Dipole Perturbations Research Articles

Stability of galaxies in binaries with account of tidal forces

Abstract The stability of elliptical disks in pairs and inside a uniform halo is investigated. A density distribution giving a quadratic gravitational potential of the disk is considered. Tidal forces in binaries and the uniform halo do not violate the quadratic form of the potential. Quadrupole and dipole perturbations are investigated. A dipole instability of the elliptical disk in the ellipsoidal halo is obtained. Elliptical disks in binaries may be elongated and compressed relative to the companion. At low mass components, the elongated disks are stable at slow rotation and compressed disks, at the rapid one. The region of various stability are constructed for quadrupole disk perturbations in binaries and inside the spheroidal halos for different masses, distances between companions and axis ratios.

Summary of group theoretical results for microwave and infrared studies of H2O2

Group theoretical treatments found in the literature for other molecules, based on double-groups of appropriate permutation–inversion groups, are modifed slightly and applied to H2O2. This permits a more unified view of many theoretical results derived in various earlier studies of the molecule. Briefly, if no effects due to internal rotation tunneling were observed in the H2O2 spectrum, the molecule could be treated using the C2 point group of its equilibrium geometry. If effects due to internal rotation tunneling through only the trans barrier are observed (as is presently the case), the molecule should be treated using the C2h point group of its trans planar conformation at the top of the tunneling barrier. If effects due to internal rotation through both the trans and cis barriers can be detected, it will be necessary to treat the molecule using a double group [Formula: see text] of the C2h, point group. Vibrational, torsional, and rotational basis function symmetry species, energy level diagrams, selection rules for electric dipole transitions and perturbations, etc. are presented here for the [Formula: see text] double group, but these results can easily be converted to those for the C2h point group by dropping all s and d subscripts. An empirically discovered successful fitting procedure for the ground state rotational levels, reported in a treatment of microwave and millimetre wave measurements on H2O2, can be rationalized on the basis of the present theoretical results.

Quadrupole perturbation effects upon theHg201magnetic resonance. II. Relaxation due to an anisotropic perturbation

The theory of relaxation of a weakly perturbed spin system is extended to the case of a nonisotropic perturbation. The calculation follows the method of Happer who uses spherical basis operators. Explicit expressions are derived for a spin-$\frac{3}{2}$ system in the presence of dipole and quadrupole perturbations. The results are then applied to the quadrupole relaxation of oriented vapor-phase atoms which occurs while these atoms are adsorbed onto the walls of containers of various shapes. Although the relaxation rates due to the cell wall depend upon the orientation of the wall with respect to the externally applied magnetic field, it is found that the sum of the contributions to the relaxation due to the six faces of a cube-shaped container is independent of the orientation of the container. This prediction is verified experimentally.

Stability of a spherical star system

The stability of a spherically symmetric aggregate of point gravitating particles relative to arbitrary small perturbations is studied. It is assumed that in the absence of perturbations the particles move along circular trajectories chaotically oriented in space so that the total moment of the aggregate is zero. Dimensions of the aggregate are large in comparison to the gravitational radius, and particle velocities are nonrelativistic. It is shown that there exist initial mass-density distributions unstable relative to any perturbations with the exception of radial and dipole perturbations. A general stability criterion is formulated, with the form dΩ2/dr > 0, where\(\Omega ^2 = (4\pi G / r^3 )\int\limits_0^r {p_0 r^2 dr, \rho _0 (r)} \) is the aggregate mass density, and G is the gravitational constant. The dependence of the increment onl, the perturbation harmonic number, is studied. In the case of weak inhomogeneity r(dΩ2/dr)/Ω2 ≪ 1 the increment is maximum for quadrupole perturbations (l = 2) and decreases monotonically with increase inl. In the opposite case of high inhomogeneity r(dΩ2/dr)/Ω2 ≫l the increment increases with increase inl. In the case of weak inhomogeneity the increment may be as small as desired. For high inhomogeneity, instability develops over a time period smaller than the period of revolution of an individual particle. For dΩ2/dr < 0 the system is stable. Consideration of system microstructure in this case leads to damping of macrooscillations (system “heating”).

Nonradial Pulsation of General-Relativistic Stellar Models. V. Analytic Analysis for L = 1

view Abstract Citations (82) References (9) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Nonradial Pulsation of General-Relativistic Stellar Models. V. Analytic Analysis for L = 1 Campolattaro, Alfonso ; Thorne, Kip S. Abstract The theory of small, adiabatic, dipole perturbations of a star away from hydrostatic equilibrium is developed within the framework of general relativity. The analysis is linearized in the perturbation amplitudes. The "odd-parity" perturbations describe differential rotation, while the "even-parity" perturbations describe pulsation. In the pulsational case there are two degrees of freedom associated with the fluid motion and no degrees of freedom in the gravitational field (no dipole gravitational waves). During the pulsation the star's external gravitational field is completely unperturbed, to first order in the amplitude, despite the fact that its surface performs a finite, back-and-forth motion. In both the pulsational and rotational cases, the Einstein field equations are put into simple forms suitable for numerical integration. Publication: The Astrophysical Journal Pub Date: March 1970 DOI: 10.1086/150362 Bibcode: 1970ApJ...159..847C full text sources ADS | Related Materials (5) Part 1: 1967ApJ...149..591T Part 2: 1969ApJ...155..163P Part 3: 1969ApJ...158....1T Part 4: 1969ApJ...158..997T Part 6: 1973ApJ...181..181I

The effect of statistical perturbations on angular correlations

The influence of an arbitrary statistical interactions, which is also random in space, on the angular correlation of two particles successively by a nucleus is investigated. The resulting time-dependent angular correlation function has the form c 0+Σ ic iƒ i(θ) e λit , in which the ƒ i(θ) represent characteristic angular distributions given by the properties of the interaction in the source by the type of particle emitted in the second decay. Some special cases are considered. If, for example, the statistical interaction consists of small electric quadrupole and magnetic dipole perturbations and the second particle is a photon, the ƒ i(θ) become identical to Legendre polynomials, as has been shown by Abragam and Pound. Sufficiently accurate measurements of the characteristics angular distributions and decay constants will give information on the mechanisms of the spin relaxation by the statistical interaction in the source.

On the Adiabatic Demagnetization of Caesium Titanium Alum

Titanium salts should behave more simply than most materials under magnetic cooling, since the ground level of the paramagnetic ion is here inherently doubly degenerate and so unaffected by crystalline fields. De Haas and Wiersma show that as long as the magnetic moment remains constant during adiabatic demagnetization, the temperature is a linear function of a field strength, a most valuable fact since it permits the establishment of a thermodynamic temperature scale. The present paper computes when deviation of the moment from constancy should commence because of the perturbing effect of second-order terms (the first nonvanishing order) in the dipole-dipole coupling energy. The calculated moment does not remain constant to as low field strengths as reported experimentally. The discrepancy cannot be ascribed to a counter-balancing effect of exchange coupling but may be due to the neglect of third and higher order dipole terms. Because of these large dipole perturbations, the status of the experimental temperature scale in titanium alum becomes rather uncertain. The present stage of the theory may be tested more accurately by using much lower initial fields than in the existing Leiden experiments.