Function Of Angular Momentum Research Articles

Ortho-Para Conversion for H+ + H2 Collision in Low Temperature: A Fully Close-Coupled Time-Dependent Wave Packet Study.

The collision-induced rate coefficients of ortho-para conversion for the H+ + H2 reaction provide accurate information to probe the lifetime of cold environments in interstellar media. Rotationally resolved reaction probabilities are calculated at the low collision energy regime (0 < Ecol ≤ 0.3 eV) by employing the coupled three-dimensional (3D) time-dependent wave packet (TDWP) formalism in hyperspherical coordinates on a recently constructed ab initio ground adiabatic potential energy surface of H3+ [J. Chem. Phys. 2014, 141, 204306] for the process H+ + H2 (v = 0, j = 0-5) → H+ + H2 (v' = 0, j'). Cross-sections are then computed from the converged reaction probabilities as a function of total angular momentum (J) over the same energy regime and subsequently employed to obtain the rate constants for the ortho-to-para (O-P) and para-to-ortho (P-O) conversions and their ratio. The ratio of ortho-para conversion shows (a) appropriate convergence with the inclusion of a higher number of initial rotational states as well as a reasonable agreement with the results from a quantum statistical method and (b) a peak at lower temperature that could be due to the available collision energy for transitions involving lower rotational states (j = 0 → j' = 1).

Orbital motion and epicyclic oscillations around Bardeen black hole surrounded by perfect fluid dark matter

We study the orbital and oscillatory motion of test particles moving around a rotating Bardeen black hole immersed in perfect fluid dark matter. We obtain the analytical solutions for the radial profiles of specific energy as well as the specific angular momentum of the equatorial stable circular orbits. Using the effective potential approach, we also discuss the stability of circular orbits. We compute the frequencies of radial and latitudinal harmonic oscillations as a function of mass, charge, and angular momentum of the black hole as well as the parameter describing the perfect fluid dark matter. The main characteristics of test particle quasi-periodic oscillations near stable circular orbits are examined in the equatorial plane. Furthermore, we study precessions of Periastron and Lense-Thirring. It is observed that the particle's motion around the black hole is strongly influenced by the model parameters.

Propagation of twisted laser carrying orbital angular momentum in magnetized plasma

The propagation of electromagnetic beams carrying orbital angular momentum l is investigated in a cold collisionless plasma where a static magnetic field is applied in the axial direction. The relativistic and ponderomotive nonlinearities are taken into consideration simultaneously. A stationary nonlinear Schrödinger equation is derived using the Wentzel–Kramers–Brillouin method and the slowly varying envelope approximation. The critical condition for the self-trapped mode is achieved as a function of orbital angular momentum (OAM), magnetic field, and initial laser intensity of the beam. The response of the medium to the two types of polarizations, i.e., left circular polarization (LCP) and right circular polarization (RCP), is compared, and it is observed that the RCP laser shows better focusing than the LCP laser and also requires a smaller beam radius for achieving the self-trapped mode. The effect of applied magnetic field and OAM of the laser is also studied on the beam width evolution. The laser is found to be focused earlier in the cases of a larger applied magnetic field. A Laguerre–Gaussian laser with higher OAM is observed to show efficient self-focusing. This study enables exploration in the fields of particle acceleration, electron bunch generation, x-ray sources, and more.

Calculation of the half-life of proton radioactivity using the empirical formula depending on angular momentum

In this paper, considering the power of the daughter nuclear charge as a function of the orbital angular momentum taken away by the emitted proton, we propose a formula for the half-life of proton radioactivity. In this formula, we have three coefficients with orbital angular momentum dependence. Using experimentally measured half-lives for 8 proton emitters with [Formula: see text], 14 proton emitters with [Formula: see text] and 18 proton emitters with [Formula: see text], we have obtained the coefficients. The root mean square deviations of our formula respect to the experimental value are found 0.2514, 0.4442 and 0.1846 for emitters [Formula: see text], 2 and 5, respectively. We have compared our results with Sreeja formula, the semiempirical relation of Hatsukawa and theoretical models such as the Coulomb and proximity potential model (CPPM) and the Gamow-like model. The better agreement with experimental data was observed for our formula in comparison with other theoretical models and Sreeja and Hatsukawa formulas.

Brickwall in rotating BTZ: a dip-ramp-plateau story

In this article, building on our recent investigations and motivated by the fuzzball-paradigm, we explore normal modes of a probe massless scalar field in the rotating BTZ-geometry in an asymptotically AdS spacetime and correspondingly obtain the Spectral Form Factor (SFF) of the scalar field. In particular, we analyze the SFF obtained from the single-particle partition function. We observe that, a non-trivial Dip-Ramp-Plateau (DRP) structure, with a Ramp of slope one (within numerical precision) exists in the SFF which is obtained from the grand-canonical partition function. This behaviour is observed to remain stable close to extremality as well. However, at exact extremality, we observe a loss of the DRP-structure in the corresponding SFF. Technically, we have used two methods to obtain our results: (i) An explicit and direct numerical solution of the boundary conditions to obtain the normal modes, (ii) A WKB-approximation, which yields analytic, semi-analytic and efficient numerical solutions for the modes in various regimes. We further re-visit the non-rotating case and elucidate the effectiveness of the WKB-approximation in this case, which allows for an analytic expression of the normal modes in the regime where a level-repulsion exists. This regime corresponds to the lower end of the spectrum as a function of the scalar angular momentum, while the higher end of this spectrum tends to become flat. By analyzing the classical stress-tensor of the probe sector, we further demonstrate that the back-reaction of the scalar field grows fast as the angular momenta of the scalar modes increase in the large angular momenta regime, while the back-reaction remains controllably small in the regime where the spectrum has non-trivial level correlations. This further justifies cutting the spectrum off at a suitable value of the scalar angular momenta, beyond which the scalar back-reaction significantly modifies the background geometry.

Bogoliubov spectrum and the dynamic structure factor in a quasi-two-dimensional spin-orbit coupled BEC

We compute the Bogoliubov–de Gennes excitation spectrum in a trapped two-component spin-orbit-coupled (SOC) Bose–Einstein condensate (BEC) in quasi-two-dimensions as a function of linear and angular momentum and analyze them. The excitation spectrum exhibits a minima-like feature at finite momentum for the immiscible SOC-BEC configuration, which implies dynamical instability. We augment these results by computing the dynamic structure factor in the density and pseudo-spin sector, and discuss its interesting features that can be experimentally measured through Bragg spectroscopy of such ultracold condensates.

Magnetic properties of the excited states of &lt;sup&gt;156&lt;/sup&gt;Gd

Theoretical calculations within the framework of a phenomenological model with Coriolis mixing of states of low-lying positive-parity rotational bands were performed for 156Gd. The Coriolis interaction allows to explain the observed non-adiabaticity effects in the properties of the excited states. Reduced probabilities of the M1 transitions B(M1) and multipole mixing coefficients \(\delta ({{E{\text{2}}} \mathord{\left/ {\vphantom {{E{\text{2}}} {M{\text{1}}}}} \right.} {M{\text{1}}}})\) for transitions from vibrational states were calculated. The behavior of the probabilities of M1 transitions from the mixing states as a function of the total angular momentum was studied. The agreement of the theoretical results with experimental data is, in the whole, satisfactory.

Simple Physical Model for the Estimation of Irreversible Dissociation Rates for Bimolecular Complexes.

In this article, we propose a simple method of estimating dissociation rates of bimolecular van der Waals complexes ("wells"), rooted in rigid body dynamics, requiring as input parameters only the bimolecular binding energy, together with the intermolecular equilibrium distance and moments of inertia of the complex. The classical equations of motion are solved for the intermolecular and rotational degrees of freedom in a coordinate system considering only the relative motion of the two molecules, thus bypassing the question of whether the energy of the complex is statistically distributed. Well-escaping trajectories are modeled from these equations, and the escape rate as a function of relative velocity and angular momentum is fitted to an empirical function, which is then integrated over a probability distribution of said quantities. By necessity, this approach makes crude assumptions on the shape of the potential well and neglects the impact of energy quantization, and, more crucially, the coupling between the degrees of freedom included in the equations of motion with those that are not. We quantify the error caused by the first assumption by comparing our model potential with a quantum chemical potential energy surface (PES) and show that while the model does make several compromises and may not be accurate for all classes of bimolecular complexes, it is able to produce physically consistent dissociation rate coefficients within typical atmospheric chemistry confidence intervals for triplet state alkoxyl radical complexes, for which the detailed balance approach has been shown to fail.

Geodetic residual time series: A combined series by minimization of their internal noise level

This study aims to assess the hydrological effects of polar motion calculated from different combinations of geophysical excitations at decadal, seasonal, and non-seasonal periods. The geodetic residuals GAO, being a difference between observed geodetic excitation function of polar motion Geodetic Angular Momentum (GAM) and atmospheric (Atmospheric Angular Momentum—AAM) plus oceanic excitation functions (Oceanic Angular Momentum—OAM), are compared. Estimating hydrological effects on Earth’s rotation differs significantly, especially when using various oceanic models. Up to now, studies of geophysical excitations of polar motion containing AAM, OAM, and hydrological angular momentum (HAM) have not achieved entire agreement between geophysical (sum of AAM, OAM, and HAM obtained from the models) and geodetic excitation. Many geophysical models of the atmosphere, oceans, and land hydrology can be used to compute polar motion excitation. However, these models are very complex and still have uncertainties in the process descriptions, parametrization, and forcing. This work aims to show differences between various GAO solutions calculated from different mass and motion terms of various AAM and OAM models. Justifying to use one combination of GAO to estimate geodetic residuals is comparing those time series to hydrological excitations computed from Gravity Recovery and Climate Experiment (GRACE) data and the Land Surface Discharge Model (LSDM) model. Especially the quality of each geodetic residual time series is determined by estimating their noise level using a generalized formulation of the “three-cornered hat method” (3CH). This study presents a combined series of geodetic residuals GAO in polar motion (PM), wherein the internal noise level is shortened to a minimum by using the 3CH method. The combined GAO time series are compared with results obtained from the GRACE/GRACE Follow-On (GRACE-FO) solution provided by International Combination Service for Time variable Gravity Fields (COST-G) and the single solution elaborated by the Center for Space Research (CSR) and from the HAM LSDM hydrological model. The results show that higher consistency between GAO and HAM excitations can be achieved by minimizing the internal noise level in the GAO combined excitation series using the 3CH method, especially for the overall broadband and seasonal oscillations. For seasonal spectral bands, an agreement between combined GAO and the best-correlated series of GRACE CSR achieve correlations as high as 0.97 and 0.83 for the χ1 and χ2 equatorial components of PM excitation, respectively. This study’s combined geodetic residual time series slightly improved consistency between observed geodetic polar motion excitations and geophysical ones.

Modeling a semi-optimal deceleration of a rigid body rotational motion in a resisting medium

This paper studies the shortest time of slowing rotation of a free dynamically asymmetric rigid body (RB), analogous to Euler’s case. This body is influenced by a rotatory moment of a tiny control torque with closer coefficients but not equal, a gyrostatic moment (GM) due to the presence of three rotors, and in the presence of a modest slowing viscous friction torque. Therefore, this problem can be regarded as a semi-optimal one. The controlling optimal decelerating law for the rotation of the body is constructed. The trajectories that are quasi-stationary are examined. The obtained new results are displayed to identify the positive impact of the GM. The dimensionless form of the regulating system of motion is obtained. The functions of kinetic energy and angular momentum besides the square module are drawn for various values of the GM’s projections on the body’s principal axes of inertia. The effect of control torques on the body's motion is investigated in a case of small perturbation, and the achieved results are compared with the unperturbed one. For the case of a lack of GM, the comparison between our results and those of the prior ones reveals a high degree of consistency, in which the deviations between them are examined. As a result, these outcomes generalized those that were acquired in previous studies. The significance of this research stems from its practical applications, particularly in the applications of gyroscopic theory to maintain the stability and determine the orientation of aircraft and undersea vehicles.

Semi-empirical relation to understand matter properties at neutron star interiors

The occurrence of quark matter at the center of neutron stars is still in debate. This study defines some semi-empirical parameters that try to quantify the presence and the amount of quark matter at star interiors. We find that one needs unusually accurate measurement to qualitatively deduce the occurrence of quark core at the center of stars by studying the compactness of a fast rotating star as a function of angular momentum. Nevertheless one can deduce the quark content of a static 1.4 solar mass star and extend it for a rotating star. The quark fractions in a star depend on the stiffness of the equation of state and the critical density for phase transition. As the phase transition from the neutron star to a hybrid star happens, the star shrinks, releasing significant energy. A massive neutron star usually collapses into a black hole if the phase transition happens at constant baryonic mass. Given a hadronic EoS, we have shown how one can have a critical mass of the neutron star and the corresponding maximum mass of the hybrid star for a given equation of state.

Angular momentum effects on the decay modes of hot compound nuclei formed in 86Kr+134,138Ba reactions

The dependence of decay modes of hot compound nuclei formed in [Formula: see text]Kr[Formula: see text]Ba reactions on the angular momentum has been analyzed using the dynamical cluster-decay model. This has been done by analyzing the change of fragmentation potential, preformation probability, penetrability and cross-section as a function of the fragment mass number at various values of the angular momentum. The evaporation residue cross-section calculated using dynamical cluster-decay model has been compared with the measured one for the channels: [Formula: see text], [Formula: see text], [Formula: see text] for the decay of [Formula: see text]U[Formula: see text] and [Formula: see text] for [Formula: see text]U[Formula: see text]. The summed up fragment cross-sections for the light particles, intermediate mass fragments and fission fragments as a function of angular momentum have been studied which gives an idea for the change of reaction mechanism with angular momentum. The charge distribution of the fission fragment cross-section shows an odd–even staggering, i.e., the probability of even-Z fission fragments is relatively higher than others. The mass distributions obtained within the dynamical cluster-decay model for the decay of [Formula: see text]U[Formula: see text] are in conformity with mass distributions determined by means of the double kinetic-energy technique in literature. The position of the most probable channel has been found to be fixed to a constant atomic number instead of mass number.

Angular momentum projection in the deformed relativistic Hartree-Bogoliubov theory in continuum

The angular momentum projection (AMP) method is implemented in the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) with the point-coupling density functional. The wave functions of angular momentum projected states are expanded in terms of the Dirac Woods-Saxon (WS) basis, providing a proper description of the asymptotic behavior of the wave functions. The contribution of continuum induced by the pairing is considered by treating the pairing correlation with the Bogoliubov transformation. We present the formulas and numerical checks for the DRHBc$+$AMP approach in detail and use it to study low-lying excited states of axially deformed nuclei. Our calculations show that neutron-rich magnesium isotopes $^{36,38,40}\mathrm{Mg}$ are all well-deformed nuclei. The low-lying spectra of these three nuclei are obtained. The ground-state rotational bands of $^{36,38,40}\mathrm{Mg}$ are reproduced reasonably well by using this new DRHBc$+$AMP approach with the density functional PC-F1.

High-spin intruder states in the mirror nuclei S31 and P31

Mirror energy differences (MED) between excited states in the A=31, T=1/2 mirror pair S31 and P31 have been measured up to high spin yrast states of positive and negative parity. The mirror nuclei were populated in the Mg24(C12, αn) and Mg24(C12, αp) reactions, respectively. For the first time the MED are described in the framework of the shell model in a valence space that includes three main shells. The theoretical MED values as a function of angular momentum indicate that the main contribution arises from the Coulomb interaction, however, the isospin symmetry breaking term is not at all negligible and needs to be considered to reproduce the experimental findings.Received 17 November 2020Revised 27 December 2020Accepted 1 June 2021DOI:https://doi.org/10.1103/PhysRevC.104.024309©2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNuclear spin & parityNucleon distributionShell modelProperties20 ≤ A ≤ 38Nuclear Physics

Frustrated tunneling dynamics in ultrashort laser pulses

We study a model for frustrated tunneling ionization using ultrashort laser pulses. The model is based on the strong field approximation and it employs the saddle point approximation to predict quasiclassical trajectories that are captured on Rydberg states. We present a classification of the saddle-point solutions and explore their behavior as functions of angular momentum of the final state, as well as the carrier-envelope phase (CEP) of the laser pulse. We compare the final state population computed by the model to results obtained by numerical propagation of the time-dependent Schrödinger equation (TDSE) for the hydrogen atom. While we find qualitative agreement in the CEP dependence of the populations in principal quantum numbers, n, the populations to individual angular momentum channels, ℓ, are found to be inconsistent between model and TDSE. Thus, our results show that improvements of the quasiclassical trajectories are in order for a quantitative model of frustrated tunneling ionization.

Testing the flux-based statistical prediction of the three-body problem

Abstract We present an extensive comparison between the statistical properties of non-hierarchical three-body systems and the corresponding three-body theoretical predictions. We perform and analyse 1 million realizations for each different initial condition considering equal and unequal mass three-body systems to provide high accuracy statistics. We measure 4 quantities characterizing the statistical distribution of ergodic disintegrations: escape probability of each body, the characteristic exponent for escapes by a narrow margin, predicted absorptivity as a function of binary energy and binary angular momentum, and, finally, the lifetime distribution. The escape probabilities are shown to be in agreement down to the 1 per cent level with the emissivity-blind, flux-based theoretical prediction. This represents a leap in accuracy compared to previous three-body statistical theories. The characteristic exponent at the threshold for marginally unbound escapes is an emissivity-independent flux-based prediction, and the measured values are found to agree well with the prediction. We interpret both tests as strong evidence for the flux-based three-body statistical formalism. The predicted absorptivity and lifetime distributions are measured to enable future tests of statistical theories.

Photoionization of Rydberg atoms in optical lattices

We develop a formalism for photoionization (PI) and potential energy curves (PECs) of Rydberg atoms in ponderomotive optical lattices and apply it to examples covering several regimes of the optical-lattice depth. The effect of lattice-induced PI on Rydberg-atom lifetime ranges from noticeable to highly dominant when compared with natural decay. The PI behavior is governed by the generally rapid decrease of the PI cross sections as a function of angular-momentum (ℓ), lattice-induced ℓ-mixing across the optical-lattice PECs, and interference of PI transition amplitudes from the lattice-mixed into free-electron states. In GHz-deep lattices, ℓ-mixing leads to a rich PEC structure, and the significant low-ℓ PI cross sections are distributed over many lattice-mixed Rydberg states. In lattices less than several tens-of-MHz deep, atoms on low-ℓ PECs are essentially ℓ-mixing-free and maintain large PI rates, while atoms on high-ℓ PECs trend towards being PI-free. Characterization of PI in GHz-deep Rydberg-atom lattices may be beneficial for optical control and quantum-state manipulation of Rydberg atoms, while data on PI in shallower lattices are potentially useful in high-precision spectroscopy and quantum-computing applications of lattice-confined Rydberg atoms.

Mirror energy differences in T=1/2f7/2 -shell nuclei within isospin-dependent density functional theory

Background: Small asymmetry between neutrons and protons, caused by the differences in masses and charges of the up and down constituent quarks leads to the isospin symmetry breaking. The isospin non-conservation affects broad range of observables from superallowed Fermi weak interaction to isospin-forbidden electromagnetic rates. Its most profound and cleanest manifestation are systematic shifts in masses and excitation energies of mirror atomic nuclei. Purpose: Recently, we constructed the charge-dependent DFT that includes class II and III local interactions and demonstrated that the model allows for very accurate reproduction of Mirror and Triplet Displacement energies in a very broad range of masses. The aim of this work is to further test the charge-dependent functional by studying Mirror Energy Differences (MEDs) in function of angular momentum $I$. Methods: To compute MEDs we use DFT-rooted no core configuration interaction model. This post mean-field method restores rotational symmetry and takes into account configuration mixing within a space that includes relevant (multi)particle-(multi)hole Slater determinants. Results: We applied the model to $f_{7/2}$-shell mirror pairs of $A=43$, $45$, $47$, and $49$ focusing on MEDs in low-spin part (below band crossing) what allowed us to limit the model space to seniority one and three (one broken pair) configurations. Conclusions: We demonstrate that, for spins $I\leq 15/2$ being subject of the present study, our model reproduces well experimental MEDs which vary strongly in function of $I$ and $A$. The quality of model's predictions is comparable to the nuclear shell-model results by Bentley et al. Phys. Rev. C 92, 024310 (2015).

Two-Dimensional Master Equation Modeling of Some Multichannel Unimolecular Reactions.

Multichannel thermal decomposition reactions of n-propyl radicals, 1-pentyl radicals, and toluene are investigated by solving a two-dimensional master equation formulated as a function of total energy (E) and angular momentum (J). The primary aim of this study is to elucidate the role of angular momentum in the kinetics of multichannel unimolecular reactions. The collisional transition processes of the reactants colliding with argon are characterized based on the classical trajectory calculations and implemented in the master equation. The rate constants calculated by using the two-dimensional master equation are compared with those of one-dimensional master equations. The consequence of the explicit treatment of angular momentum depends on the J dependence of the microscopic rate constants and is particularly emphasized in the thermal decomposition of toluene, for which the C-H and C-C bond fission channels are considered. The centrifugal effect is insignificant in the energetically favored C-H bond fission but is substantial in the energetically higher C-C bond fission, which causes rotational channel switching of the microscopic rate constants. The proper treatment of the J-dependent channel coupling effect, weak collisional transfer of J, and initial-J-dependent collisional energy transfer are found to be essential for predicting the branching fractions at low pressures.

Persistent currents in toroidal dipolar supersolids

We investigate the rotational properties of a dipolar Bose-Einstein condensate trapped in a toroidal geometry. Studying the ground states in the rotating frame and at fixed angular momenta, we observe that the condensate acts in distinctly different ways depending on whether it is in the superfluid or in the supersolid phase. We find that intriguingly, the toroidal dipolar condensate can support a supersolid persistent current which occurs at a local minimum in the ground state energy as a function of angular momentum, where the state has a vortex solution in the superfluid component of the condensate. The decay of this state is prevented by a barrier that in part consists of states where a fraction of the condensate mimics solid-body rotation in a direction opposite to that of the vortex. Furthermore, the rotating toroidal supersolid shows hysteretic behavior that is qualitatively different depending on the superfluid fraction of the condensate.