Total Orbital Angular Momentum Research Articles

Shifted nondiffractive Bessel beams

Nondiffractive Bessel beams are well known to have infinite energy and infinite orbital angular momentum (OAM). However, when normalized to unity of energy, their OAM is finite. In this work, we derive an analytical relationship for calculating the normalized OAM of the superposition of off-axis Bessel beams characterized by the same topological charge. We show that if the constituent beams of the superposition have real-valued weight coefficients, the total OAM of the superposition of the Bessel beams equals that of an individual nonshifted Bessel beam. This property enables generating nondiffractive beams with different intensity distributions but identical OAM. The superposition of a set of identical Bessel beams centered on an arbitrary-radius circle is shown to be equivalent to an individual constituent Bessel beam put in the circle center. As a result of a complex shift of the Bessel beam, the transverse intensity distribution and OAM of the beam are also shown to change. We show that, in the superposition of two or more complex-shifted Bessel beams, the OAM may remain unchanged, while the intensity distribution is changed. Numerical simulation is in good agreement with theory.

Spin-orbit decomposition ofab initionuclear wave functions

Although the modern shell-model picture of atomic nuclei is built from single-particle orbits with good total angular momentum $j$, leading to $j$-$j$ coupling, phenomenological models suggested decades ago that for $0p$-shell nuclides a simpler picture can be realized via coupling of total spin $S$ and total orbital angular momentum $L$. I revisit this idea with large-basis, no-core shell model (NCSM) calculations using modern \textit{ab initio} two-body interactions, and dissect the resulting wavefunctions into their component $L$- and $S$-components. Remarkably, there is broad agreement with calculations using the phenomenological Cohen-Kurath forces, despite a gap of nearly fifty years and six orders of magnitude in basis dimensions. I suggest $L$-$S$ may be a useful tool for analyzing \textit{ab initio} wavefunctions of light nuclei, for example in the case of rotational bands.

Energy angular momentum closed-loop guidance

A novel guidance algorithm for launch vehicle ascent to the desired mission orbit is proposed. The algorithm uses total specific energy and orbital angular momentum as new state vector parameters. These parameters are ideally suited for the ascent guidance task, since the guidance algorithm steers the launch vehicle along a pre-flight optimal trajectory in energy angular momentum space. The guidance algorithm targets apogee, perigee, inclination and right ascension of ascending node. Computational complexities are avoided by eliminating time in the guidance computation and replacing it with angular momentum magnitude. As a result, vehicle acceleration, mass, thrust, length of motor burns, and staging times are also eliminated from the pitch plane guidance calculations. The algorithm does not involve launch vehicle or target state propagation, which results in minimal computational effort. Proof of concept of the new algorithm is presented using several numerical examples that illustrate performance results.

Generalized Hund's rule for two-atom systems

Hund's rule is one of the fundamentals of the correlation physics at the atomic level, determining the ground state multiplet of the electrons. It consists of three laws: (i) maximum $S$ (total spin), (ii) maximum $L$ (total orbital angular momentum) under the constraint of (i), and (iii) the total angular momentum $J$ is $|L\ensuremath{-}S|$ for electron number less than half, while $J=L+S$ for more than half due to the relativistic spin-orbit interaction (SOI). In real systems, the electrons hop between the atoms and gain the itinerancy, which is usually described by the band theory. The whole content of theories on correlation is to provide a reliable way to describe the intermediate situation between the two limits. Here we propose an approach toward this goal, i.e., we study the two-atom systems of three ${t}_{2g}$ orbitals and see how the Hund's rule is modified by the transfer integral $t$ between them. It is found that the competition between $t$ and the Hund's coupling $J$ at each atom determines the crossover from the molecular orbital limit to the strong correlation limit. Especially, the focus is on the generalization of the third rule, i.e., the inter- and intra-atomic SOI's in the presence of the correlation. We have found that there are cases where the effective SOI's are appreciably enhanced by the Hund's coupling. The conditions for the enhancement are the intermediate Hund's coupling and the filling of four or five electrons.

Non-collinear interaction of photons with orbital angular momentum

We study the nonlinear interaction between two non-collinear light beams that carry orbital angular momentum (OAM). More specifically, two incident beams interact at an angle in a medium with a second order nonlinearity and thus generate a third, non-collinear beam at the second harmonic frequency that experiences a reduced conversion efficiency in comparison to that expected based on conventional phase-matching theory. This reduction scales with the input beam OAM and, differently from previous spiral bandwidth calculations, is due to a geometric effect whereby the input OAM is projected along the non-collinear interaction direction. The effect is relevant even at small interaction angles and is further complicated at large angles by a non-conservation of the total OAM in the nonlinear interaction. Experiments are performed under different conditions and are in excellent agreement with the theory. Our results have implications beyond the specific case studied here of second-harmonic generation, in particular for parametric down-conversion of photons or in general for phase-matched non-collinear interactions between beams with different OAM.

Morphology effects of self-assembled quantum dots on the energy spectrum of magneto-excitons

In this paper we analyze the changes experienced by the energy spectra of a confined exciton in type II semiconductor quantum dots, considering the quantum dot as a possible functional part that, in the future devices, can be applied in spintronics, optoelectronics, and quantum information technologies. We studied the lowest energy states of an exciton (X) confined in type II InP/GaInP self-assembled quantum dot (SAQDs), with axial symmetry in the presence of a uniformly applied magnetic field in the growth direction. In our model, it is considered that the electron is located within the point of InP and the hole is in the GaInP barrier. The solution of the Schrödinger equation for this system is obtained by a variational separation process of variables in the adiabatic approximation limit and within the effective mass approximation. We study the energy levels associated with the electron and the hole, and the energy of the exciton. Due to the axial symmetry of the problem the z component of the total orbital angular momentum, Lz=le+lh, is preserved and the exciton states are classified according to the values of this component. Quantum dots have a finite and variable thickness, with the purpose of analyzing the effects related to the variation of the morphology and the presence of a wet layer.

Orbital angular momentum control by a multihelicoidal fibre with a twist defect

We have theoretically demonstrated that by creating a controllable twist defect in an l-helicoidal fibre one can control the orbital angular momentum of the generated beam at a constant power. We have studied the passage of the Gaussian beam through such a defect fibre and shown that by varying the twist defect angle one can change the total orbital angular momentum of the generated optical field from 0 to l (in dimensionless units). We have also studied the distribution of the angular momentum density in the cross-section of the generated optical field.

DFT Calculation of Russell–Saunders Splitting for Lanthanide Ions Doped in Hexagonal (β)-NaYF4Nanocrystals

A systematic investigation is reported of the optimized geometry and electronic structure of trivalent lanthanide ions (Ln3+) doped in hexagonal (β)-NaYF4 nanocrystals in the basis of density functional theory with a spin polarization approach. A model Na24Y23Ln1F96 nanocrystal with a single central lanthanide dopant (Ln3+) is used. Electron spins couple to give a total spin, S, and electron orbital angular momenta couple to give total orbital angular momentum, L. Spin–orbit coupling is neglected in this initial study. Several key observables are found to be strongly related to the number of unpaired f-electrons in the model. After geometry optimization, the phenomenon of the lanthanide contraction is observed, and the configurations of 4f-electron-like orbitals satisfy Hund’s Rule under the orbital decomposition. Spin-polarized density functional theory is applied to generate the Russell–Saunders terms (2S+1L) terms of lanthanide ions. The energy differences between the first and the second terms are calculated and show good agreement with experimental measurements. The free-ion-like behavior of Ln3+ ions in the nanocrystal is observed as well.

Probing parton orbital angular momentum in longitudinally polarized nucleon

While the total orbital angular momentum (OAM) of a definite quark flavor in a longitudinally-polarized nucleon can be obtained through a sum rule involving twist-two generalized parton distribution (GPDs), its distribution as a function of parton momentum in light-front coordinates is more complicated to define and measure because it involves intrinsically twist-three effects. In this paper, we consider two different parton OAM distributions. The first is manifestly gauge invariant, and its moments are local operators and calculable in lattice QCD. We show that it can potentially be measured through twist-three GPDs. The second is the much-debated canonical OAM distribution natural in free-field theory and light-cone gauge. We show the latter in light-cone gauge can also be related to twist-three GPDs as well as quantum phase-space Wigner distributions, both being measurable in high-energy experiments.

A novel correlation of vibrational circular dichroism spectra with the electronic ground state for Δ-SAPR-8-cesium-tetrakis((+)-heptafluorobutyryl-camphorato)lanthanide(iii) complexes

For Δ-SAPR-8-Cs[Ln((+)-hfbc)4]((+)-hfbc = (+)-heptafluoro-butyrylcamphorate; Cs-Ln), the vibrational circular dichroism pattern and intensity of Cs-La, Cs-Nd, Cs-Gd, Cs-Ho, Cs-Er, Cs-Lu and Cs-Sm, Cs-Eu, Cs-Tb, Cs-Dy, Cs-Tm, Cs-Yb, respectively, are correlated with the even and the odd parity of total orbital angular momentum in the ground state terms.

Spectroscopy and correlations probed in direct two-nucleon knockout reactions

Nucleon knockout reactions from fast radioactive secondary beams colliding with light nuclear targets provide a useful tool for studying structure away from the valley of (β-stability. An efficient means of producing specific exotic nuclei, the technique has been recently applied to study nuclear halos, isospin symmetry and cross-shell excitations, and in tracking the evolution of single-particle states, and probing the associated quenching (N=20, N=28) and emergence (N=16) of shell gaps. Recent theoretical work has demonstrated the sensitivity of residue momentum distributions following two-nucleon removal to the underlying structure. In particular, there is a sensitivity to the total orbital angular momentum of the removed pair, providing additional tests of (shell- or many-body-) structure-model two-nucleon overlaps. We illustrate the structural sensitivities in the context of nucleon knockout from 12C and 16O, and discuss the prospects for studying np-correlations along the N = Z line, highlighting the need for new final-state exclusive measurements, including those with stable beams.

The pretzelosity TMD and quark orbital angular momentum

We study the connection between the quark orbital angular momentum and the pretzelosity transverse-momentum dependent parton distribution function. We discuss the origin of this relation in quark models, identifying as key ingredient for its validity the assumption of spherical symmetry for the nucleon in its rest frame. Finally we show that the individual quark contributions to the orbital angular momentum obtained from this relation cannot be interpreted as the intrinsic contributions, but include the contribution from the transverse centre of momentum which cancels out only in the total orbital angular momentum.

Hyperspherical hidden crossing method applied to Ps(1s)-formation in low energy e+ − H, e+ − Li and e+ − Na collisions

The hyperspherical hidden crossing method with the correction term (HHCM+cor) has been used to calculate partial wave Ps(1s)-formation cross sections for low-energy e+ − H, e+ − Li and e+ − Na collisions. The Stückelberg phase varies in a systematic way as a function of atomic number Z, incident positron momentum k+, and total orbital angular momentum L and provides an explanation for the small S-wave cross section for all three systems.

Spatial particle correlations in light nuclei. I two-particle systems

Expressions for spatial two-particle correlations in an LS-coupled basis of the harmonic oscillator are used to display the probability distribution of two identical nucleons as a function of their relative distance and their distance from the center of the nucleus. It is shown that a two-nucleon state in the p shell with total orbital angular momentum L=0 and total spin S=0 contains a di-neutron and a cigar-like component with equal probability. This result can also be proven analytically with the use of angular correlation functions. Scattering of the nucleons from the p shell to other shells leads to the enhancement of the di-neutron configuration. A semi-quantitative application to 6He is presented which shows that the probability of the di-neutron configuration in the ground state is of the order of 60%. The long-term goal of this work is to obtain a geometric insight into the properties of nuclei with several nucleons in a valence shell.

Subwave spikes of the orbital angular momentum of the vortex beams in a uniaxial crystal

We have theoretically predicted gigantic spikes of orbital angular momentum caused by conversion processes of the centered optical vortex in the circularly polarized components of an elliptic vortex beam propagating perpendicularly to the crystal optical axis. We have experimentally observed the conversion process inside subwave deviations of the crystal length. We have found that the total orbital angular momentum of the wave beam is conserved.

A theoretical study of Ne3 using hyperspherical coordinates and a slow variable discretization approach

We study theoretically the ground and excited bound states of the bosonic rare gas van der Waals trimer Ne(3). A slow variable discretization approach is adopted to solve the nuclear Schrödinger equation, in which the Schrödinger equation in hyperangular coordinates is solved using basis splines at a series of fixed finite-element methods discrete variable representation hyper-radii. We consider not only zero total nuclear orbital angular momentum, J = 0, states but also J > 0 states. By using the best empirical neon dimer interaction potentials, all the bound state energy levels of Ne(3) will be calculated for total angular momenta up to J = 6, as well as their average root-mean-square radii. We also analyze the wave functions in hyperspherical coordinates for several selected bound states.

Variational calculations of the HT+rovibrational energies

In this Brief Report, we use the exponential explicitly correlated variational basis set of the type $\mathrm{exp}(\ensuremath{-}{\ensuremath{\alpha}}_{n}R\ensuremath{-}{\ensuremath{\beta}}_{n}{r}_{1}\ensuremath{-}{\ensuremath{\gamma}}_{n}{r}_{2})$ to calculate systematically the nonrelativistic bound-state energies for the hydrogen molecular ion ${\text{HT}}^{+}$. We perform calculations for the states of the total orbital angular momentum $L=0$ and 1 with the complete set of vibrational quantum numbers $v=$ 0--23, as well as for the states of $L=$ 2--5 and $v=$ 0--5. The $E1$ dipole transition moments, which are of importance for the planning of spectroscopic laser experiments, have been obtained as well.

Correlations probed in direct two-nucleon removal reactions

Final-state-exclusive momentum distributions of fast, forward travelling residual nuclei, following two nucleon removal from fast secondary radioactive beams of projectile nuclei, can and have now been measured. Assuming that the most important reaction mechanism is the sudden direct removal of a pair of nucleons from a set of relatively simple, active shell-model orbital configurations, such distributions were predicted to depend strongly on the total angular momentum I carried by the two nucleons - the final state spin for spin 0+ projectiles. The sensitivity of these now-accessible observables to specific details of the (correlated) two-nucleon wave functions is of importance. We clarify that it is the total orbital angular momentum L of the two nucleons that is the primary factor in determining the shapes and widths of the calculated momentum distributions. It follows that, with accurate measurements, this dependence upon the L make-up of the two-nucleon wave functions could be used to assess the accuracy of (shell- or many-body) model predictions of these two-nucleon configurations. By use of several tailored examples, with specific combinations of active two-nucleon orbitals, we demonstrate that more subtle structure aspects may be observed, allowing such reactions to probe and/or confirm the details of theoretical model wave functions.

Adiabatic hyperspherical study of weakly bound He2H−, He2H, and HeH2 systems

The He(2)H(-), He(2)H, and HeH(2) triatomic systems are studied using the adiabatic hyperspherical representation. By adopting the best empirical interaction potentials, we search for weakly bound states of (4)He(2) H(-), (4)He(2) H, and (4)HeH(2). We consider not only zero total nuclear orbital angular momentum, J=0, states but also J>0 states. We find no bound state for the (4)He(2) H systems, while the (4)He(2) H(-) and (4)HeH(2) systems are shown to possess three and one bound states, respectively, for J(Pi)=0(+). Interestingly, one bound state has been found each for the J(Pi)=1(-) and 2(+) symmetries of the (4)He(2) H(-) anion. We shall calculate the bound state energies and analyze the molecular structure of these species in detail.

Two electrons in a cylindrical box: An exact configuration-interaction solution

The problem of two Coulombically interacting electrons confined in a cylindrical potential box with impenetrable walls is solved by the method of full configuration interaction (CI) for states with zero axial component of the total orbital angular momentum, including the ground state {sup 1{Sigma}}{sub g}{sup +}. The number of variables in the Schroedinger equation is reduced from six to five by separating the L{sub z} operator from the complete Hamiltonian. Two-electron basis sets of symmetry-adapted configuration state functions are constructed from real eigenfunctions of the one-electron Hamiltonian for a cylindrical potential box. Kinetic energy integrals are evaluated analytically. Electron repulsion integrals are computed by developing a separable expression for the 1/r{sub 12} operator in the form of a double Fourier-Bessel-Fourier-cosine series and using enough terms to achieve a relative accuracy of 10{sup -10} for the eigenvalues. Energy-level ordering and electron densities of selected electronic states are reported for cylindrical cavities of varying size with a fixed 1:1 length-to-diameter ratio. A remarkable feature of this system is that convergence of the full CI energy with respect to the one-electron basis set varies dramatically with the extent of confinement: For small cavities, the rate of approaching the basis-set limit is similar tomore » that for two-electron atoms but is significantly faster for large cavities. Formation of singlet and triplet Wigner molecules is observed in cylindrical cavities with radii greater than about 5 bohrs.« less