Large Angular Momentum

Gamma-ray beams with a large angular momentum may affect astrophysical phenomena, which calls for appropriate earth-based experimental investigations. For this purpose, we investigate the generation of well-collimated γ-ray beams with a very large orbital angular momentum using nonlinear Compton scattering of a strong laser pulse of twisted photons at ultrarelativistic electrons. Angular momentum conservation among absorbed laser photons, quantum radiation, and electrons is numerically demonstrated in the quantum radiation-dominated regime. We point out that the angular momentum of the absorbed laser photons is not solely transferred to the emitted γ photons, but due to radiation reaction shared between the γ photons and interacting electrons. The efficiency of the angular momentum transfer is optimized with respect to the laser and electron beam parameters. The accompanying process of electron-positron pair production is furthermore shown to enhance the orbital angular momentum gained by the γ-ray beam.

Yu and Littlejohn recently studied in (2011 Phys. Rev. A 83 052114 (arXiv:1104.1499)) some asymptotics of Wigner symbols with some small and large angular momenta. They found that in this regime the essential information is captured by the geometry of a tetrahedron, and gave new formulae for 9j-, 12j- and 15j-symbols. We present here an alternative derivation which leads to a simpler formula, based on the use of the Ponzano–Regge formula for the relevant tetrahedron. The approach is generalized to Wigner 3nj-symbols with some large and small angular momenta, where more than one tetrahedron are needed, leading to new asymptotics for Wigner 3nj-symbols. As an illustration, we present 15j-symbols with one, two and four small angular momenta, and give an alternative formula to Yu’s recent 15j-symbol with three small spins.

For a rotating black hole to be nonsingular, it means that there are no spacetime singularities at its center. The destruction of the event horizon of such a rotating black hole is not constrained by the weak cosmic censorship conjecture, which may provide possibilities to understand the internal structure of black hole event horizons. In this paper, we employ test particles with large angular momentum and a scalar field with large angular momentum to investigate the potential of destroying the event horizon of rotating black-bounce black holes. Additionally, we investigate the possibility of destroying the event horizon of a rotating black-bounce black hole by considering test particles with large angular momentum and scalar fields with large angular momentum, covering the entire range of the rotating black-bounce black hole. We analyze the influence of the parameter m on the possibility of destroying the event horizon in this spacetime. Our analysis reveals that under extreme or near-extreme conditions, the event horizon of this spacetime can potentially be destroyed after the absorption of particles energy and angular momentum, as well as the scattering of scalar fields. Additionally, we find that as the parameter m increases, the event horizon of this spacetime model becomes more susceptible to destruction after the injection of test particles or the scattering of scalar fields.

The effect of large angular momenta on multifragmentation of hot nuclei

Cross sections for forming compound nuclei in symmetric very-heavy-ion reactions are calculated by use of the criterion that the dynamical trajectory for the fusing system must pass inside the fission saddle point in a multidimensional space in order to form a compound nucleus. The dynamical trajectory is obtained by solving numerically the modified classical Lagrange equations of motion for a system whose shape is specified in terms of smoothly joined portions of three quadratic surfaces of revolution. This restriction to nuclear shapes that are axially symmetric (about an axis that is in general rotating in space) is a good approximation for systems with small angular momentum, but it may be seriously deficient for systems with large angular momentum. The nuclear potential energy of deformation is determined by means of a macroscopic model that includes the Coulomb energy and the nuclear macroscopic energy. This latter quantity is calculated in terms of a double volume integral of a Yukawa two-body interaction potential, which includes the surface energy of the liquid-drop model but also takes into account the lowering in energy due to the finite range of the nuclear force. For systems with angular momentum, we include a centrifugal pseudopotential calculated for rigid-body rotation. The kinetic energy of collective motion is calculated for nuclear flow that is a superposition of incompressible, nearly irrotational collective-shape motion and rigid-body rotation. Nuclear dissipation (the transfer of energy of collective motion into internal single-particle excitation energy) is included in the formulation by means of Rayleigh's dissipation function. However, to emphasize that compound-nucleus cross sections become small for very heavy systems even in the absence of dissipation, our current results are presented for the case of zero dissipation. For nuclear systems lighter than about $^{110}\mathrm{Pd}$ + $^{110}\mathrm{Pd}$ \ensuremath{\rightarrow} $^{220}\mathrm{U}$ and for relatively low angular momentum, the fission saddle point lies outside the point of hard contact in heavy-ion reactions, which permits the compound-nucleus cross section at relatively low bombarding energy to be calculated in terms of a one-dimensional interaction barrier, as is customarily done. For heavier nuclear systems and/or for high angular momentum, the fission saddle point lies inside the contact point, which reduces the compound-nucleus cross section compared with that calculated for a one-dimensional interaction barrier.NUCLEAR REACTIONS $^{100}\mathrm{Mo}$ + $^{100}\mathrm{Mo}$ \ensuremath{\rightarrow} $^{200}\mathrm{Po}$, $^{110}\mathrm{Pd}$ + $^{110}\mathrm{Pd}$ \ensuremath{\rightarrow} $^{220}\mathrm{U}$, $^{124}\mathrm{Sn}$ + $^{124}\mathrm{Sn}$ \ensuremath{\rightarrow} $^{248}\mathrm{Fm}$. Calculated compound-nucleus cross sections. Liquid-drop model, hydrodynamical model, nuclear potential energy of deformation, nuclear inertia, dynamical trajectory, compound-nucleus formation, heavy-ion fusion, quasifission, highly inelastic heavy-ion collisions.

We propose a new laser-plasma-based method to generate bright γ-rays carrying large orbital angular momentum by interacting a circularly polarized Laguerre–Gaussian laser pulse with a near-critical hydrogen plasma confined in an over-dense solid tube. In the first stage of the interaction, it is found via fully relativistic three-dimensional particle-in-cell simulations that high-energy helical electron beams with large orbital angular momentum are generated. In the second stage, this electron beam interacts with the laser pulse reflected from the plasma disc behind the solid tube, and helical γ beams are generated with the same topological structure as the electron beams. The results show that the electrons receive angular momentum from the drive laser, which can be further transferred to the γ photons during the interaction. The γ beam orbital angular momentum is strongly dependent on the laser topological charge l and laser intensity a 0, which scales as . A short (duration of 5 fs) isolated helical γ beam with an angular momentum of −3.3 × 10−14 kg m2 s−1 is generated using the Laguerre–Gaussian laser pulse with l = 2. The peak brightness of the helical γ beam reaches 1.22 × 1024 photons s−1 mm−2 mrad−2 per 0.1% BW (at 10 MeV), and the laser-to-γ-ray angular momentum conversion rate is approximately 2.1%.

Analysis of the masses and angular momenta of galaxies

Microscopic derivation of cranking for nuclear systems with large angular momentum

Collision of nucleons with large angular momenta

The behavior of a nonlinear oscillator (NO) coupled to a radiation field is investigated. The NO considered is an angular momentum oscillator, of energy $\ensuremath{\hbar}\ensuremath{\omega}{L}_{3}$, that describes the collective effect of a number of identical two-level (or spin-\textonehalf{}) systems under given idealized conditions, a large total angular momentum quantum number ${L}_{0}$ corresponding to a large number of two-level systems. The field is described by a set of modes. Free decay---with the NO initially excited and the radiation field in the ground state---and forced oscillation---with the NO subject to a prescribed resonant driving field---are studied. The analysis is performed both classically and quantum mechanically, using the classical and Heisenberg equations of motion, respectively, so as to display explicitly the difference in the results. Interest in the comparison between the two formalisms is motivated by the expectation that for large ${L}_{0}$, the NO should behave essentially classically, except near its highest-energy state in the absence of a driving field. The general equations of motion are reduced to equations for the NO variables only. In the classical analysis of free decay, expressions for the energy and oscillating coordinates are derived. The decay time is shown to approach infinity as ${L}_{3}(0)$ approaches ${L}_{0}$ (the limiting condition being that of unstable equilibrium) and the radiative frequency shift is shown to be approximately proportional to ${L}_{3}(t)$. It is also shown that use of the rotating-wave approximation alters qualitatively the expression for the frequency shift. In the classical analysis of forced oscillation, approximate results are obtained for a weak driving field and a strong driving field, the NO being initially in the ground state. The weakfield results exhibit a monotonic approach of ${L}_{3}(t)$ to a constant (negative) value---or steady state---at which the power absorbed equals the power radiated; in the strong-field case, ${L}_{3}(t)$ oscillates periodically between the limits $\ifmmode\pm\else\textpm\fi{}{L}_{0}$, the coupling to the radiation field having negligible effect on the frequency of this oscillation. In the quantum-mechanical analysis, the equations of motion become simplified for ${L}_{0}=\frac{1}{2}$, and this case is treated first. The free-decay results are essentially similar to those of the Weisskopf-Wigner theory, exhibiting an exponential decay of $〈{L}_{3}(t)〉$ and a radiative frequency shift in the oscillating coordinates. Under forced oscillation, with $〈{L}_{3}(0)〉=\ensuremath{-}{L}_{0}, 〈{L}_{3}(t)〉$ approaches a constant value either monotonically, if the driving field is sufficiently weak, or by means of a damped oscillation, if the driving field is strong. For ${L}_{0}>\frac{1}{2}$, the free decay is treated by a method that involves the derivation of a set of expressions for the $k\mathrm{th}$ derivative of $〈{L}_{3}(t)〉$ as an expectation value of a polynomial in ${L}_{3}$ of order $k+1$. This set, together with the eigenvalue equation for ${L}_{3}$, is shown to lead to a solution for all the moments of ${L}_{3}$. The method is used to obtain complete solutions for several low values of ${L}_{0}$, and also to obtain initial derivatives of $〈{L}_{3}(t)〉$ as polynomials in ${L}_{0}$ for $〈{L}_{3}(0)〉={L}_{0}$. For large ${L}_{0}$, a comparison of classical and quantum-mechanical equations shows that only the condition $〈{L}_{3}(0)〉\ensuremath{\approx}{L}_{0}$ requires quantum-mechanical treatment, and that for a short time only. The free-decay problem with initial condition $〈{L}_{3}(0)〉={L}_{0}$ solved quantum mechanically up to such a time ${t}_{1}$ by means of the initial derivatives previously derived, and then this solution if used to provide initial conditions determining a classical solution for $t\ensuremath{\ge}{t}_{1}$. The statistical aspects introduced by the quantum mechanics are preserved in the classical solution, and their significance is discussed, with several examples, comparison is also made with a nonstatistical approximation. In the case of forced oscillation, the behavior of $〈{L}_{3}(t)〉$---for arbitrary ${L}_{0}$---is examined in detail for a strong field, and turns out to be described by a damped oscillation, the existence of the damping being independent of ${L}_{0}$. The apparent inconsistency of this result with the expectation that a large system subject to strong forces should behave classically is discussed, and $〈{L}_{2}^{3}(t)〉$ is examined. It is concluded that in a single experiment, the NO energy oscillates approximately like the classical energy, without damping; quantum mechanics introduces, however, a slight randomness (or unpredictability) in the frequency of this oscillation, because of the coupling with the radiation field. Since $〈{L}_{3}(t)〉$ describes the average over an ensemble of which each member consists of a NO coupled to a radiation field, the random frequency variation among the members accounts for the damping of the average. The usefulness of the combination of classical and quantum-mechanical analyses in achieving and interpreting theoretical results for a class of phenomena involving the collective interaction between a number of atoms and a radiation field is pointed out.

Based on orbital calculations of Keplerian planetesimals incident on a planet with various initial orbital elements, we develop a numerical model which describes the accretional and dynamical evolution of planet-satellite systems in a swarm of planetesimals on heliocentric orbits with given spatial and velocity distributions. In the plane of orbital radius of the satellite vs. satellite/planet mass ratio, a satellite with some initial value moves quickly toward the balanced orbital radius, where accretion drag compensates with tidal repulsion, and then grows toward the equilibrium mass ratio. Using the model, we propose two types of co-accretion scenarios for the origin of the Moon, both of which satisfy the most fundamental dynamical constraints: the large angular momentum of the Earth-Moon system and the large Moon/Earth mass ratio. In the first scenario the Moon starts from a small embryo and grows in a swarm of planetesimals with low velocity dispersion and nonuniform spatial distribution, so that large spin angular momentum is supplied to the planet. Such a situation would be realized when the Earth grows up rapidly before dissipation of the solar nebula. Second one considers co-accretion after a giant impact during Earth accretion, which produces enough angular momentum as large as that of the present Earth-Moon system as well as a lunar-sized satellite. In this case, solar nebula would have already dissipated and random velocities of incident planetesimals are rather high, so that the Earth grows slowly. We find that the total angular momentum decreases by 5–25% during this co-accretion stage.

The purpose of this study is to evaluate the jumping smash technique in badminton from the viewpoint of conservation of angular momentum. Angular momentum estimates for the whole body were calculated, and the application of the principle of conservation of angular momentum was discussed for the smash motion. A cinematographic technique was used to determine the angular momentum of the human body about its mass center for general three-dimensional movements. The three orthogonal components of the angular momentum of 15 body segments, composed of a transfer term and a local term, were computed. The total angular momentum of the whole body was considered to be composed of the sum of the angular momenta of all body segments. Three-dimensional coordinates for determining the angular momentum were computed using Direct Linear Transformation method from film data. According to the principle of conservation of angular momentum,the smash motion is supported by the cooperation of all body segments. As the jumping smash movement is initiated, the lower limbs acquire some angular momentum on take-off from the ground, and then transmit it to the smashing arm. The torso and the left arm act as intermediaries in transmission of the initial angular momentum between the lower limbs and the swing arm. During the fore swing phase of the arm, a large angular momentum is generated by rapid arm rotation. The lower limbs and the head react to the arm swing with an equal and opposite angular momentum to keep the angular momentum constant. This kind of counter rotation to the smash arm is useful to keep the body balanced and reinforce the hitting arm. Key points in learning the jumping smash technique are to acquire an initial angular momentum on take-off and to create some counter rotation opposite to the swing arm.

A technique is presented for determining the angular momentum of the human body about its mass centre for general three-dimensional movements. The three orthogonal components of the angular momentum X, Y, and Z of 15 body segments composed of a transfer term and a local term were computed. The total angular momentum of the whole body was considered to be composed of the sum of the angular momentum of each body segment. The three-dimensional coordinates for determining the angular momentum were computed by a Direct Linear Transformation Method from film data. For calculated individual angular momentum the relative error is estimated to be within 7.2%. The application of the principle of conservation of angular momentum was discussed for the jumping smash of badminton. A large angular momentum was generated by rotation of the smash arm during the airborne phases. The lower limbs react upon the arm with an equal and opposite angular momentum to keep the angular momentum constant. This kind of counter rotation to the smash arm was useful to keep the body balance and reinforce the hitting arm.

The key characteristic of single-molecule magnets (SMMs) is the anisotropy-induced blocking barrier, which should be as efficient as possible, i.e., to be able to provide long magnetic relaxation times at elevated temperatures. The strategy for the design of efficient SMMs on the basis of transition-metal complexes such as Mn12Ac is well established, which is not the case of complexes involving strongly anisotropic metal ions such as cobalt(II) and lanthanides (Ln). While strong intraionic anisotropy in the latter allows them to block the magnetization already in mononuclear complexes, the presence of several such ions in a complex does not result automatically in more efficient SMMs. Here, the magnetic blocking in the series of isostructural 3d-4f complexes Co(II)-Ln(III)-Co(II), Ln = Gd, Tb, and Dy, is analyzed using an originally developed ab initio based approach for the investigation of blocking barriers. The theoretical analysis allows one to explain the counterintuitive result that the Co-Gd-Co complex is a better SMM than terbium and dysprosium analogues. It turns out that the highly efficient magnetic blockage in the Co-Gd-Co complex results from a concomitant effect of unexpectedly large unquenched orbital momentum on Co(II) ions (ca. 1.7 μB) and the large spin on the gadolinium (S = 7/2), which provides a multilevel blocking barrier, similar to the one of the classical Mn12Ac. We conclude that efficient SMMs could be obtained in complexes combining strongly anisotropic and isotropic metal ions with large angular momentum rather than in polynuclear compounds involving strongly anisotropic ions only.

In order to select more suitable characteristic lines as the analysis lines of the elements, laser-induced breakdown spectroscopy is used to detect the self-made soil sample doped with Cd and Fe elements. Using Savitzky-Golay convolution smoothing method to preprocessed spectral data. Select the common line Cd I: 288.122nm, 346.62 nm, Fe I: 357.001 nm, 363.146 nm to establish the calibration curve by external standard method, calculate the detection limit ， the influences of atomic configuration and angular momentum on the calibration curve and detection limit of the spectral transition level are studied. The study shows that the detection limit calculated by the analysis lines with high SNR are relatively low and more sensitive to the detection of elements; The SNR of the analysis lines with the same atomic configuration of the transition show the same trend with the change of element content. The analytical lines Cd I: 346.62 nm (2-1) and Fe I: 363.146 nm (4-3) with relatively large angular momentum are better excitation, and the correlation coefficient R2 of the obtained calibration curves are relatively higher, the limit of detection is smaller than the Cd I: 288.122 nm (1-1) and Fe I: 357.001 nm (1-1), the lines with large angular momentum are more suitable for element detection.