Angular momentum of a system of particles in the center‐of‐mass frame

1980 ◽  
Vol 48 (7) ◽  
pp. 546-547
Author(s):  
G. Faucher
Keyword(s):  
Angular Momentum ◽  
Center Of Mass ◽  
System Of Particles ◽  
Mass Frame

THE STEREODYNAMICS STUDY OF THE C(3P) + OH (X2 Π) → CO(X1Σ+) + H(2S) REACTION

2010 ◽  
Vol 09 (05) ◽  
pp. 935-943 ◽  
Author(s):  
PENG SONG ◽  
YONG-HUA ZHU ◽  
JIAN-YONG LIU ◽  
FENG-CAI MA
Keyword(s):  
Angular Momentum ◽  
Cross Sections ◽  
Collision Energy ◽  
Energy Surface ◽  
Center Of Mass ◽  
Title Reaction ◽  
High Collision Energy ◽  
Dependency Relationship ◽  
Energy Dependency ◽  
Mass Frame

The stereodynamics of the title reaction on the ground electronic state X2A' potential energy surface (PES)1 has been studied using the quasiclassical trajectory (QCT) method. The commonly used polarization-dependent differential cross-sections (PDDCSs) of the product and the angular momentum alignment distribution, P(θr) and P(Φr), are generated in the center-of-mass frame using QCT method to gain insight of the alignment and orientation of the product molecules. Influence of collision energy on the stereodynamics is shown and discussed. The results reveal that the distribution of P(θr) and P(Φr) is sensitive to collision energy. The PDDCSs exhibit different collision energy dependency relationship at low and high collision energy ranges.

ACCELERATION OF PARTICLES AS A UNIVERSAL PROPERTY OF ERGOSPHERE

2013 ◽  
Vol 28 (11) ◽  
pp. 1350037 ◽  
Author(s):  
O. B. ZASLAVSKII
Keyword(s):  
Black Hole ◽  
Angular Momentum ◽  
Recent Observation ◽  
Center Of Mass ◽  
Kerr Black Hole ◽  
Acceleration Of Particles ◽  
Axially Symmetric ◽  
Fixed Energy ◽  
Mass Frame

We show that recent observation made by Grib and Pavlov, [A. A. Grib and Yu. V. Pavlov, Europhys. Lett.101, 20004 (2013)] for the Kerr black hole is valid in the general case of rotating axially symmetric metric. Namely, collision of two particles in the ergosphere leads to indefinite growth of the energy in the center-of-mass frame, provided the angular momentum of one of the two particles is negative and increases without limit for a fixed energy at infinity. General approach enabled us to elucidate why the role of the ergosphere is crucial in this process.

A QUASI-CLASSICAL TRAJECTORY STUDY ON STEREODYNAMICS OF THE F + HCl (v = 0, j = 0) → HF + Cl REACTION

2012 ◽  
Vol 11 (03) ◽  
pp. 663-674 ◽  
Author(s):  
XIAN-FANG YUE ◽  
PEI FENG
Keyword(s):  
Angular Momentum ◽  
Cross Sections ◽  
Ground State ◽  
Energy Surface ◽  
Center Of Mass ◽  
Classical Trajectory ◽  
Polar Coordinates ◽  
Angular Distributions ◽  
Title Reaction ◽  
Mass Frame

Quasiclassical trajectory (QCT) calculations for the title reaction are carried out by employing the recent developed accurate potential energy surface of the 12A′ ground state. Two angular distributions, P(θr) and P(ϕr), with θr, ϕr being the polar angles of the product angular momentum, and two commonly used polarization dependent differential cross sections, (2π/σ)(dσ00/dωt) and (2π/σ)(dσ20/dωt), with ωt being the polar coordinates of the product velocity, are generated in the center-of-mass frame. It was found that the product rotational angular momentum j′ is not only aligned, but also oriented along the negative direction of y-axis. We also investigated the product state distributions in the present work, and found that the vibrational and rotational state distributions are inverted. Influences of collision energies on the product polarization and state distributions are also shown and discussed.

COLLISION ENERGY IN THE CENTER-OF-MASS FRAME FOR ROTATING AND ACCELERATING BLACK HOLES

2012 ◽  
Vol 27 (03) ◽  
pp. 1250017 ◽  
Author(s):  
IBRAR HUSSAIN
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Angular Momentum ◽  
Collision Energy ◽  
Center Of Mass ◽  
The Other ◽  
Extremal Case ◽  
Mass Frame ◽  
Critical Angular Momentum ◽  
Proper Angular Momentum

The center-of-mass (CM) energy of collision for two uncharged particles falling freely from rest at infinity is investigated in the background of charged, rotating and accelerating black hole. It is found that the CM energy of collision is unlimited at the acceleration horizon and at the event horizon (in the extremal case) if one of the colliding particles has critical angular momentum and the other one has a proper angular momentum such that the particle can reach the horizon.

THEORETICAL STUDY OF THE STEREO-DYNAMICS OF THE REACTION O + HCl → ClO + H

2011 ◽  
Vol 10 (01) ◽  
pp. 1-7 ◽  
Author(s):  
QIANG WEI ◽  
YING KE XIE ◽  
WEN LIN FENG
Keyword(s):  
Angular Momentum ◽  
Cross Sections ◽  
Collision Energy ◽  
Energy Surface ◽  
Theoretical Study ◽  
Center Of Mass ◽  
Classical Trajectory ◽  
Title Reaction ◽  
Mass Frame ◽  
Product Vector

Quasi-classical trajectory (QCT) method is used to study the stereo-dynamics of the title reaction on the ground 1 1A′ potential energy surface (PES). Differential cross-sections (DCSs) and alignments of the product rotational angular momentum for the reaction are reported. The influence of collision energy on the product vector properties is also studied in the present work. The distribution of angle between k and j′, P(θr), the distribution of dihedral angle denoting k-k′-j′ correlation, P(ϕr) ⋅ (2π/σ)( d σ00/ d ωt), (2π/σ)( d σ20/ d ωt), (2π/σ)( d σ22+/ d ωt) and (2π/σ)(dσ21-/dωt) have been calculated in the center of mass frame, respectively.

scholarly journals Super-Penrose process due to collisions inside ergosphere

2017 ◽  
Vol 26 (02) ◽  
pp. 1750009
Author(s):  
O. B. Zaslavskii
Keyword(s):  
Black Hole ◽  
Angular Momentum ◽  
Center Of Mass ◽  
Black Hole Horizon ◽  
Mass Frame ◽  
Penrose Process

If two particles collide inside the ergosphere, the energy in the center of mass frame can be made unbound provided at least one of particles has a large negative angular momentum [A. A. Grib and Yu. V. Pavlov, Europhys. Lett. 101 (2013) 20004]. We show that the same condition can give rise to unbounded Killing energy of debris at infinity, i.e. super-Penrose process. Proximity of the point of collision to the black hole horizon is not required.

scholarly journals Hyperbolic Center of Mass for a System of Particles in a Two-Dimensional Space with Constant Negative Curvature: An Application to the Curved 2-Body Problem

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 531
Author(s):  
Pedro Pablo Ortega Palencia ◽  
Ruben Dario Ortiz Ortiz ◽  
Ana Magnolia Marin Ramirez
Keyword(s):  
Negative Curvature ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Simple Expression ◽  
Two Dimensional ◽  
Constant Negative Curvature ◽  
Euclidean Case ◽  
System Of Particles ◽  
Material Points ◽  
The One

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsic coordinates, and we showed how this extends the definition for the Euclidean case. The argument is constructive and serves to define the center of mass of a system of particles on the one-dimensional hyperbolic sphere LR1.

scholarly journals Infrared effects in the late stages of black hole evaporation

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Éanna É. Flanagan
Keyword(s):  
Black Hole ◽  
Angular Momentum ◽  
Center Of Mass ◽  
Planck Scale ◽  
Black Hole Mass ◽  
Order Unity ◽  
Intrinsic Angular Momentum ◽  
Hole Position ◽  
Late Stages ◽  
Shear Tensor

Abstract As a black hole evaporates, each outgoing Hawking quantum carries away some of the black holes asymptotic charges associated with the extended Bondi-Metzner-Sachs group. These include the Poincaré charges of energy, linear momentum, intrinsic angular momentum, and orbital angular momentum or center-of-mass charge, as well as extensions of these quantities associated with supertranslations and super-Lorentz transformations, namely supermomentum, superspin and super center-of-mass charges (also known as soft hair). Since each emitted quantum has fluctuations that are of order unity, fluctuations in the black hole’s charges grow over the course of the evaporation. We estimate the scale of these fluctuations using a simple model. The results are, in Planck units: (i) The black hole position has a uncertainty of $$ \sim {M}_i^2 $$ ∼ M i 2 at late times, where Mi is the initial mass (previously found by Page). (ii) The black hole mass M has an uncertainty of order the mass M itself at the epoch when M ∼ $$ {M}_i^{2/3} $$ M i 2 / 3 , well before the Planck scale is reached. Correspondingly, the time at which the evaporation ends has an uncertainty of order $$ \sim {M}_i^2 $$ ∼ M i 2 . (iii) The supermomentum and superspin charges are not independent but are determined from the Poincaré charges and the super center-of-mass charges. (iv) The supertranslation that characterizes the super center-of-mass charges has fluctuations at multipole orders l of order unity that are of order unity in Planck units. At large l, there is a power law spectrum of fluctuations that extends up to l ∼ $$ {M}_i^2/M $$ M i 2 / M , beyond which the fluctuations fall off exponentially, with corresponding total rms shear tensor fluctuations ∼ MiM−3/2.

Measurement of the Cross Section for the Process $${e^{+}e^{-}}{\to}{K}^{{+}}{K}^{{-}}{\pi}^{{0}}$$ with the SND Detector at Collision Energies of $$\sqrt{{s}}{=}{1.3{-}2.0}$$ GeV in the Center-of-Mass Frame

2021 ◽  
Vol 84 (1) ◽  
pp. 59-62
Author(s):  
M. N. Achasov ◽  
A. Yu. Barnyakov ◽  
M. Yu. Barnyakov ◽  
K. I. Beloborodov ◽  
A. V. Berdyugin ◽  
...  
Keyword(s):  
Cross Section ◽  
Center Of Mass ◽  
Mass Frame ◽  
The Cross
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