Geometric phase effect study in electric dipole moment rings
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Abstract:
Several proposals to measure a possible small electric dipole moment (EDM) of charged particles aligned with the spin and the well-known magnetic dipole moment (MDM) are based on the concept to circulate bunches with an initial polarization in the horizontal plane and to observe the buildup of a vertical spin component caused by the EDM. Most proposals aim at operating the ring with ``frozen spin,'' such that, with an MDM only, the spin remains aligned with the trajectory. The signature of a finite EDM is the buildup of a vertical spin component. Machine imperfections may lead as well to a vertical spin buildup, which can be misinterpreted as an EDM and thus limit the sensitivity of the experiment. For that reason, a good understanding of spin dynamics is mandatory to estimate and limit such systematic errors in the measurement. In this paper, a coordinate system attached to the trajectory is introduced to expand the spin. This is of particular interest for fully electric EDM rings operated at the ``magic energy'' to satisfy the frozen spin condition. The procedure is used for a straightforward analysis of geometric phase and other second order effects, which limit the possible sensitivity, i.e., the smallest EDM which can be detected in presence of systematic effects.The fact that a magnetic dipole μ moving with velocity βc has an electric dipole moment p = β×μ/c has made periodic appearance in the literature but the importance of this fact and its general utility have not been given sufficient expression. It is the purpose of this paper to show how to derive the equation p=β×/c and then to use it for a simple description of the atomic spin-orbit interaction.
Bond dipole moment
Neutron magnetic moment
Force between magnets
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We analyze a number of different procedures for calculating molecular electric polarizabilities. We find that one particular method should give reliable polarizablitiy values for nonpolar molecules, having no permanent electric dipole. It seems questionable that this method will yield accurate polarizability values for polar molecules, but in that case it may be used to calculate the electric dipole moment. We use the method to calculate the electric polarizabilities of the hydrogen molecule and the hydrogen molecular ion and we obtain satisfactory results.
Bond dipole moment
Chemical polarity
Hydrogen molecule
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It is shown that in the experiments for search of the EDM of an electron (atom, molecule) the T-odd magnetic moment induced by an electric field and the T-odd electric dipole moment induced by a magnetic field will be also measured. It is discussed how to distinguish these contributions.
Bond dipole moment
Neutron magnetic moment
Proton magnetic moment
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Bond dipole moment
Polarity (international relations)
Chemical polarity
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The dipole moment of an H 2 O molecule in ice is greater than the moment of an isolated H 2 O molecule, 1·84 D, owing to the electric fields of neighbouring molecules. The magnitude and direction of the field arising from the nearest 85 neighbours is computed here by representing each molecule as a series of electric multipoles. It is found that the field has the direction of the dipole moment of the central molecule and is sufficiently strong to increase its total dipole moment to about 2·60 D.
Bond dipole moment
Chemical polarity
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Abstract Several magnetic materials consisting of dipoles owe their properties to the specific nature of the dipole–dipole interaction. In the present work, systems of particles possessing a dipole moment arranged on various types of 2D and 3D structures, completely arbitrary and, in some 2D instances, periodic (albeit finite), are studied. Noteworthy, the work is in the regime of strong dipole moments where a classical treatment is possible. The ultimate goal is to quantitatively address the unknown relation existing between the minimum possible energy of a system of dipoles and the concomitant total dipole moment. To such an end, classical numerical methods are used to the previous minimum energy–total dipole moment tandem for various magnetic configurations at zero temperature. An analytic bound for the minimal energy valid for any dimension is also obtained. With this exploration, new light is shed on the connection between the two former physical quantities, establishing an analytic inequality for particles, and describing other instances of physical interest.
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The molecular beam electric resonance spectra of SiO and GeO have been measured. The electric dipole moments (in Debye) of SiO and GeO in the lower vibrational states are: VSiO28GeO7403.09823.282413.11783.303223.13723.323933.1574 The difference between observed and calculated dipole moment is quite similar in CO and SiO.
Bond dipole moment
Debye
Molecular beam
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Bond dipole moment
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Abstract We use a previously proposed variation‐perturbation method to calculate the electric polarizabilities and the electric dipole moment at equilibrium nuclear distance of the BH molecule. We obtain 3.56 × 10 −24 cm 3 for the perpendicular polarizability α xx and 3.22 × 10 −24 cm 3 for the parallel polarizability α zz . Our result for the electric dipole moment μ 0 is 1.734 debye units; there is no reliable experimental result to compare it with.
Debye
Bond dipole moment
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