Nuclear rotational anomaly and the HFB equations

We show that the S-shape of the plot of moment of inertia versus square of the angular frequency observed experimentally for the rotational spectrum of rare-earth nuclei follows naturally from the solution of the Hartree-Fock-Bogoliubov equations. We consider the case of eight particles in the $\text{1}\text{h}\text{11}\text{2}$ level outside a closed shell and use the Sussex interaction for the nucleon-nucleon potential. Some properties of the upper, middle and lower branches are looked into and it is established that the transition indeed occurs due to reduction in the strength of the pairing part of the interaction due to the Coriolis force. Methods for calculating the moment of inertia and other nuclear properties in the transitional region, i.e. the middle branch, are suggested and it is found that the properties there are intermediate between the upper and lower branch. We also suggest the importance of higher (> 0) particle-particle channel coupled angular momentum of the nucleon force for the rotational spectrum of deformed nuclei at high angular momentum. A comment is also made on misleading results that can be obtained for e.g. moment of inertia, by projecting only even integral values of angular momentum in Hartree-Fock type solutions and thereby ignoring finer details.     

Fission barriers at high angular momentum and the ground state rotational band of the nucleus 254No

We study the superheavy nucleus 254No in the framework of the Hartree-Fock-Bogoliubov approximation with the finite-range density-dependent Gogny force, at zero and high angular momentum. The properties of the ground state rotational band and the fission barriers are discussed as a function of angular momentum. We found a two-humped barrier up to spin values of (30-40)Planck's over 2pi and a one-humped barrier for higher spins. We reproduce fairly well with the binding energy, the ground state deformation, the gamma-ray energies, and the bound on the fission barrier height measured at high spin.     

Stability of nuclear rotational states

The stability of rotational states described by using a procedure of the Hartree-Fock-Bogoliubov method is discussed. The stability condition is obtained in a general form and some of its properties are examined with the aid of simplifying approximations. It is pointed out in conclusion that the Coriolis force might lead to the instability of rotational states for sufficiently large angular momenta. The instability of rotational states is caused by the instability of the pairing density, and also by that of the nuclear density distribution. In the former case it is shown that below the critical angular momentum, a first-order phase transition takes place and in some cases the rotational band breaks off. In the latter case, it might be considered that the assumption of an axially symmetric deformation is broken or large change of the equilibrium deformation is brought suddenly. Then discontinuous change of the rotational level might be seen at the unstable point.     

The analysis of rovibrational motion equations of a diatomic molecule in the linear regime

The motion equations of diatomic molecules are here extended from the absolute vibrational case to a more general and real rotational and vibrational (rovibrational) case. The rovibrational Hamiltonian is heuristically formed by substituting the respective number and angular momentum operators for the vibrational and rotational quantum numbers in the energy eigenvalues of a diatomic molecule which was first introduced by Dunham. The motion equations of observable quantities such as the position and linear momentum are then determined by implementing the well-known Heisenberg relation in quantum mechanics. We face with the second-order imaginary differential equations for describing the temporal variations of the relative position and the linear momentum of two oscillating atoms, which are coupled in the x–y horizontal plane. The possible rovibrational oscillations are distinguished by the three quantum numbers n, l and m associated with the energy and angular momentum quantities. It is finally demonstrated that the simultaneous solutions of rovibrational equations satisfy the energy conservation during all quantised oscillations of a diatomic molecule in space.     

Statistical mechanics of confined systems with rotational excitations

New experimental and numerical investigations of confined systems of particles demonstrate the existence of rotational excitations. We develop here a statistical theory of finite systems, including rotational modes, by introducing the angular momentum into the formalism and constructing the relevant distributions. As special applications we study systems driven to a prescribed kinetic energy by negative friction or special isokinetic thermostats. Several distribution functions which are solutions of the Liouville or Fokker–Planck equations are given. The theory is applied to Coulomb clusters confined by parabolic forces.     

Magnetic rotation and chiral symmetry breaking

The deformed mean field of nuclei exhibits various geometrical and dynamical symmetries which manifest themselves as various types of rotational and decay patterns. Most of the symmetry operations considered so far have been defined for a situation wherein the angular momentum coincides with one of the principal axes and the principal axis cranking may be invoked. New possibilities arise with the observation of rotational features in weakly deformed nuclei and now interpreted as magnetic rotational bands. More than 120 MR bands have now been identified by filtering the existing data. We present a brief overview of these bands. The total angular momentum vector in such bands is tilted away from the principal axes. Such a situation gives rise to several new possibilities including breaking of chiral symmetry as discussed recently by Frauendorf. We present the outcome of such symmetries and their possible experimental verification. Some possible examples of chiral bands are presented.     

On the stationary axisymmetric Einstein-Maxwell equations

This paper is concerned with the class of exterior stationary axisymmetric solutions of the Einstein-Maxwell equations that arise from sources in which the mass is proportional to the charge and the angular momentum is proportional to the magnetic moment. With the use of Ernst's formulation the Einstein-Maxwell equations for this class are reduced to two coupled equations for two unknowns.     

The dynamics of rapidly rotating bodies

The dynamics of rapidly rotating bodies is formulated in a rotationally invariant form in all frames rotating with constant angular velocities relative to each other. This includes the energy, angular momentum, rotational frequency, and moment of inertia. The transformation between these quantities, when expressed in different frames, is then given explicitly and expressed in terms of both the angular momentum and the rotational frequency variables. Comparison with the approximate formula for the Routhian is made, and some consequences of physical interest are drawn.     

Hartree-Fock-Bogoliubov calculations of the rotational band of the very heavy 254No nucleus

We report on Hartree-Fock-Bogoliubov (HFB) calculations of the ground-state rotational band of the heavy nucleus ²⁵⁴No recently observed experimentally. The calculated quadrupole deformation is consistent with the experimental value of β = 0.27 and is almost constant over the whole band. We also reproduce fairly well the excitation spectra and moments of inertia of this isotope up to the maximal experimentally observed state of spin 20. The rather high stability of this nucleus against fission is illustrated by the deformation energy curve providing very high fission barriers at zero spin within the HFB and HFB plus Lipkin-Nogami formalisms. The variation of these barriers with increased angular velocities is also studied. Received: 23 November 2000 / Accepted: 24 October 2001     

Angular-momentum-projected cranked hfb approach to the study of nuclear rotations

Employing a pairing-plus-quadrupole interaction hamiltonian and projecting out good angular momentum states from the cranked Hartree-Fock-Bogoliubov (CHFB) intrinsic wave functions the yrast spectra of ¹⁵⁸Dy and ¹⁶⁸Yb are calculated up to moderately high spins (I_max = 16) as to include the backbending region. Then the variation of pairing correlation, g-factor and rotational alignment of neutron spin as a function of total angular momentum is studied. The effect of particle number projection on the spin-projected CHFB wave functions is also investigated and is found to be unimportant for the calculation of g-factors. On the other hand, corrections of the excitation energies for number fluctuations in the CHFB wave functions are essential. Furthermore, looking at the distribution of the total projection quantum number K in various cranking wave functions we are able to throw some light on the K ≠ 0 nature of the aligned s-band.A variation-after-spin projection calculation strictly for the axial shape, without cranking, is also carried out for both the nuclei considered here. In the low-spin region this numerically “cheaper” scheme produces energy spectra similar to that of the CHFB method, and may thus be used to readjust the interaction parameters.     

Induced rotation in the Papapetrou equations

We obtain an integral form of the Papapetrou equations, which describes the motion of an extended body in an external gravitational field. Using the Fock method, we calculate an explicit form for the components of the spin tensor and derive relativistic equations of rotational motion in the Schwarzschild space V₄. We show that the spin of the body becomes proportional not only to the angular velocity but also to the angular momentum. Thus, induced rotation also follows from the Papapetrou equations.Astrophysics Institute, Kazan Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 117–124, October, 1992.     

Angular momentum of isolated systems in general relativity

Solutions of Einstein's equations which describe isolated scattering systems are discussed and a set of asymptotic boundary conditions, which appear to characterize such solutions, is proposed. These conditions are then used to obtain a canonical definition of the total amount of angular momentum radiated by such a system.S.R.C. postdoctoral research fellow.     

On quadrupole and octupole gravitational radiation in the ANK formalism

Following the approach of Adamo–Newman–Kozameh (ANK) we derive the equations of motion for the center of mass and intrinsic angular moment for isolated sources of gravitational waves in axially symmetric spacetimes. The original ANK formulation is generalized so that the angular momentum coincides with the Komar integral for a rotational Killing symmetry. This is done using the Winicour–Tamburino Linkages which yields the mass dipole-angular momentum tensor for the isolated sources. The ANK formalism then provides a complex worldline in a fiducial flat space to define the notions of center of mass and spin. The equations of motion are derived and then used to analyse a very simple astrophysical process where only quadrupole and octupole contributions are included. The results are then compared with those coming from the post newtonian approximation.     

Laser-induced gas vortices

Recently, several femtosecond-laser techniques have demonstrated molecular excitation to high rotational states with a preferred sense of rotation. We consider collisional relaxation in a dense gas of such unidirectionally rotating molecules, and suggest that due to angular momentum conservation, collisions lead to the generation of macroscopic vortex gas flows. This argument is supported using the Direct Simulation Monte?Carlo method, followed by a computational gas-dynamic analysis.     

Eine relativistische Bewegungsgleichung für das strahlende Elektron,die keine Selbstbeschleunigungs-Lösungen enthält

By analyzing the equations of motion of a spatially extended charge distribution, we are lead to classical equations of motion for a radiating charged point particle. We describe the particle by an intrinsic and an extrinsic momentum and not, as is normally done, by the mechanical momentum and the Lorentz force. We thus obtain a differential equation with retarded argument, which is free of run-away solutions and also contains the physical solutions of the older theories. Open questions are pointed out in detail.     

Poincaré-sphere equivalent for light beams containing orbital angular momentum

The polarization state of a light beam is related to its spin angular momentum and can be represented on the Poincaré sphere. We propose a sphere for light beams in analogous orbital angular momentum states. Using the Poincaré-sphere equivalent, we interpret the rotational frequency shift for light beams with orbital angular momentum [Phys. Rev. Lett. 80, 3217 (1998)] as a dynamically evolving geometric phase.     

Atmospheric turbulence and orbital angular momentum of single photons for optical communication

The effects of propagation through random aberrations on coherence for single-photon communication systems based on orbital angular momentum states are quantified. A rotational coherence function is derived which leads to scattering equations for azimuthal modes of different orbital angular momentum states. The effect on a single-photon communication system is quantified using the channel capacity. The work shows that the decoherence effect of atmospheric turbulence on such systems is important even for weak turbulence.     

Approximate Analytical Solutions of Dirac Equation with Spin and Pseudo Spin Symmetries for the Diatomic Molecular Potentials Plus a Tensor Term with Any Angular Momentum

Approximate analytical solutions of the Dirac equation are obtained for some diatomic molecular potentials plus a tensor interaction with spin and pseudospin symmetries with any angular momentum. We find the energy eigenvalue equations in the closed form and the spinor wave functions by using an algebraic method. We also perform numerical calculations for the Pöschl-Teller potential to show the effect of the tensor interaction. Our results are consistent with ones obtained before.     

Ba原子与溴代烷烃反应产物转动取向的动力学研究

本文应用准三体模型及扩展的LEPS势能面 (PES)、准经典轨线和CPOAM模型计算了Ba+RBr(R=CH3,C2H5,C3J7,C4H9,n-C5H11)→BaBr+R反应体系产物 BaBr的转动取向,结果表明产物BaBr的转动取向随碰撞能的增加越趋强烈,随烷基的增大而减弱.