scholarly journals Three-Body Scattering Amplitude. I. Separation of Angular Momentum

1964 ◽  
Vol 134 (6B) ◽  
pp. B1358-B1364 ◽  
Author(s):  
Roland L. Omnes
Keyword(s):  
Angular Momentum ◽  
Scattering Amplitude ◽  
Three Body

scholarly journals Three-Body Scattering Amplitude. II. Extension to Complex Angular Momentum

1964 ◽  
Vol 136 (4B) ◽  
pp. B1137-B1153 ◽  
Author(s):  
Roland L. Omnes ◽  
Victor A. Alessandrini
Keyword(s):  
Angular Momentum ◽  
Scattering Amplitude ◽  
Complex Angular Momentum ◽  
Three Body

THE ANGULAR MOMENTUM DEPENDENT CALCULATION OF THE GROUND STATE ENERGY OF LIQUID 3He

2005 ◽  
Vol 19 (30) ◽  
pp. 1793-1802 ◽  
Author(s):  
M. MODARRES
Keyword(s):  
Angular Momentum ◽  
Ground State Energy ◽  
Ground State ◽  
Correlation Functions ◽  
State Energy ◽  
Interatomic Potentials ◽  
Channel Correlation ◽  
P Waves ◽  
Effective Interactions ◽  
Three Body

We investigate the possible angular momentum, l, dependence of the ground state energy of normal liquid 3 He . The method of lowest order constrained variational (LOCV) which includes the three-body cluster energy and normalization constraint (LOCVE) is used with angular momentum dependent two-body correlation functions. A functional minimization is performed with respect to each l-channel correlation function. It is shown that this dependence increases the binding energy of liquid 3 He by 8% with respect to calculations without angular momentum dependent correlation functions. The l=0 state has completely different behavior with respect to other l-channels. It is also found that the main contribution from potential energy comes from the l=1 state (p-waves) and the effect of l≥11 is less than about 0.1%. The effective interactions and two-body correlations in different channels are being discussed. Finally we conclude that this l-dependence can be verified experimentally by looking into the magnetization properties of liquid helium 3 and interatomic potentials.

Waldmann-Snider Collision Integrals and Nonspherical Molecular Interaction. I. Collision Integrals for Pure Gases

1974 ◽  
Vol 29 (12) ◽  
pp. 1705-1716 ◽  
Author(s):  
W. E. Köhler
Keyword(s):  
Angular Momentum ◽  
Cross Sections ◽  
Molecular Interaction ◽  
Scattering Amplitude ◽  
Collision Operator ◽  
Positive Definiteness ◽  
Collision Integrals ◽  
General Properties ◽  
Relaxation Coefficients ◽  
Rotational Angular Momentum

Collision integrals of the linearized Waldmann-Snider collision operator for pure gases are defined. General properties due to invariances of the molecular interaction are discussed. Effective cross sections are introduced and expressed in terms of convenient bracket symbols. The positive definiteness of the relaxation coefficients is proved. The approximation of small nonsphericity for the scattering amplitude is explained and consequences for the collision integrals are investigated. Molecular cross sections describing the orientation and reorientation of the molecular rotational angular momentum are defined. Expressions for effective cross sections relevant for the various nonequilibrium alignment phenomena are presented.

scholarly journals Two Conjectures of G.D. Birkhoff

1999 ◽  
Vol 172 ◽  
pp. 439-440
Author(s):  
Christopher K. Mccord ◽  
Kenneth R. Meyer
Keyword(s):  
Angular Momentum ◽  
Integral Manifold ◽  
Center Of Mass ◽  
Angular Momentum Vector ◽  
Momentum Vector ◽  
Algebraic Set ◽  
Special Values ◽  
Integral Manifolds ◽  
Energy Center ◽  
Three Body

The spatial (planar) three-body problem admits the ten (six) integrals of energy, center of mass, linear momentum and angular momentum. Fixing these integrals defines an eight (six) dimensional algebraic set called the integral manifold, 𝔐(c, h) (m(c, h)), which depends on the energy level h and the magnitude c of the angular momentum vector. The seven (five) dimensional reduced integral manifold, 𝔐R(c, h) (mR(c, h)), is the quotient space 𝔐(c, h)/SO2 (m(c, h)/SO2) where the SO2 action is rotation about the angular momentum vector. We want to determine how the geometry or topology of these sets depends on c and h. It turns out that there is one bifurcation parameter, ν = −c2h, and nme (six) special values of this parameter, νi, i = 1, …, 9.At each of the special values the geometric restrictions imposed by the integrals change, but one of these values, ν5, does not give rise to a change in the topology of the integral manifolds 𝔐(c, h) and 𝔐R(c, h). The other eight special values give rise to nine different topologically distinct cases. We give a complete description of the geometry of these sets along with their homology. These results confirm some conjectures and refutes several others.

scholarly journals Origin of Binary Systems

1992 ◽  
Vol 151 ◽  
pp. 9-19
Author(s):  
Peter Bodenheimer
Keyword(s):  
Angular Momentum ◽  
Binary Systems ◽  
Theoretical Calculations ◽  
Pressure Effects ◽  
Close Binaries ◽  
Rotating Stars ◽  
Multiple Systems ◽  
The Individual ◽  
Protostellar Collapse ◽  
Three Body

Recent observational studies of the properties of binary systems among young stars indicate that the majority of binaries are formed very early in the history of a star, perhaps during the protostellar collapse. Major observational facts to be explained include the overall binary frequency, the non-negligible occurrence of multiple systems, and the distributions of period, eccentricity, and mass ratio among the individual binaries. Theoretical calculations of the collapse of rotating protostars during the isothermal phase indicate instability to fragmentation into multiple systems. This process in general produces systems with periods greater than a few hundred years, although somewhat shorter periods are possible. Fragmentation during later, optically thick, phases of collapse tends to be suppressed by pressure effects. Therefore, major theoretical problems remain concerning the origin of close binaries. Fission of rapidly rotating stars, tidal capture, and three-body capture have been shown to be improbable mechanisms for formation of close binaries. Mechanisms currently under study include gravitational instabilities in disks, orbital interactions and disk-induced captures in fragmented multiple systems, hierarchical fragmentation, and orbital decay of long-period systems. Single stars, on the other hand, could result by escape from multiple systems or by the collapse of clouds of low angular momentum, coupled with angular momentum transport after disk formation.

scholarly journals A Global Analysis of The Generalized Sitnikov Problem

1999 ◽  
Vol 172 ◽  
pp. 291-302
Author(s):  
Steven R. Chesley
Keyword(s):  
Angular Momentum ◽  
Global Analysis ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Bounded Motion ◽  
Type Symmetry ◽  
The Stability ◽  
Two Parameters ◽  
Three Body ◽  
Area Preserving

AbstractThe isosceles three-body problem with Sitnikov-type symmetry has been reduced to a two-dimensional area-preserving Poincaré map depending on two parameters: the mass ratio, and the total angular momentum. The entire parameter space is explored, contrasting new results with ones obtained previously in the planar (zero angular momentum) case. The region of allowable motion is divided into subregions according to a symbolic dynamics representation. This enables a geometric description of the system based on the intersection of the images of the subregions with the preimages. The paper also describes the regions of allowable motion and bounded motion, and discusses the stability of the dominant periodic orbit.

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