Values Of Total Angular Momentum Research Articles

On the world sheet of anyon in the external electromagnetic field

We study the issue of description of spinning particle dynamics by means of recently proposed world sheet concept. A model of irreducible spinning particle in the 3d Minkowski space with two gauge symmetries is considered. The classical trajectories of free particle lie on a circular cylinder with a time-like axis. The direction of cylinder axis is determined by the particle momentum, and its position in space-time depends on the value of total angular momentum. The radius of cylinder is determined by the representation. The model admits inclusion of consistent interactions with a general (not necessarily uniform) electromagnetic field. The classical trajectories of the particle lie on the cylindrical hypersurface in space time, whose position is determined by the initial values of the momentum and total angular momentum. All the world paths that lie on one and the same representative in the set of hypersurfaces are connected by gauge transformations. The general construction is illustrated by the example of unform electric field. In this case, the particle paths are shown to be general pseudotoroidal lines.

Worldsheet of a continuous helicity particle

We consider the class of spinning particle theories, whose quantization corresponds to the continuous helicity representation of the Poincare group. The classical trajectories of the particle are shown to lie on the parabolic cylinder with a lightlike axis irrespectively to any specifics of the model. The space-time position of the cylinder is determined by the values of momentum and total angular momentum. The value of helicity determines the focal distance of parabolic cylinder. Assuming that all the world lines lying on one and the same cylinder are connected by gauge transformations, we derive the geometrical equations of motion for the particle. The timelike world paths are shown to be solutions to a single relation involving the invariants of trajectory up to fourth order in derivatives. Geometrical equation of motion is non-Lagrangian, but it admits equivalent variational principle in the extended set of dynamical variables. The lightlike paths are also admissible on the cylinder, but they do not represent the classical trajectories of this spinning particle. The classical trajectories of massless particle (with zero helicity) are shown to lie on hyperplanes, whose space-time position depends on momentum and total angular momentum.

Multiparameter estimation for qubit states with collective measurements: a case study

Quantum estimation involving multiple parameters remains an important problem of both theoretical and practical interest. In this work, we study the problem of simultaneous estimation of two parameters that are respectively associate with the length and direction of the Bloch vector for identically prepared qubit states that is confined to a plane, where in order to obtain the optimal estimation precision for both parameters, collective measurements on multiple qubits are necessary. Upon treating N qubits as an ensemble of spin-1/2 systems, we show that simultaneous optimal estimation for both parameters can be attained asymptotically with a simple collective measurement strategy—first, we estimate the length parameter by measuring the populations in spaces corresponding to different total angular momentum values j, then we estimate the direction parameter by performing a spin projection onto an optimal basis. Furthermore, we show that when the state is nearly pure, for sufficiently but not arbitrarily large N, most information will be captured in the largest three j-subspaces. Then, we study how the total angular-momentum measurement can be realized by observing output signatures from a Bell multiport setup, either exactly for N = 2, 3, or approximately when the qubits are nearly pure for other N values. We also obtain numerical results that suggest that using a Bell multiport setup, one can distinguish between projection onto the j = N/2 and j = N/2 − 1 subspaces from their respective interference signatures at the output.

Calculation of double differential cross sections of electron–atom bremsstrahlung by the relativistic partial-wave method at electron energies greater than 3 MeV

This work describes an extension of the relativistic partial-wave (PW) method for calculation of the double differential cross sections (DDCS) of electron–atom bremsstrahlung at incident electron energies (T1) of the order of 10 MeV. The PW method is extended to higher energies by replacing some of the radial matrix elements with interpolated values, and by extrapolating the truncated PW series to a sufficiently high value of the maximum total angular momentum of the electron (jmax). Although the current analysis has been mostly limited to the cases with the outgoing electron energy T2≤10MeV and all values of Z from 1 to 100, this method allows to obtain accurate values of the DDCS even when T2>20MeV, using a relatively small number of partial waves (jmax<300), as demonstrated by a case study described in the present work (Z=1, T1=30MeV, T2=24MeV).

Efficient Method for an Approximate Treatment of the Coriolis Effect in Calculations of Quantum Dynamics and Spectroscopy, with Application to Scattering Resonances in Ozone.

A numerical approach is developed to capture the effect of rotation-vibration coupling in a practically affordable way. In this approach only a limited number of adjacent rotational components are considered to be coupled, while the couplings to other rotational components are neglected. This partially coupled (PC) approach permits to reduce the size of Hamiltonian matrix significantly, which enables the calculations of ro-vibrational states above dissociation threshold (scattering resonances) for large values of total angular momentum. This method is employed here to reveal the role of the Coriolis effect in the ozone formation reaction at room temperature, dominated by large values of total angular momentum states, on the order of J = 24 and 28. We found that, overall, the effect of ro-vibrational coupling is not minor for large J. Compared to the results of symmetric top rotor approximation, where the ro-vibrational coupling is neglected, we found that the widths of scattering resonances, responsible for the lifetimes of metastable ozone states, remain nearly the same (on average), but the number of these states increases by as much as 20%. We also found that these changes are nearly the same in symmetric and asymmetric ozone isotopomers 16O18O16O and 16O16O18O. Therefore, based on the results of these calculations, the Coriolis coupling does not seem to favor the formation of asymmetric ozone molecules and thus cannot be responsible for symmetry-driven mass-independent fractionation of oxygen isotopes.

Shell model structure of proxy-SU(3) pairs of orbitals

The Nilsson orbitals used in the substitutions occurring in the proxy-SU(3) scheme, which are the orbitals bearing the maximum value of total angular momentum in each shell, have an extremely simple structure in the shell model basis $$|N l j \Omega \rangle $$ , with each Nilsson orbital corresponding to a single-shell model eigenvector. This simple structure is valid at all deformations for these orbitals, while in other orbitals it is valid only at small deformations. Nilsson 0[110] pairs are found to correspond to $$|1 1 1 0\rangle $$ pairs in the spherical shell model basis, paving the way for using the proxy-SU(3) approximation within the shell model.

On Mathematical Modeling of Swirling Turbulent Wakes with Varied Total Excess Momentum and Angular Momentum

The flow in swirling turbulent wakes with varying total excess momentum and angular momentum is described using two second-order mathematical models. The first one includes averaged equations of momenta, turbulence energy balance, and dissipation rate in the far-wake approximation. The closure of the mathematical model relies on Rodi’s algebraic model for Reynolds stresses. The second model is based on simplified representations of the turbulent viscosity coefficients. For small distances, the calculated profiles of averaged motion velocities and turbulence energy are in good agreement with the experimental data of Lavrent’ev Institute of Hydrodynamics of SB RAS. At large distances, numerical experiments have yielded a self-similar solution of problems of dynamics of turbulent wake behind a self-propelled body and momentumless swirling turbulent wake. Group-theoretical analysis of the simplified mathematical model has been done. The model had been reduced to a system of ordinary differential equations, which was solved numerically using asymptotic expansions. The solution obtained was compared with the self-similar solution found by direct numerical integration of the differential equations of the model at large distances from the body, and good agreement was observed. In addition, the problem of asymptotic behavior of swirling turbulent wake behind a sphere with non-zero values of total excess momentum and angular momentum was considered. The group-theoretical analysis has shown the absence of physically meaningful self-similar solutions to the equations of the turbulence model under consideration.

The Allure of High Total Angular Momentum Levels in Multiply-Excited Ions

In the interaction of fast ions with dense matter, the collision frequency is high enough to facilitate the simultaneous excitation of several electrons. Such multiply-excited few-electron systems have been exploited variously for plasma diagnostics. Beam-foil spectroscopic techniques, benefiting from the inherent time-resolution offered by the geometry of typical experiments, have proven particularly fruitful for the study of emission patterns and level lifetimes of specific multiply-excited levels, especially those of maximum spin and total angular momentum. Typical cases are recalled to illustrate some general principles. Among many others, earlier beam-foil measurements have targeted the core-excited 2p53s3p 4D7/2 – 2p5 3s3d 4F9/2 transition in several Na-like spectra ranging from S VI to Cu XIX. Data on the six intermediate elements missing at that time are now added. The interest in such atomic systems with multiple excitations and high total angular momentum values is discussed with a variety of examples.

Exact bound rovibrational spectra of the neon tetramer.

Exact quantum dynamics calculations are performed for the bound rovibrational states of the neon tetramer (Ne4) in its ground electronic state, using pair-wise Lennard-Jones potentials and the ScalIT suite of parallel codes. The vibrational states separate into a low-lying group mostly localized to a single potential well and a higher-energy delocalized group lying above the isomerization threshold-with such a structure serving as a testament to the "intermediate" quantum nature of the Ne4 system. To accurately and efficiently represent both groups of states, the phase-space optimized discrete variable representation (PSO-DVR) approach was used, as implemented in the ScalIT code. The resultant 1D PSO effective potentials also shed significant light on the quantum dynamics of the system. All vibrational states were computed well up into the isomerization band and labeled up to the classical isomerization threshold-defined as the addition of the classical energy of a single bond, ϵ = 24.7 cm-1, to the quantum ground state energy. Rovibrational energy levels for all total angular momentum values in the range J = 1-5 were also computed, treating all Coriolis coupling exactly.

Generation of an optical ball bearing facilitated by coupling between handedness of polarization of light and helicity of its phase

We report on mutual transformation of spin and orbital angular momenta (SAM and OAM) of light upon tight focusing of circularly polarized vortex beams. In some regions of the focal spot, the OAM of light changes by a value ±2ℏ, while the circular polarization (CP) there reverses its rotation direction, resulting in adjacent rings (or core and adjacent ring) of opposite CP handedness. Moreover, the SAM has a transverse angular momentum (AM) component. We show that while the whole pattern rotates around the optical axis at the rate of the optical frequency divided by the value of total AM, the 3D SAM “balls” between adjacent rings (or between a ring and a core) spin in an opposite direction at the rate of the optical frequency, constituting an optical analog of a ball bearing. The applications include manipulation of particles, e.g., optical tweezers or spanners.

Origin of the orbital period change in contact binary stars

The evolution of contact binary star systems in mass asymmetry (transfer) coordinate is considered. The orbital period changes are explained by an evolution in mass asymmetry towards the symmetry (symmetrization of binary system). It is predicted that decreasing and increasing orbital periods are related, respectively, with the nonoverlapping and overlapping stage of the binary star during its symmetrization. A huge amount of energy [Formula: see text][Formula: see text]J is converted from the potential energy into internal energy of the stars during the symmetrization. As shown, the merger of stars in the binary systems, including KIC 9832227, is energetically an unfavorable process. The sensitivity of the calculated results to the values of total mass and orbital angular momentum is analyzed.

Isotope shifts and band progressions in SO2 rovibrational energy levels: using quantum theory to extract rotational constants

ABSTRACTWe report the isotope shifts of the rotational constants and vibrational band progressions of the sulfur dioxide molecule (SO), for all four stable sulfur isotopes32S,33S,34S, and36S. These are extracted from exact quantum theoretical calculations of the SO rovibrational energy levels, as reported in Chem. Phys. 450–451, 59 (2015) and Chem. Phys. 461, 34 (2015) and by fitting these levels to a J-shifting (JS)-type scheme, applied to a representative set of total angular momentum (J) values. The approach used to obtain the rotational constants is unusual in that it is derived directly from the quantum theoretical framework used for the earlier calculation, which gives rise to a flexible (i.e., vibrational- and rotational-state-dependent) but symmetric rotor description. The usual rotational quantum numbers are thus replaced with a single body-fixed azimuthal rotation quantum number, K, with various strategies introduced a posteriori to address rotor asymmetry. The new model fits the numerically computed rovibrational levels well, over a fairly broad range of vibrational (v) and rotational (J) excitations. The computed rotational constants agree well with previously reported experimental values [J. Chem. Phys. 58, 265 (1973)]. The explicitly v- and J-dependent approach used here should thus prove valuable in broader contexts—e.g., for an analysis of self-shielding in sulfur mass-independent fractionation, even though the rovibrational levels themselves exhibit mass-dependent fractionation.

Nuclear pairing fluctuations and angular momentum dependence of superconductivity in 94Mo nucleus

The effects of thermal fluctuations on pairing properties of nuclei with inclusion of angular momentum have been investigated. To treat nuclei at finite temperature and angular momentum, we have extended the formalism in which the mean value of the gap parameter is used to obtain thermal properties of nuclei based on the BCS scheme [Z. Kargar and V. Dehghani, J. Phys. G, Nucl. Part. Phys. 40 (2013) 045108] let us name it MEGBCS. The results obtained for [Formula: see text] nucleus show the appearance of thermally assisted pairing correlations with increasing angular momentum. Also, the [Formula: see text]-shaped heat capacity found experimentally [K. Kaneko et al., Phys. Rev. C 74 (2006) 024325] and theoretically, interpreted as the second phase transition in mesoscopic systems, disappears with increasing angular momentum above a critical value. The nuclear level density of [Formula: see text] is calculated versus excitation energy at various values of total angular momentum. The total level density matches the experimental data closely.

The Belgian repository of fundamental atomic data and stellar spectra (BRASS)

Context. Fundamental atomic parameters, such as oscillator strengths, play a key role in modelling and understanding the chemical composition of stars in the Universe. Despite the significant work underway to produce these parameters for many astrophysically important ions, uncertainties in these parameters remain large and can propagate throughout the entire field of astronomy. Aims. The Belgian repository of fundamental atomic data and stellar spectra (BRASS) aims to provide the largest systematic and homogeneous quality assessment of atomic data to date in terms of wavelength, atomic and stellar parameter coverage. To prepare for it, we first compiled multiple literature occurrences of many individual atomic transitions, from several atomic databases of astrophysical interest, and assessed their agreement. In a second step synthetic spectra will be compared against extremely high-quality observed spectra, for a large number of BAFGK spectral type stars, in order to critically evaluate the atomic data of a large number of important stellar lines. Methods. Several atomic repositories were searched and their data retrieved and formatted in a consistent manner. Data entries from all repositories were cross-matched against our initial BRASS atomic line list to find multiple occurrences of the same transition. Where possible we used a new non-parametric cross-match depending only on electronic configurations and total angular momentum values. We also checked for duplicate entries of the same physical transition, within each retrieved repository, using the non-parametric cross-match. Results. We report on the number of cross-matched transitions for each repository and compare their fundamental atomic parameters. We find differences in log(gf) values of up to 2 dex or more. We also find and report that ~2% of our line list and Vienna atomic line database retrievals are composed of duplicate transitions. Finally we provide a number of examples of atomic spectral lines with different retrieved literature log(gf) values, and discuss the impact of these uncertain log(gf) values on quantitative spectroscopy.

Geometric phase effects in the ultracold D + HD D + HD and D + HD H + D2 reactions

The results of accurate quantum reactive scattering calculations for the D + HD(v = 4, j = 0) D + HD(, ), D + HD(v = 4, j = 0) H + D2(, ) and H + D2(v = 4, j = 0) D + HD(, ) reactions are presented for collision energies between and . The ab initio BKMP2 PES for the ground electronic state of H3 is used and all values of total angular momentum between are included. The general vector potential approach is used to include the geometric phase. The rotationally resolved, vibrationally resolved, and total reaction rate coefficients are reported as a function of collision energy. Rotationally resolved differential cross sections are also reported as a function of collision energy and scattering angle. Large geometric phase effects appear in the ultracold reaction rate coefficients which result in a significant enhancement or suppression of the rate coefficient (up to 3 orders of magnitude) relative to calculations which ignore the geometric phase. The results are interpreted using a new quantum interference mechanism which is unique to ultracold collisions. Significant effects of the geometric phase also appear in the rotationally resolved differential cross sections which lead to a very different oscillatory structure in both energy and scattering angle. Several shape resonances occur in the 1– energy range and the geometric phase is shown to significantly alter the predicted resonance spectrum. The geometric phase effects and ultracold rate coefficients depend sensitively on the nuclear spin. Thus, experimentalists may be able to control the reaction by the selection of a particular nuclear spin state.

Formation of ground and excited hydrogen atoms in proton–potassium inelastic scattering

The inelastic scattering of proton with a potassium atom is treated for the first time as a three-channel problem within the framework of the improved coupled static approximation by assuming that the ground (1s state) and the excited (2s state) hydrogen formation channels are open for seven values of total angular momentum, l (0≤l≤6) at energies between 50 and 500 keV. The Lipmann–Swinger equation and the Green’s function iterative numerical method are used to calculate iterative partial and total cross-sections. This can be done by calculating the reactance matrix at different values of the considered incident energies to obtain the transition matrix that gives partial and total cross-sections. Present results are in reasonable agreement with previous results.

On the absence of higher generations of incompressible daughter states of composite Fermion quasiparticles

Jain [1] introduced a simple mean-field (MF) composite Fermion (CF) picture by attaching to each electron in a quantum Hall system a flux tube producing a Chern- Simons magnetic field b(r) = 2pϕ0 Σi δ(r - ri)ẑ. Here ϕ0 = hc/e is the quantum of flux, and the sum is over all electron coordinates ri. He then averaged the total flux and the total charge (electronic plus positive background) over the entire sample. This MF picture gave a system of noninteracting CFs in an effective magnetic field B*0 = νB0. It predicted incompressible quantum liquid (IQL) states at filling factors ν = n(1 + 2pn)-1 for integral values of n. Chen and Quinn [2] demonstrated that Jain’s MF CF picture predicted the total angular momentum values of the lowest energy band of states for any value of the applied magnetic field B0. Justification of when the MFCF picture was valid was given by Wojs and Quinn [3], who extended the CF hierarchy scheme of Sitko et al. [4]. The CF hierarchy gave the Jain states for integrally filled CF Landau levels (CF LLs), and the Haldane hierarchy of all odd denominator fractions when quasiparticles in the highest (partially filled) CF angular momentum shell had interactions sufficiently similar to the Coulomb interactions of electrons in the lowest Landau level. Sitko et al. showed that the predictions of the CF hierarchy scheme were not always correct. By using a simple pair angular momentum identity and the concept of fractional grandparentage, Wojs and Quinn showed that higher generations of CFs could result from the interactions of the original CF quasiparticles only if their interaction energy VQP(L2) as a function of their pair angular momentum L2 increased with increasing L2 faster than L2(L2 + 1). For Laughlin quasielectrons of the ν = 1/3 IQL state this condition was not satisfied. Therefore, no second generation of CFs could occur. The observed IQL at electron filling factor ν = 4/11 can not be attributed to a daughter IQL state at νQE = 1/3 in a totally spin polarized system. Rather, it is an IQL state of electron pairs with pair angular momentum ιp = 2ι – 1. A description of the IQL state of electron pairs and its low energy excitations will be presented, and the possibility of a spin flip quantum phase transition as a function of well width and applied magnetic field will be discussed.

Born-Oppenheimer and Renner-Teller Quantum Dynamics of CH(X(2)Π) + D((2)S) Reactions on Three CHD Potential Surfaces.

The quantum dynamics of three CH(X(2)Π) + D((2)S) reactions is studied by means of the coupled-channel time-dependent real-wavepacket (WP) and flux methods at collision energy Ecol ≤ 0.6 eV and on three potential energy surfaces (PESs): the Born-Oppenheimer (BO) ground PES X̃(3)A″ and the excited ones ã(1)A' and b̃(1)A″, coupled by nonadiabatic (NA) Renner-Teller (RT) effects. This three-state model is suitable for obtaining initial-state-resolved observables, is based on a complete analysis of the correlation diagram of the lowest electronic states of the CHD intermediate and of their NA interactions, and neglects the smaller coupling effects due to the asymptotic electronic angular momenta that become important in state-to-state dynamics. WPs are propagated on each PES at total angular momentum values J ≤ 70, with CH in the two lowest vibrational states v0 and in the ground rotational state j0 = 1. Reaction probabilities are obtained for three possible final products (f): (dP) CH decay and C((3)P) + HD(X(1)Σ(+)) formation that occurs on the uncoupled ground PES, (dD) CH decay and C((1)D) + HD(X(1)Σ(+)) formation that depends on the RT-coupled singlet species, and (ex) exchange to CD(X(2)Π) + H((2)S) available adiabatically from the X̃(3)A″ PES and nonadiabatically from ã(1)A' and b̃(1)A″. Observable cross sections σf,v0j0 and rate constants kf,v0j0 in the temperature range T = 100-2000 K are obtained for (dP), (dD), and (ex) channels. Comparing BO with RT probabilities, we show that NA effects are important at high J values for the (ex) channel at v0 = 1. Real time mechanisms on the three PESs show that RT couplings are opened after some time and clearly point out the formation of the product channels. Both cross sections and rate constants present the same sequence, for example σex,11 > σdP,01 ∼ σex,01 > σdP,11 ≫ σdD,11 ≫ σdD,01, and the CH vibrational excitation enhances the total removal CH+D reactivity by a factor of ∼1.7, mainly due to the increase of the (ex) channel contribution from ∼47% at v0 = 0 to ∼76% at v0 = 1. This fact implies a considerable vibrational enhancement of combustion processes at high temperature. In agreement with the probability results, the ã(1)A'/b̃(1)A″ RT coupling increases both σex,11 and kex,11 up to ∼30%. Moreover, including the three PESs in the dynamics simulation of CH+D increase by far the (ex)/(dP) branching ratio with respect to the CH + H' reaction. Thus, at room temperature, kdP,01 changes from 10.8 × 10(-11) to 3.4 × 10(-11) cm(3) s(-1) substituting H atom by D.

Structural features and magnetic behavior of nanocrystalline powders of terbium oxide prepared by the thermal decomposition of terbium acetate in air

Nanostructured powders of terbium oxides were prepared by the thermal decomposition of terbium acetate at different temperatures. The powders were investigated by means of XRD, HRTEM, magnetic measurements, and IR spectroscopy. It has been found that the most likely composition of the oxides is Tb4O7, and the powders containing more than one crystalline phase. At low temperatures the prepared oxides exhibit antiferromagnetic ordering with the Weiss constants ranging from −14 to −22 K. At 2 K the effective value of total angular momentum per one Tb ion in the paramagnetic state J = 2.5 ± 0.1. The effects of the calcination temperature on the crystal structure, microstructure and magnetic behaviors of the samples are discussed in terms of that surface impurities presented in the nanocrystalline powders of Tb oxides influence the cation Tb4+/Tb3+ ratio in their crystal lattice.

Rovibrational bound states of SO2 isotopologues. II: Total angular momentum J = 11–20

In a two-part series, the rovibrational bound states of SO2 are investigated in comprehensive detail, for all four stable sulfur isotopes 32–34,36S. All low-lying rovibrational energy levels—both permutation-symmetry-allowed and not allowed—are computed, for all values of total angular momentum in the range J=0–20. The calculations have carried out using the ScalIT suite of parallel codes. The present study (Paper II) examines the J=11–20 rovibrational levels, providing symmetry and rovibrational labels for every computed state, relying on a new lambda-doublet splitting technique to make completely unambiguous assignments. Isotope shifts are analyzed, as is the validity of “J-shifting” as a predictor of rotational fine structure. Among other ramifications, this work will facilitate understanding of mass-independent fractionation of sulfur isotopes (S-MIF) observed in the Archean rock record—particularly as this may have arisen from self shielding. S-MIF, in turn is highly relevant in the broader context of understanding the “oxygen revolution”.