Center-of-mass Frame Research Articles

Electronic and centre of mass transitions driven by Laguerre–Gaussian beams

We derive the interaction Hamiltonian of a Laguerre-Gaussian beam with a simple atomic system, under the assumption of a small spread of the center of mass wave function in comparison with the waist of the Laguerre-Gaussian beam. The center of mass motion of the atomic system is taken into account. Using the properties of regular spherical harmonics the internal and center of mass coordinates are separated without making any multipolar expansion. Then the selection rules of the internal and of the center of mass motion transitions follow immediately. The influence of the winding number of the Laguerre-Gaussian beams on the selection rules and transition probability of the center of mass motion is discussed.

Measurement of the angular distribution in [formula omitted

We present the first measurement of the angular distribution for the exclusive process p¯p→ψ(2S)→e+e− based on a sample of 6844 events collected by the Fermilab E835 experiment. We find that the angular distribution is well described by the expected functional form dNdcosθ∗∝1+λcos2θ∗, where θ∗ is the angle between the antiproton and the electron in the center of mass frame, with λ=0.67±0.15(stat)±0.04(sys). The measured value for λ implies a small but non-zero ψ(2S) helicity 0 formation amplitude in p¯p, comparable to what is observed in J/ψ decays to baryon pairs.

Transient fluid slosh and its effect on the rollover-threshold analysis of partially filled conical and circular tank trucks

The transient forces and roll moment caused by fluid slosh within partly filled circular and conical cross-section tanks, subject to a time-varying lateral acceleration field, are evaluated numerically and compared with those estimated from a quasi-static formulation. The variations in the centre of mass coordinates, vertical and lateral forces and roll moment are applied to the roll-moment model of a 6-axle tractor-semi-trailer articulated tank vehicle for analysis of the steady-turning rollover threshold. The results show that the magnitudes of transient lateral force and roll moment approach significantly higher values, than those estimated from the quasi-static formulations. The mean values of the force and moment, however, are similar to those predicted from the quasi-static solution. The steady-turning rollover-threshold accelerations of the vehicle combination with partly filled tanks are thus considerably lower when transient slosh forces and moment are considered in the moment equilibrium, specifically for the intermediate fill volumes. The results further show that the static roll stability limits of the combination with a conical cross-section tank are considerably higher than that with a circular cross-section tank.

Finite temperature pion vector form factors in chiral perturbation theory

We discuss the thermal behaviour of the pion vector form factors and calculate them in one-loop chiral perturbation theory. The perturbative result is used to analyze the T-dependent electromagnetic pion charge radius, obtaining a rough estimate of the deconfinement critical temperature. Imposing thermal unitarity, we generate the ρ resonance pole for the form factor in the center of mass frame. The ρ peak height in the modulus of the form factor decreases for increasing temperature, while its width increases and the peak position is slightly shifted downwards for T≃150 MeV. These results point in the direction suggested by many analysis of dilepton production data in relativistic heavy ion collisions.

Solvable scalar and spin models with near-neighbors interactions

We construct new solvable rational and trigonometric spin models with near-neighbors interactions by an extension of the Dunkl operator formalism. In the trigonometric case we obtain a finite number of energy levels in the center of mass frame, while the rational models are shown to possess an equally spaced infinite algebraic spectrum. For the trigonometric and one of the rational models, the corresponding eigenfunctions are explicitly computed. We also study the scalar reductions of the models, some of which had already appeared in the literature, and compute their algebraic eigenfunctions in closed form. In the rational cases, for which only partial results were available, we give concise expressions of the eigenfunctions in terms of generalized Laguerre and Jacobi polynomials.

Theoretical study of the stereodynamics of the reaction Cl+C3H8→C3H7+HCl

The product rotational polarization of the reaction Cl + C 3 H 8 → C 3 H 7 + HCl is calculated via the quasiclassical trajectory method based on extended London–Eyring–Polanyi–Sato potential energy surface (PES) at collision energies of 6.0, 7.4, and 8.0 kcal/mol. Compared the dynamics of Cl substituting the primary and secondary hydrogen of C 3 H 8 , four polarization dependent generalized differential cross-sections (2π/ σ )(d σ 00 /d ω t ), (2π/ σ )(d σ 20 /d ω t ), (2π/ σ )(d σ 22+ /d ω t ) and (2π/ σ )(d σ 21− /d ω t ) have been presented in the center of mass frame, respectively. The distribution of dihedral angle p ( ϕ r ), the distribution of angle between k and j ′, p ( θ r ), and the angular distribution of product rotational vectors in the form of polar plots in θ r and ϕ r are calculated as well. The different character of the abstraction of primary vs. secondary hydrogen atoms from C 3 H 8 may be ascribed to that the different PESs and substituent site. The calculated results are in agreement with the experimental data.

Measurements ofF17scattering byPb208with a new type of large solid angle detector array

A new pixel-structure detector array with a large solid angle coverage has been used for the first time to study the elastic scattering of exotic $^{17}\mathrm{F}$ nuclei from a $^{208}\mathrm{Pb}$ target at $90.4\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$. The experimental data have been analyzed in the framework of the optical model potential and the real and imaginary strong absorption radii have been evaluated. These quantities have been compared with those obtained for the system $^{19}\mathrm{F}+^{208}\mathrm{Pb}$ at the same energy in the center of mass frame. The $^{17}\mathrm{F}+^{208}\mathrm{Pb}$ reaction cross section is more similar to those of the systems $^{16,17}\mathrm{O}+^{208}\mathrm{Pb}$ rather than to the one of the system $^{19}\mathrm{F}+^{208}\mathrm{Pb}$ at similar energies: this indicates that in the energy range around the Coulomb barrier the breakup channel is still weak. The exclusive breakup cross section $^{17}\mathrm{F}\ensuremath{\rightarrow}^{16}\mathrm{O}+p$ has been measured for the first time at energy below the Coulomb barrier.

I = 2 pion-pion scattering phase shift in the continuum limit calculated with two-flavor full QCD

We present a calculation of the scattering phase shift for the I = 2 S-wave pion-pion system in the continuum limit with two-flavor full QCD. Calculations are made at three lattice spacings, using the finite volume method of Lüscher in the center of mass frame, and its extension to the laboratory frame.

Angular momentum of electromagnetic pulses

Electromagnetic pulses are shown to have an intrinsic angular momentum along the direction of the net momentum of the pulse, unchanged by Lorentz boosts along this direction, and invariant to change of spatial origin. This intrinsic angular momentum is evaluated (together with the energy and momentum) for two types of pulses based on a localized oscillatory solution of the wave equation. The Lorentz boost required to bring each pulse to its zero-momentum frame is evaluated analytically.

Data analysis process of a toroidal analyzer for electron–ion collision experiments

A toroidal analyzer has been developed to measure angular differential cross sections for electron scattering in electron–ion collisions. Energy and angular dispersed electron images are recorded by using a two-dimensional position sensitive detector. Operation and calibration of the analyzer are described with particular emphasis on a procedure to deduce the differential cross sections from the acquired two-dimensional data. Angular differential cross sections for elastic scattering of electrons from Ar7+ and Ar8+ ions are presented in the angular range from 34° to 85° at a collision energy of 100 eV in the center of mass frame.

Simulation of Electron Decoherence Induced by Carrier-Carrier Scattering

We study, by means of numerical simulations, the decoherence induced by a low-energy carrier-carrier scattering event on the spatial degrees of freedom of one of the two distinguishable carriers. The two-particle time-dependent Schrodinger equation is solved in the center of mass frame and the decoherence is quantified, at a number of time steps, by evaluating the entanglement between the two particles. We find that the decoherence rate is higher for higher kinetic energy of the particles and that a scattering between two carriers with opposite charge produces more decoherence than one between carriers with equal charge. The parallel algorithm used for the entanglement calculation is described.

Gravitational memory effect in “boosted” black hole perturbation theory

Black hole perturbation theory, or more generally, perturbation theory on a Schwarzschild background, has been applied in several contexts, but usually under the simplifying assumption that the Arnowitt-Deser-Misner (ADM) momentum vanishes, namely, that the evolution is carried out and observed in the ``center of momentum frame.'' In this paper we consider some consequences of the inclusion of a nonvanishing ADM momentum in the initial data. We first provide a justification for the validity of the transformation of the initial data to the ``center of momentum frame,'' and then analyze the effect of this transformation on the gravitational wave amplitude. The most significant result is the possibility of a type of gravitational memory effect that appears to have no simple relation to the well known Christodoulou effect.

Energy and momentum of electromagnetic pulses

We show that free-space pulse solutions of Maxwell's equations which are localized in space and time have energy greater than c times their momentum. Thus a Lorentz transformation to a zero-momentum frame is always possible, in contradistinction to Einstein's light quantum, for which a zero-momentum frame does not exist. However, free-space pulse solutions of Maxwell's equations are not subluminal: their momentum is less than their energy divided by c due to necessary spreading or convergence.

Uniqueness of Centauro-type events

Analysis to discriminate Centauro events from normal events is made without previous identification of secondary emitted particles. For this purpose their energy and derived quantities like distance from the center of momenta it were mainly used. As a result we found in a sample of (280+87) experimental events only 3 were compatible with 5 Centauro events, but none of them dad a high content of hadrons, characteristic of Centauro events. With this result we are confident about the uniqueness of Centauro events, especially for two events that have vertex directly determined. Comparing with some interaction models features we depict a possible scenario to explain Centauro events.

A dynamical definition of quasibound molecular clusters

Molecular configurations which count as snapshots of a quasibound cluster are identified through a retrospective dynamical definition. The trajectory of a molecular cluster is followed, and a clear evaporation event is considered to have occurred when a molecule moves a very long distance away from the others. The cluster is judged to have broken before this condition is satisfied, however, at the instant that the energy of the departing molecule in the center of mass frame becomes positive. The decay of a cluster is therefore defined dynamically as the production of a molecule with positive energy on a separating trajectory. Not all positive energy molecules created by the system follow such a trajectory, hence the need to examine the subsequent behavior in molecular dynamics. We simulate a sequence of decays by repairing broken clusters as they occur. This approach enables us to calculate mean decay rates of isolated Lennard-Jones clusters in what promises to be a physically realistic fashion.

Electromagnetic pulses which have a zero momentum frame

One set of the Ziolkowski family of exact solutions of the wave equation are shown to represent pulses propagating with momentum smaller than energy/c. This is explicitly demonstrated for special cases by calculating the total electromagnetic momentum and energy. Since the ratio of momentum to energy is a constant smaller than 1/c, there exists a Lorentz transformation to a frame in which the total momentum is zero. In the zero-momentum frame the fields are those of an annular pulse converging onto or diverging from a focal region.

Perturbation theory for bound states and resonances where potentials and propagators have arbitrary energy dependence

Standard derivations of ``time-independent perturbation theory'' of quantum mechanics cannot be applied to the general case where potentials are energy dependent or where the inverse free Green function is a nonlinear function of energy. Such derivations cannot be used, for example, in the context of relativistic quantum field theory. Here we solve this problem by providing a new, general formulation of perturbation theory for calculating the changes in the energy spectrum and wave function of bound states and resonances induced by perturbations to the Hamiltonian. Although our derivation is valid for energy-dependent potentials and is not restricted to inverse free Green functions that are linear in the energy, the expressions obtained for the energy and wave function corrections are compact, practical, and maximally similar to the ones of quantum mechanics. For the case of relativistic quantum field theory, our approach provides a direct covariant way of obtaining corrections to wave functions that are not in the center of mass frame.

The Nelson Model with Less Than Two Photons

We study the spectral and scattering theory of the Nelson model for an atom interacting with a photon field in the subspace with less than two photons. For the free electron-photon system, the spectral property of the reduced Hamiltonian in the center of mass coordinates and the large time dynamics are determined. If the electron is under the influence of the nucleus via spatially decaying potentials, we locate the essential spectrum, prove the absence of singular continuous spectrum and the existence of the ground state, and construct wave operators giving the asymptotic dynamics.

Forward-backward charge asymmetry ine+e−annihilation into hadrons at high energies

The forward-backward asymmetry in ${e}^{+}{e}^{\ensuremath{-}}$ annihilation into a quark-antiquark pair is considered in the double-logarithmic approximation at energies much higher than the masses of the weak bosons. It is shown that after accounting for the exchange of virtual photons and $W,Z$ bosons to all orders one is led to the following effect (asymmetry): quarks with positive electric charge (e.g., u, $\overline{d})$ tend to move in the ${e}^{+}$ direction whereas quarks with negative charges (e.g., d, $\ifmmode \bar{u}\else \={u}\fi{})$ tend to move in the ${e}^{\ensuremath{-}}$ direction. The value of the asymmetry grows with increasing energy when the produced quarks are within a cone with an opening angle, in the center of mass frame, ${\ensuremath{\theta}}_{0}\ensuremath{\sim}{2M}_{Z}/\sqrt{s}$ around the ${e}^{+}{e}^{\ensuremath{-}}$ beam. Outside this cone, at ${\ensuremath{\theta}}_{0}\ensuremath{\ll}\ensuremath{\theta}\ensuremath{\ll}1,$ the asymmetry is inversely proportional to $\ensuremath{\theta}.$

A position-sensitive coincidence spectrometer to image the kinematics of thebimolecular reactions of molecular dications

This paper describes the design and operation of a position-sensitive coincidencespectrometer which detects the pairs of ions formed in the bimolecularreactions of dications. In the experiment a pulsed, energy-selected beam ofdications interacts with a neutral collision gas in the source region of atime-of-flight mass spectrometer. Product ions formed in these interactionsare detected in coincidence at a position-sensitive detector. From theresulting data, we can derive the velocity vectors, in the centre of massframe, of both of the product ions. From these pairs of vectors, detailedinformation on the reaction dynamics and kinematics can be extracted. Thepower of the new technique has been demonstrated by a study of theelectron transfer reaction between Ar2+ and He, which shows that the 3P and1Dstates of Ar2+ react with He, via electron transfer, to form pairs of singly chargedions with markedly different angular distributions.