two-electron momentum properties for helium to neon atoms

Two-electron properties in momentum space for the atoms helium to neon have been calculated starting from explicitly correlated wave functions. The different integrals involved in the calculation have been evaluated by using the Monte Carlo algorithm. In particular, the spherically averaged interelectronic momentum distribution, γ(2)(p12),its radial moments 〈p12n〉, with n=−2 to +3, the expectation value 〈p1⋅p2〉, and both the electron–electron coalescence, γ(2)(0), and counterbalance, Γ(2)(0), densities have been calculated. A systematic study of the electronic correlation has been performed by comparing the correlated results with the corresponding Hartree–Fock ones. Finally an analysis of the structure of the interelectronic momentum distribution in terms of its parallel and antiparallel components has been carried out.

Optically Detected Electron Spin Echo Envelope Modulation on a Photoexcited Triplet State in Zero Magnetic Field—A Comparison between the Zero-Field and High-Field Limits

Electron spin echo envelope modulation (ESEEM) has been studied at zero and low magnetic fields (B </= 100 G) by means of optically detected magnetic resonance. Qualitative differences of the ESEEM effect for an electronic triplet state (S = 1) under low-field and high-field conditions are observed and discussed. They are related to the different properties of the total spin angular momentum operator S and the hyperfine interaction at zero and high magnetic field. The novel method was applied to the photoexcited triplet state of acridine-d9 in a fluorene-h10 matrix. An analysis of the observed nitrogen quadrupole splitting is done by a quantitative description of the ESEEM effect in zero field. Copyright 1998 Academic Press.

New Aspects in the Calculation of Electronic Momentum Properties; an All-Quantum Study

Abstract The electronic properties of the C6H6 and C6D6 molecules have been studied by an all-quantum approach, where the classical and quantum degrees of freedom of the nuclei are taken into ac-count in the evaluation of electronic expectation values. In the all-quantum approach suggested a Feynman path integral Monte Carlo (PIMC) formalism has been linked to an electronic ab initio Hamiltonian. The electronic expectation values have been calculated as averages over the manifold of nuclear configurations populated in thermal equilibrium. This theoretical setup leads to electronic expectation values that depend on the temperature and on the mass of the nuclei. The ensemble averaged electronic properties differ sizeably from the results derived on the basis of a single nuclear configuration of minimum energy. This behaviour should have physical implications for the theoretical calculation of electronic momentum properties such as Compton profiles, reciprocal form factors, etc. We describe an error source in the theoretical determination of electronic momentum properties which has not been commented so far.

Spin-polarized electron excitation of neon 3p ( J =1) states

The angular momentum properties of incident transversely polarized electrons and radiated photons have been combined with scattering symmetries to reveal the effects of exchange and spin - orbit coupling as well as some propensity rules for excitation and decay of the 3p states of the neon atom. Integrated Stokes parameters, , and , have been measured for the decay radiations of wavelengths 616.4, 603.0, 626.7, 638.3 and 703.3 nm from the , , and states, respectively. While these states are intermediately (jl) coupled, their LS compositions partially explain some phenomena. For the states having a dominant triplet component, both the exchange and the spin - orbit interaction within the atom are important in the excitation, while the spin - orbit interaction plays the significant role for the state dominated by a singlet component. Decay photons from a common upper state with have larger linear polarization than those with and -1 while those from a core upper state have larger linear polarizations than those from a core upper state. The state multipoles are derived from the measured Stokes parameters. The influence of negative-ion resonances near threshold on the Stokes parameters and the state multipoles is very strong in some cases. The core state effects on the alignment of excited states are investigated.

A causal statistical family of dissipative divergence-type fluids

In this paper we investigate some properties, including causality, of a particular class of relativistic dissipative fluid theories of divergence type. This set is defined as those theories coming from a statistical description of matter, in the sense that the three tensor fields appearing in the theory can be expressed as the three first momenta of a suitable distribution function. In this set of theories the causality condition for the resulting system of hyperbolic partial differential equations is very simple and allow to identify a subclass of manifestly causal theories, which are so for all states outside equilibrium for which the theory preserves this statistical interpretation condition. This subclass includes the usual equilibrium distributions, namely Boltzmann, Bose or Fermi distributions, according to the statistics used, suitably generalized outside equilibrium. Therefore this gives a simple proof that they are causal in a neighborhood of equilibrium. We also find a bigger set of dissipative divergence type theories which are only pseudo-statistical, in the sense that the third rank tensor of the fluid theory has the symmetry and trace properties of a third momentum of an statistical distribution, but the energy-momentum tensor, while having the form of a second momentum distribution, it is so for a different distribution function. This set also contains a subclass (including the one already mentioned) of manifestly causal theories.

Momentum space: effects of correlation in the doubly excited state of He-like ions

Momentum properties are examined for the -like systems when . Each doubly excited state (DES) is represented in momentum space by the Dirac - Fourier transform of the Aspromallis configuration-interaction (A-CI) wavefunction. Various truncations of the natural expansions of the transformed A-CI functions are used to investigate characteristics of several probability distribution functions and momentum expectation values. The sensitivity of such properties with respect to the ordered introduction of Coulomb correlation effects is of particular interest. This is especially so in the region of low momenta since, in position (or real) space, it corresponds to the outer or valence regions of an electron density. Coulomb shifts, based on distribution functions for momentum differences, and the separate angular and radial correlation effects are analysed for each Z. Comparisons are made, in momentum space, with the doubly occupied ground states and, briefly for He, with the singly excited state . Shapes and magnitudes of the Coulomb shifts are also related to the Coulomb holes in position space. Changes in statistical correlation coefficients highlight variations in the radial and angular components of electron correlation for the and states of the He-like ions as the electronic momenta decrease in magnitude.

Radiation forces on a two-level atom in a σ+ − σ− configuration of Laguerre-Gaussian beams

Abstract We investigate the radiation forces associated with the J = 0 → J = 1 transition of a two-level atom in a laser configuration of two counter-propagating Laguerre-Gaussian (LG) beams with opposite circular polarisations. It is shown that, in addition to the usual dissipative and dipole forces, the atom experiences a torque about the beam axis. The latter arises from the orbital angular momentum properties of the Laguerre-Gaussian beams. The atom experiences either a static torque or a purely velocity-dependent torque, depending on the relative signs of the orbital angular momenta of the two LG beams. The trajectories of the atom are calculated in each case by solving the optical Bloch equations together with the classical equation of motion for the atom.

Atom dynamics in multiple Laguerre-Gaussian beams.

The leading radiation forces acting on an atom or ion subject to linearly polarized Laguerre-Gaussian (LG) light are studied. Particular emphasis is laid on the orbital angular momentum effects associated with LG light. The optical Bloch equations appropriate for the adiabatic approximation are derived and used to evaluate the forces and associated torque governing the atomic motion. The steady-state dynamics of the atom are explored for atoms subject to a single beam and multiple independent counterpropagating beams. The main features responsible for the dynamics of the atom, together with the dipole potentials characteristic of Laguerre-Gaussian light, are identified and discussed. The theory is illustrated by the numerical integration of the equation of motion for ${\mathrm{Mg}}^{+}$ ions in various beam configurations. This yields information on trajectories, velocity evolution, and vibrational frequencies at potential minima. Interesting effects involving a reciprocal interplay between motions in orthogonal directions are demonstrated. Such features are purely dependent on the orbital angular momentum property of the light. Their possible use in controlling atomic motion is investigated. \textcopyright{} 1996 The American Physical Society.

Particle behavior in a two-fluid turbulent plasma jet

This paper is concerned with the application of a two-fluid turbulence model for plasma spray processes at atmospheric pressure, for improving our physical insight into the plasma/particle interactions. In this two-fluid turbulence model, the turbulent stream is treated as a two-phase mixture. The fluid parcels are assumed to be arranged in fragments, and they can exchange mass, momentum, and other properties. A stochastic approach is then used to study particle behavior under the influence of the two-fluid parcels. The Stokes number is introduced as an indicator of particle dispersion behavior. A series of simulations is performed to include the influence of different injection locations, particle sizes, and injection velocities. The results indicate the importance of the existence of large-scale eddies and variable property, Knudsen, and mass-transfer cooling effects on the particle motion and heating history.

Angular distribution of photoelectrons from fixed-in-space molecules

Abstract Angular distributions of 1sσ photoelectrons from spatially fixed N2 molecules have been measured around the σ ∗ shape resonance in the K-shell continuum. This has been realized with the use of a coincidence technique: by detecting the photoelectron in coincidence with the fragment ion having the information on the molecular orientation at a moment of photoabsorption. The angular distributions obtained by this technique are rich in structure, which are completely different from usual photoelectron angular distributions from randomly oriented molecules. The orbital angular momentum properties of the 1sσ photoelectrons at the σ ∗ shape resonance have been revealed.

Angular distributions of 1s sigma photoelectrons from fixed-in-spaceN2 molecules.

The angular distributions of $1s\ensuremath{\sigma}$ photoelectrons from ${\mathrm{N}}_{2}$ molecules held fixed in space have been measured around the ${\ensuremath{\sigma}}^{*}$ shape resonance for the first time. The angular distributions have been very rich in structure, which are completely different from usual photoelectron angular distributions from randomly oriented molecules, as predicted by Dill. The orbital angular momentum properties of the $1s\ensuremath{\sigma}$ photoelectrons around the ${\ensuremath{\sigma}}^{*}$ shape resonance have been made clear from the angular distribution patterns.

Momentum of a Photon—Electromagnetic Method of Measurement

A simple experiment establishing the property of mechanical momentum of photon is described. An attempt has also been made to give a quantitative formulation.

Application of orbital momentum properties to the analysis of the quality of basis sets

The contribution of the orbital values to the operators relate with 〈 p t 〉 can be used as a quality test of basis sets. Momentum expectation values are applied as a criterion of basis set quality for the Mn( 6 S) atom employing both GTO and STO basis sets. Detailed comparison suggests that orbital and total momentum values give information about the behavior of a basis set. A formulation of momentum expectation values for GTO functions is also included.

Momentum, angular momentum, and equations of motion for test bodies in space-time with torsion

The definitions and transformation properties of momentum and angular momentum of test bodies possessing both macroscopic rotation and net spin are discussed. The equations of motion for momentum and angular momentum of test bodies are derived and written in a covariant form when the energy-momentum tensor is symmetric.

Optical measurement with direct traceability to the primary standards of length and time: toward a system of metrology based entirely on the properties of the photon

It is proposed that the primary standards of length and time have now reached a sufficient level of maturity that they may be removed from the standards laboratories and used directly for measurement calibration with minimal recourse to the use of intermediate secondary standards. In particular, if a measurement can be configured to give a time-related output such as decay time, time of flight (TOF), frequency, or phase shift, then direct traceability to the primary atomic clock standard can be realized through use of the LORAN C or global position satellite systems. Twelve illustrative examples are considered covering a wide range of optical and spectroscopic measurements. This approach is then extended to mass, the remaining primary standard that is not currently photon based. An optical definition of mass is realizable in terms of length and time through the angular momentum properties of the photon measured using the torsion balance. The constant 2π/h gives the circularly polarized photon flux required to produce a torque of 1 N . m from which mass may be derived in terms of the mechanical moment of inertia. The need to distinguish the sign as well as the magnitude ofthe photon angular momentum then suggests that the unit of time should also have a sign. This sign distinguishes the roles of left and right circularly polarized light for matter and antimatter.