Hawking Radiation of Charged Particles from a Rotating Black String

Using Damour-Ruffini method, Hawking radiation of rotating black strings is studied. Under the condition that the total energy, total angular momentum and total charge are conservative, the transition probability from initial state (energy M+ω, charge Q+e and angular momentum J+m) to final state (energy M, charge Q and angular momentum J) for black strings is derived considering the reaction of radiation particles to spacetime. That is, the probability that black strings radiate particles with energy ω, charge e and angular momentum m is obtained. The real spectrum is not a strictly pure thermal spectrum. Our result is consistent with Parikh and Wilczek’s result. It satisfies the unitary principle of quantum mechanics. However, in our result there are not only the term that denotes effect of energy and charge of radiation particles but also the term that denotes effect of radiation particles angular momentum on rotating black strings angular momentum. We provide a new way for investigating radiation of black strings.     

Equations governing the energy-momentum tensor of a system of charged particles

In this paper the equations governing the energy, momentum, and angular momentum of a system of charged particles in motion are obtained as a series in inverse powers of c. The mass motion and time-symmetric part of the retarded electromagnetic field are shown to contribute to these equations a total time derivative which is an even power series in c⁻¹. The radiation-reaction terms of O(c⁻⁵) are evaluated and discussed as a prototype for higher order, odd power terms in the asymptotic expansions of the equations.     

Motion of extended bodies in general relativity and gravitational radiation

In the framework of general relativity, we consider the motion of extended spherically symmetric bodies coupled together only by gravitational interactions. The self-gravitational radiation of the bodies is taken into account. The problem is solved by the Fock method of successive approximations in harmonic coordinates, assuming slow motion and weak fields (v²/c² U/c^{2 2} 1) with terms up to and including the fifth order in taken into account. The equations of motion of the two bodies are derived, including the gravitational radiation reaction terms. It is shown that the system is conservative up to fifth order but to second order in e the six classical integrals of the motion are replaced by only two (the total energy and total angular momentum). An induced rotation effect in a system of initially nonrotating bodies is obtained. It is shown that in the fifth order approximation the system is nonconservative because of gravitational radition. An expression is obtained for the rate of loss of energy from the system directly from the equations of motion.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 12–16, January, 1985.     

Energy,momentum and angular momentum of gravitational radiation from a particle plunging into a non-rotating black hole

We have computed the energy ΔE, the momentum ΔP and the angular momentum ΔJ of gravitational radiation induced by a particle of mass μ and angular momentum μL_z plunging into a Schwarzschild black hole of mass M (?μ). It is found that the maximum value of ΔP is 4.5 × 10^?2 (μ/M) μc, ΔE/ΔJ ≈ 0.15c/(GM/c²), and a rotating ring plunging into a black hole emits less energy than a non-rotating one.     

Gravitational radiation from a particle with zero orbital angular momentum plunging into a Kerr black hole

We have computed the energy ΔE, the momentum ΔP and the angular momentum ΔJ of gravitational radiation induced by a particle of mass μ and of zero orbital angular momentum plunging in the θ = π/2 plane into a Kerr black hole of mass M(?μ) and angular momentum Ma. It is found that ΔE for a = 0.99M is 4.45 × 10^-2 (μ²/M)c², which is 4.27 times larger than that for the a = 0 case.     

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.     

Angular momentum polarization of the molecules in the Li + HF reaction

A theoretical analysis of the orientation and alignment of the rotational angular momenta of the reactants and products of the Li + HF(v _r = 0, j _r = 3) → LiF(v, j) + H reaction at a collision energy of E _coll = 0.317 eV is performed. The polarization of the angular momentum of the molecules involved in the reaction is based on the technique of spherical tensor operators (state multipoles). Quantum-mechanical calculations of the S-matrix of the reaction are carried out using the wave packet method. In particular, the influence of the orientation of the angular momentum of the HF reactant on the differential cross section is examined. It is shown that the contribution to the differential cross section comes only from be reactants with an angular momentum perpendicular to the reaction plane. In addition, the angular dependence of the orientation and alignment of the angular momenta of the reaction products are examined. It is shown that, for an isotropic distribution of reactant molecules, the orientation of the angular momenta of the products differs from zero only in the direction perpendicular to the reaction plane. Different experimental geometries, based on radiation enhanced multiphoton ionization, are proposed to detect the predicted effects.     

NN correlations measured in <Superscript>3</Superscript>He(e,e'pp)n

We have measured the ³He (e, e'pp)n reaction in the Jefferson Lab CLAS with 2.2 and 4.4 GeV electrons. We looked at the energy distribution of events with all three nucleons at high momentum (p > 250 MeV/c). This distribution has peaks where two nucleons each have 20% or less of the energy transfer (i.e., the third or ?leading? nucleon carries most of the kinetic energy). The angular distribution of these two ?fast? nucleons shows a very large back-to-back peak, indicating the effect of correlations. While there is some theoretical disagreement, experimental evidence, plus calculations at lower energy by W. Glöckle, indicates that these events are primarily sensitive to NN correlations.Received: 1 November 2002, Published online: 15 July 2003PACS: 21.45.+v Few-body systems - 25.30.Dh Inelastic electron scattering to specific statesL.B. Weinstein: For the CLAS Collaboration     

Screening Length of Rotating Heavy Meson from AdS/CFT

In this paper we consider a quark-antiquark (q[`(q)]q\bar{q}) pair which can be interpreted as a meson in N=4{\mathcal{N}}=4 SYM thermal plasma. We assume that the string moves at speed v and rotates around its center of mass simultaneously. By using the AdS/CFT correspondence, we obtain the momentum densities of the rotating string and determine its motion for small angular velocities. Then in general case, we calculate the screening length of q[`(q)]q\bar{q} pair numerically and show that its velocity dependance is in consistent with the well known formula L _s T∼(1−v ²)^1/4 in the literature.     

Structure in momentum-transfer for (pπ−) systems produced in diffractive dissociation of neutrons on protons

The four-momentum transfer distribution of (pπ^?) systems produced in the neutron dissociation reaction n + p → (pπ^?) + p has substantial structure which depends strongly on the mass and on the angular decay properties of the produced (pπ^?) system. No significant energy dependence is observed in the data for incident neutrons in the momentum range between 50 GeV/c and 300 GeV/c. The results are compared with a Deck-type of model.     

The mutual interaction of molecular rotation and translation

The dynamics of molecular rototranslation are treated with an equation of motion with a non-Markovian, stochastic force/torque. It is shown that this Mori/Kubo/Zwanzig representation is equivalent to a multidimensional Markov equation which may be identified with analytical models of the molecular motion. Langevin and Fokker-Planck equations for two such models are derived from the general equations of motion. The analytical results are compared with a computer simulation of the velocity/angular velocity mixed autocorrelation function, C _vω(t) = <v(0) . ω(t)> for a triatomic of C _2v symmetry.     

Gravitational interaction of two spinning particles in general relativity

We consider gravitational interaction between two spinning pointlike particles. We use a fastmotion approximation and we obtain the first-order gravitational field and motion equations. Following the method developed by Bel and Martin we get up to the first order: the accelerations, momentum, energy, and a Hamiltonian of the system. This Hamiltonian, when it is expanded in a power series ofc ^–1, agrees with those of earlier authors, who use different techniques.     

Thermally stimulated luminescence of poly(ethylene 2,6-naphthalenedicarboxylate)

We compute reaction cross sections at several post-threshold energies in the J_z conserving approximation for the three-dimensional hydrogen exchange reaction. These cross sections and reaction probabilities agree closely with accurate close-coupling results, particularly for smaller values of the total angular momentum J, but with an enormous saving in computer time. For this approximation, three steps are required, and are as follows: (a) pick a single value of l for each j by examining hindered rotor wavefunctions near the transition state; (b) modify the J = 0 rotational energy correlation diagram for the case J>0 ; (c) assume the close-coupling matrix elements linking alternative rotational channels for J>0 are identical to those for J=0. We discuss each of these approximations in detail.     

Effective Values of Komar Conserved Quantities and Their Applications

We calculate the effective Komar angular momentum for the Kerr-Newman (KN) black hole. This result is valid at any radial distance on and outside the black hole event horizon. The effective values of mass and angular momentum are then used to derive an identity (K_c^m=2STK_{\chi^{\mu}}=2ST) which relates the Komar conserved charge (K_c^mK_{\chi^{\mu}}) corresponding to the null Killing vector (χ ^μ ) with the thermodynamic quantities of this black hole. As an application of this identity the generalised Smarr formula for this black hole is derived. This establishes the fact that the above identity is a local form of the inherently non-local generalised Smarr formula.     

On the maximum in the differential cross sections of the F + H2 reaction in the region of small scattering angles

By means of quantum mechanical simulation of the reaction F + H₂(v = 0; j = 0, 1, 2) → H + HF(v′, j′) on the Stark-Werner ground state potential energy surface at collision energies of 1.84, 2.74, and 3.42 kcal/mol, we have analyzed interference of the “partial waves” corresponding to different values of the total angular momentum J. As the vibrational quantum number v′ of the HF(v′, j′) product increases, the interference for the HF forward scattering becomes noticeably more constructive. This is probably the reason for the maximum in the angular distributions of the HF(v′= 3) molecules at small scattering angles that was discovered experimentally by D.M. Neumark, A.M. Wodtke, G.N. Robinson, C.C. Hayden, and Y.T. Lee, J. Chem. Phys. 82 (7), 3045 (1985) at the same collision energies. We have also determined the intervals of J values most effective for forward scattering of the HF(v′, j′) molecules.     

Mass and stability of rigidly rotating relativistic polytropes by energy method

The energy of a rigidly rotating star is written in the first and second post-Newtonian approximation. Conditions for equilibrium and stability are derived, as well as evolutionary paths for stars shedding angular momentum or mass. For polytropic index n > 1, these analytic results agree with exact numerical results to within a few percent as long as the general relativity index (P/c²)_c < 0.1. The energy method is applied to low mass white dwarfs, to semirelativistic neutron stars and to supermassive stars.     

Effective Dynamics for Particles Coupled to a Quantized Scalar Field

We consider a system of N non-relativistic spinless quantum particles (“electrons”) interacting with a quantized scalar Bose field (whose excitations we call “photons”). We examine the case when the velocity v of the electrons is small with respect to the one of the photons, denoted by c (v/c = ε ≪ 1). We show that dressed particle states exist (particles surrounded by “virtual photons”), which, up to terms of order (v/c)³, follow Hamiltonian dynamics. The effective N-particle Hamiltonian contains the kinetic energies of the particles and Coulomb-like pair potentials at order (v/c)⁰ and the velocity dependent Darwin interaction and a mass renormalization at order (v/c)². Beyond that order the effective dynamics are expected to be dissipative. The main mathematical tool we use is adiabatic perturbation theory. However, in the present case there is no eigenvalue which is separated by a gap from the rest of the spectrum, but its role is taken by the bottom of the absolutely continuous spectrum, which is not an eigenvalue. Nevertheless we construct approximate dressed electron subspaces, which are adiabatically invariant for the dynamics up to order . We also give an explicit expression for the non-adiabatic transitions corresponding to emission of free photons. For the radiated energy we obtain the quantum analogue of the Larmor formula of classical electrodynamics.     

The spin-orbit term in radiative transitions of hadrons

We point out that one finds in the literature two different results for the spin-orbit term in radiative transitions of hadrons. We analyze the problem and find that, besides the term usually quoted $$ - ie\omega (\sigma \times p) \cdot \varepsilon _\gamma /4m^2 \cong e[\nabla (V_v + V_s ) \times \sigma ] \cdot \varepsilon _\gamma /4m^2 $$ (V _v ,V _s are the Lorentz vector and scalar pieces of the binding potential and ω the photon energy), there is another term that gives as final resulte(?V _v ×σ)·ε ^γ/2m ². We use for our proof two different approaches: the Foldy-Wouthuysen transformation, and the method of Brodsky and Primack based on a dipole formula. In hadrons, the electric field has two pieces, the photon radiation field, and a strong interaction piece, of order 1/e relative to the former. These two pieces are at the origin of the two spin-orbit terms at the order (v/c)³.     

Quarkonium and hydrogen spectra with spin-dependent relativistic wave equation

The non-linear non-perturbative relativistic atomic theory introduces spin in the dynamics of particle motion. The resulting energy levels of hydrogen atom are exactly the same as that of Dirac theory. The theory accounts for the energy due to spin-orbit interaction and for the additional potential energy due to spin and spin-orbit coupling. Spin angular momentum operator is integrated into the equation of motion. This requires modification to classical Laplacian operator. Consequently, the Dirac matrices and the k operator of Dirac’s theory are dispensed with. The theory points out that the curvature of the orbit draws on certain amount of kinetic and potential energies affecting the momentum of electron and the spin-orbit interaction energy constitutes a part of this energy. The theory is developed for spin-1/2 bound state single electron in Coulomb potential and then extended further to quarkonium physics by introducing the linear confining potential. The unique feature of this quarkonium model is that the radial distance can be exactly determined and does not have a statistical interpretation. The established radial distance is then used to determine the wave function. The observed energy levels are used as the input parameters and the radial distance and the string tension are predicted. This ensures 100% conformance to all observed energy levels for the heavy quarkonium.     

Effect of entrance channel parameters on fission fragment angular momentum in medium energy fission

Independent isomeric yield ratios of¹³²I were radiochemically determined in alpha particle induced fission of²³⁸U in the energy range 25–44 MeV. Fission fragment angular momenta were deduced from the measured isomeric yield ratios using spin dependent statistical model analysis. It was seen that angular momentum of¹³²I increases with increase of excitation energy and angular momentum of the fissioning nucleus. Comparison of the present data on¹³²I in²³⁸U(α,f) with the literature data for the same product in²³⁸U(p, f) and²³⁸U(γ, f) at various excitation energies show that fragment angular momentum strongly depends on the input angular momentum in the range of excitation energy considered. Experimental fragment angular momentum at all excitation energies were seen to be in agreement with the theoretical values calculated based on thermal equilibration of the various collective rotational degrees after considering the occurence of multichance fission. Thus, strong effect of input angular momentum as well as the statistical equilibration among the various collective rotational degrees of freedom in medium energy fission is corroborated.