Angular Quantum Number Research Articles

New even parity fine structure energy levels of atomic vanadium

Four new fine structure energy levels of atomic vanadium have been discovered for the first time. Experiments were carried out with laser-induced fluorescence spectroscopy and optogalvanic spectroscopy using tunable continuous wave lasers in the wavelength ranges between 750 nm and 850 nm and between 590 nm and 650 nm, respectively. The new levels, all lying in the 42 400 to 49 940 cm−1 energy range, were each experimentally confirmed by two or more observed transitions involving previously known energy levels. Accurate energy level values were found using lines measured by Fourier transform spectroscopy. The values for the total angular momentum quantum numbers J of the new levels were found by the analysis of the hyperfine structure of the spectral lines investigated. Magnetic dipole hyperfine structure constants A for all new levels were determined. Additionally, for one previously known energy level the magnetic dipole hyperfine structure constant A from the literature was corrected.

Analysis of rescattering effects in 3pi final states

Decays into three particles are often described in terms of two-body resonances and a non-interacting spectator particle. To go beyond this simplest isobar model, crossed-channel rescattering effects need to be accounted for. We quantify the importance of these rescattering effects in three-pion systems for different decay masses and angular-momentum quantum numbers. We provide amplitude decompositions for four decay processes with total J^{PC} = 0^{--}, 1^{--}, 1^{-+}, and 2^{++}, all of which decay predominantly as rho pi states. Two-pion rescattering is described in terms of an Omnès function, which incorporates the rho resonance. Inclusion of crossed-channel effects is achieved by solving the Khuri–Treiman integral equations. The unbinned log-likelihood estimator is used to determine the significance of the rescattering effects beyond two-body resonances; we compute the minimum number of events necessary to unambiguously find these in future Dalitz-plot analyses. Kinematic effects that enhance or dilute the rescattering are identified for the selected set of quantum numbers and various masses.

High sensitivity absorption spectroscopy of acetylene near 760 nm

The Cavity Ring-Down Spectra (CRDS) of acetylene were recorded in the 13,087–13,300 cm−1 range with the sensitivity of 3.4 × 10−11 cm−1. Four cold and six hot bands of 12C2H2 were assigned in these spectra. Only five of them were observed before. The ν1+3ν3+ν41 band is the strongest one lying in this region. The line positions and intensities were recovered from the recorded spectra. The line intensities in this region are reported for the first time. The line positions were modeled using the traditional power series expression in terms of the angular momentum quantum number for an isolated band. The line intensities were modeled using the vibrational transition dipole moment squared and the Herman-Wallis parameters.

SL(2, R) × U(1) symmetry and quasinormal modes in the self-dual warped AdS black hole

The algebraic approach to the spectrum of quasinormal modes has been made as simple as possible for the BTZ black hole by the strategy developed in [16]. By working with the self-dual warped AdS black hole, we demonstrate in an explicit way that such a strategy can be well adapted to those warped AdS balck holes with the SL(2, R) × U(1) isometry. To this end, we first introduce two associated tensor fields with the quadratic Casimir of SL(2, R) × U(1) Lie algebra in the self-dual warped AdS black hole and show that they correspond essentially to the metric and volume element up to a constant prefactor, respectively. Then without appealing to any concrete coordinate system, we can further show that the solutions to the equations of motion for the scalar, vector, spinor fields all fall into the representations of the SL(2, R) × U(1) Lie algebra by a purely abstract tensor and spinor analysis. Accordingly, the corresponding spectrum of quasinormal modes for each fixed azimuthal quantum number can be derived algebraically as the infinite tower of descendants of the highest weight mode of the SL(2, R) Lie subalgebra.

Wavelength scaling of photoionization circular dichroism of atomic electron ring currents and its effect on photoelectron spin polarization

Circularly polarized orbitals in atoms are referred to as electron ring currents with a helical angular phase and thus manifest circular dichroism in photoionization by circularly polarized light fields. Opposite circular dichroism has been revealed in single-photon and nonadiabatic tunneling ionization regimes. The transition of the circular dichroism and its underlying mechanism are still not clear. Here, we systematically study the wavelength scaling of photoionization circular dichroism of electron ring currents. We present a universal description of the dichroic photoelectron energy spectra and the spin polarization from the infrared to the extreme ultraviolet regions. We reveal that the channel interference and competition via the intermediate states with different angular quantum numbers in a few-photon ionization regime give rise to the transition of the circular dichroism and the spin polarization of photoelectrons.

Flux-periodic oscillations in proximitized core–shell nanowires

Flux-periodic oscillations of the superconducting gap in proximitized core–shell nanowires are explored. Periodicity of oscillations in the energy spectrum of a cylindrical nanowire is compared with nanowires having hexagonal and square cross-section geometry, along with the effects of Zeeman and Rashba spin–orbit interaction. A transition between h/e and h/2e periodicity is found and shown to be dependent on the chemical potential, with correspondence to degeneracy points of the angular momentum quantum number. For a thin shell of a square nanowire, solely h/e periodicity is found in the infinite wire spectrum and shown to result from energy separation between the lowest groups of excited states.

Impact of multiple modes on the evolution of self-interacting axion condensate around rotating black holes

Ultra-light particles, such as axions, form a macroscopic condensate around a highly spinning black hole by the superradiant instability. Due to its macroscopic nature, the condensate opens the possibility of detecting the axion through gravitational wave observations. However, the precise evolution of the condensate must be known for the actual detection. For future observation, we numerically study the influence of the self-interaction, especially interaction between different modes, on the evolution of the condensate in detail. First, we focus on the case when condensate starts with the smallest possible angular quantum number. For this case, we perform the non-linear calculation and show that the dissipation induced by the mode interaction is strong enough to saturate the superradiant instability, even if the secondary cloud starts with quantum fluctuations. Our result indicates that explosive phenomena such as bosenova do not occur in this case. We also show that the condensate settles to a quasi-stationary state mainly composed of two modes, one with the smallest angular quantum number for which the superradiant instability occurs and the other with the adjacent higher angular quantum number. We also study the case when the condensate starts with the dominance of the higher angular quantum number. We show that the dissipation process induced by the mode coupling does not occur for small gravitational coupling. Therefore, bosenova might occur in this case.

Study of I=0 bottomonium bound states and resonances in S , P , D , and F waves with lattice QCD static-static-light-light potentials

In this paper we study $I = 0$ bottomonium in $S$, $P$, $D$ and $F$ waves considering five coupled channels, one confined quarkonium and four open $B^{(*)} \bar B^{(*)}$ and $B_s^{(*)} \bar B_s^{(*)}$ meson-meson channels. To this end we use and extend a recently developed novel approach utilizing lattice QCD string breaking potentials for the study of quarkonium bound states and resonances. This approach is based on the Born Oppenheimer approximation and the unitary emergent wave method and allows to compute the poles of the $\mbox{T}$ matrix. We compare our results to existing experimental results for $I = 0$ bottomonium and discuss masses, decay widths and the assignment of angular momentum quantum numbers. Moreover, we determine the quarkonium and meson-meson composition of these states to clarify, which of them are ordinary quarkonium, and which of them should rather be interpreted as tetraquarks.

Generation and characteristics of an anomalous Airy vortex beam from a Lommel vortex beam

A practical method for generating an anomalous Airy vortex beam is proposed, and characteristics of this novel kind beam are investigated. Results show that orbital angular momentum (OAM) quantum number n could be used to modulate the profiles of vortex rings, asymmetric parameter c would cause the beam rotation and phase distortion, and when increase control parameters α and β, more energy would concentrate on the side lobes, and the side lobes in the x-direction and y-direction separately would expand laterally and longitudinally, respectively. Particularly, the position and moving direction of the light spot could be controlled precisely according to the actual needs by altering the phase shift proportional coefficients p and q. Our work would extend potential applications of the mixed vortex beams in optical micro-manipulation and optical trapping.

Cone-Shell Quantum Structures in Electric and Magnetic Fields as Switchable Traps for Photoexcited Charge Carriers.

The optical emission of cone-shell quantum structures (CSQS) under vertical electric (F) and magnetic (B) fields is studied by means of simulations. A CSQS has a unique shape, where an electric field induces the transformation of the hole probability density from a disk into a quantum-ring with a tunable radius. The present study addresses the influence of an additional magnetic field. A common description for the influence of a B-field on charge carriers confined in a quantum dot is the Fock-Darwin model, which introduces the angular momentum quantum number l to describe the splitting of the energy levels. For a CSQS with the hole in the quantum ring state, the present simulations demonstrate a B-dependence of the hole energy which substantially deviates from the prediction of the Fock-Darwin model. In particular, the energy of exited states with a hole lh> 0 can become lower than the ground state energy with lh= 0. Because for the lowest-energy state the electron le is always zero, states with lh> 0 are optically dark due to selection rules. This allows switching from a bright state (lh= 0) to a dark state (lh> 0) or vice versa by changing the strength of the F or B field. This effect can be very interesting for trapping photoexcited charge carriers for a desired time. Furthermore, the influence of the CSQS shape on the fields required for the bright to dark state transition is investigated.

Solution of Klein-Gordon Equation in F(R) Theory of Gravity

The theory, as a modification of the general relativity theory, is frequently employed as an alternative theory of gravity and offers a promising avenue for addressing the challenges of formulating a quantum gravity theory. In this study, by applying the separation method of time, radial and angular variables, we derived the general solution of the Klein-Gordon equation in a curved space-time using modified Schwarzschild metric. We modified Ricci scalar form in Einstein’s action principle as a general function of Ricci scalar and formulated the general Schwarzschild metric. The solution of the time function was analytically obtained in exponential form, and the solution of the angular function in terms of Legendre polynomial depends on azimuthal and magnetic quantum numbers. The radial function in terms of a non-linear second-order differential equation was solved by a numerical method using Python. The solutions described the gravitational effect for a light particle on the area gravitationally has a strong interaction, represented by a spherically symmetric metric. For small (in Schwarzschild radius), the results analytically show that the gravitational effect in this region is massive. It follows that even light would be drawn into a black hole and unable to escape. For further research, it is expected to extend the Klein-Gordon equation in relativistic quantum mechanics to modified general relativity theory. This theory offers a different way of looking at the effects of gravity in quantum field theory.

On quantitative off-axis Scanning Transmission Ion Microscopy (STIM)

Spurred by a need to determine major (C, H, N and O) contents in biological tissue sections, a formalism for quantitative off-axis Scanning Transmission Ion Microscopy (OA-STIM) has been established. This can be used with, or without, simultaneous Elastic Backscattering Spectroscopy (EBS) to provide quantitative major element composition and thickness information. As part of the work, an empirical predictor with one free parameter for the proton–proton differential scattering cross section was implemented. The predictor values were in extremely close agreement with high accuracy literature data. For 2 MeV p–12C elastic scattering at forward angles ≤45°an interpolation procedure was used to determine the relative deviations from the Rutherford cross sections were determined to be ≤6.4%. The interpolation was based on a Coulomb field, angular momentum quantum number and nuclear structure dependent nuclear penetration factor. Finally, the quantitative combination of simultaneous OA-STIM and EBS data is discussed.

General expressions of molecular multicenter integrals for Slater‐type orbitals

AbstractEmploying Fourier‐transform technique, this work derives the molecular multicenter integrals for the modified Slater‐type orbitals (STOs) with arbitrary principal and angular quantum numbers, in which the spherical harmonics parts are the homogeneous solutions of original STOs. The integrands include spherical Bessel functions and associated Legendre functions. One‐electron three‐center nuclear attraction integral and two‐electron four‐center Coulomb repulsion integral are presented as numerical integrations in two dimensions and three dimensions, respectively. A simple Python script is provided to run the formulas. The correctness and computational efficiency of the script have been verified.

Adiabatic Amplification of Energy and Magnetic Moment of a Charged Particle after the Magnetic Field Inversion.

We study the evolution of the energy and magnetic moment of a quantum charged particle placed in a homogeneous magnetic field, when this field changes its sign adiabatically. We show that after a single magnetic field passage through zero value, the famous adiabatic invariant ratio of energy to frequency is reestablished again, but with a proportionality coefficient higher than in the initial state. The concrete value of this proportionality coefficient depends on the power index of the frequency dependence on time near zero point. In particular, the adiabatic ratio of the initial ground state (with zero radial and angular quantum numbers) triplicates if the frequency tends to zero linearly as a function of time. If the Larmor frequency attains zero more than once, the adiabatic proportionality coefficient strongly depends on the lengths of the time intervals between zero points, so that the mean energy behavior can be quasi-stochastic after many passages through zero value. The original Born-Fock adiabatic theorem does not work after the frequency passes through zero. However, its generalization is found: the initial Fock state becomes a wide superposition of many instantaneous Fock states, whose weights do not depend on time in the new adiabatic regime.

Novel machine-learning method for spin classification of neutron resonances

The performance of nuclear reactors and other nuclear systems depends on a precise understanding of the neutron interaction cross sections for materials used in these systems. These cross sections exhibit resonant structure whose shape is determined in part by the angular-momentum quantum numbers of the resonances. The correct assignment of the quantum numbers of neutron resonances is, therefore, paramount. In this project, we apply machine learning to automate the quantum number assignments using only the resonances' energies and widths and not relying on detailed transmission or capture measurements. The classifier used for quantum number assignment is trained using stochastically generated resonance sequences whose distributions mimic those of real data. We explore the use of several physics-motivated features for training our classifier. These features amount to out-of-distribution tests of a given resonance's widths and resonance-pair spacings. We pay special attention to situations where either capture widths cannot be trusted for classification purposes or where there is insufficient information to classify resonances by the total spin $J$. We demonstrate the efficacy of our classification approach using simulated and actual $^{52}\mathrm{Cr}$ resonance data.

Designing spin and orbital sources of Berry curvature at oxide interfaces

Quantum materials can display physical phenomena rooted in the geometry of electronic wavefunctions. The corresponding geometric tensor is characterized by an emergent field known as the Berry curvature (BC). Large BCs typically arise when electronic states with different spin, orbital or sublattice quantum numbers hybridize at finite crystal momentum. In all the materials known to date, the BC is triggered by the hybridization of a single type of quantum number. Here we report the discovery of the first material system having both spin- and orbital-sourced BC: LaAlO3/SrTiO3 interfaces grown along the [111] direction. We independently detect these two sources and probe the BC associated to the spin quantum number through the measurements of an anomalous planar Hall effect. The observation of a nonlinear Hall effect with time-reversal symmetry signals large orbital-mediated BC dipoles. The coexistence of different forms of BC enables the combination of spintronic and optoelectronic functionalities in a single material.

Multiphoton Ionization Reduction of Atoms in Two-Color Femtosecond Laser Fields.

We report the ionization reduction of atoms in two-color femtosecond laser fields in this joint theoretical-experimental study. For the multiphoton ionization of atoms using a 400nm laser pulse, the ionization probability is reduced if another relatively weak 800nm laser pulse is overlapped. Such ionization reduction consistently occurs regardless of the relative phase between the two pulses. The time-dependent Schrödinger equation simulation results indicate that with the assisted 800nm photons the electron can be launched to Rydberg states with large angular quantum numbers, which stand off the nuclei and thus are hard to be freed in the multiphoton regime. This mechanism works for hydrogen, helium, and probably some other atoms if two-color laser fields are properly tuned.

Representation and conservation of angular momentum in the Born-Oppenheimer theory of polyatomic molecules.

This paper concerns the representation of angular momentum operators in the Born-Oppenheimer theory of polyatomic molecules and the various forms of the associated conservation laws. Topics addressed include the question of whether these conservation laws are exactly equivalent or only to some order of the Born-Oppenheimer parameter κ = (m/M)1/4 and what the correlation is between angular momentum quantum numbers in the various representations. These questions are addressed in both problems involving a single potential energy surface and those with multiple, strongly coupled surfaces and in both the electrostatic model and those for which fine structure and electron spin are important. The analysis leads to an examination of the transformation laws under rotations of the electronic Hamiltonian; of the basis states, both adiabatic and diabatic, along with their phase conventions; of the potential energy matrix; and of the derivative couplings. These transformation laws are placed in the geometrical context of the structures in the nuclear configuration space that are induced by rotations, which include the rotational orbits or fibers, the surfaces upon which the orientation of the molecule changes but not its shape, and the section, an initial value surface that cuts transversally through the fibers. Finally, it is suggested that the usual Born-Oppenheimer approximation can be replaced by a dressing transformation, that is, a sequence of unitary transformations that block-diagonalize the Hamiltonian. When the dressing transformation is carried out, we find that the angular momentum operator does not change. This is a part of a system of exact equivalences among various representations of angular momentum operators in Born-Oppenheimer theory. Our analysis accommodates large-amplitude motions and is not dependent on small-amplitude expansions about an equilibrium position. Our analysis applies to noncollinear configurations of a polyatomic molecule; this covers all but a subset of measure zero (the collinear configurations) in the nuclear configuration space.

Atomic Rydberg-state excitation in strong spatially inhomogeneous fields

We investigated the Rydberg-state excitation process of a hydrogen atom subjected to spatially homogeneous and inhomogeneous laser fields by means of ab initio calculations. It is found that, comparing with atoms exposed to spatially homogeneous laser fields, the excitation probability decreases and the electron tends to occupy the states with lower principal quantum numbers and angular quantum numbers for atoms in spatially inhomogeneous laser pulses. Furthermore, calculations of a quantum model without taking into account ionization of the electron after it is coherently captured by the Rydberg state are inconsistent with the above-stated findings by ab initio calculations. Analysis indicates that the aforementioned intriguing features can be attributed to the enhanced ionization of the Rydberg states by inhomogeneous laser fields since the distributions of Rydberg states of high principal quantum numbers and angular quantum numbers locate far away from the core where the inhomogeneous electric fields become significant.

Rydberg ions in coherent motional states: a new method for determining the polarizability of Rydberg ions

We present a method for measuring the polarizability of Rydberg ions confined in the harmonic potential of a Paul trap. For a highly excited electronic state, the coupling between the electronic wave function and the trapping field modifies the excitation spectra depending on the motional state of the ion. This interaction strongly depends on the polarizability of the excited state and manifests itself in the state-dependent secular frequencies of the ion. We initialize a single trapped 40Ca+ ion from the motional ground state into coherent states with up to 12 using electric voltages on the trap segments. The internal state, firstly initialised in the long-lived 3D state, is excited to a Rydberg S-state via the 5P state in a two-photon process. We probe the depletion of the 3D state owing to the Rydberg excitation followed by a decay into the internal ground 4S state. By analysing the obtained spectra we extract the polarizability of Rydberg states which agree with numerical calculations. The method is applicable to different Rydberg states regardless of their principal or angular quantum numbers. An accurate value of the state polarizability is needed for quantum gate operations with Rydberg ion crystals.