The ponderomotive force is derived for a relativistic charged particle entering an electromagnetic standing wave with a general three-dimensional field distribution and a nonrelativistic intensity, using a perturbation expansion method. It is shown that the well-known ponderomotive gradient force expression does not hold for this situation. The modified expression is still of simple gradient form, but contains additional polarization-dependent terms. These terms arise because the relativistic translational velocity induces a quiver motion in the direction of the magnetic force, which is the direction of large field gradients. Oscillation of the Lorentz factor effectively doubles this magnetic contribution. The derived ponderomotive force generalizes the polarization-dependent electron motion in a standing wave obtained earlier [A.E. Kaplan and A.L. Pokrovsky, Phys. Rev. Lett. 95, 053601 (2005)]. Comparison with simulations in the case of a realistic, non-idealized, three-dimensional field configuration confirms the general validity of the analytical results.

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The ponderomotive force is derived for a relativistic charged particle entering an electromagnetic standing wave with a general three-dimensional field distribution and a nonrelativistic intensity, using a perturbation expansion method. It is shown that the well-known ponderomotive gradient force expression does not hold for this situation. The modified expression is still of simple gradient form but contains additional polarization-dependent terms. These terms arise because the relativistic translational velocity induces a quiver motion in the direction of the magnetic force, which is the direction of large field gradients. Consistent perturbation expansion of the equation of motion leads to an effective doubling of this magnetic contribution. The derived ponderomotive force generalizes the polarization-dependent electron motion in a standing wave obtained earlier [A. E. Kaplan and A. L. Pokrovsky, Phys. Rev. Lett. 95, 053601 (2005)]. Comparison with simulations in the case of a realistic, nonidealized, three-dimensional field configuration confirms the general validity of the analytical results.

. (1990). Intermolecular-directed reactivity in solid media. Radiogenic formation of phosphorus-centered radicals in chiral diphosphine disulfides studied by ESR. Journal of the American Chemical Society, 112(14), 5432-5447. DOI: 10.1021/ja00170a006General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. A W c t Singlecrystal, powder, and frozen-matrix ESR experiments have been performed to study the radiogenic electron-capture properties of several diastereoisomeric and asymmetric diphosphine disulfides (R,RzP(S)P(S)R3R4). The principal values of the hyperfine couplings of several phosphorus-centered radical configurations are determined and related to the spin density distribution. Attention is focused on the strong differences in radiogenic properties, observed between the meso and racemic forms of phenyl-and tolyl-substituted diphosphine disulfides. The most striking result is that X irradiation of the crystalline meso compounds MePhP(S)P(S)MePh, Me@-Tol)P(S)P(S)Me@-Tol), and Ph(PhCHz)P(S)P(S)Ph(CH2Ph) does not lead to the formation of a three-electron bond PAP u* radical but invariably results in configurations in which the unpaired electron is primarily localized on one half of the molecule. X irradiation of the corresponding racemic forms, on the other hand, gives rise to P L P u* configurations. The observed discrimination between symmetric and asymmetric configurations is explained in terms of intermolecular steric interactions affecting the geometry relaxation of the precursor molecule after initial electron addition. For a quantitative assessment, the change in van der Waals energy resulting from elongation of the P-P bond of the molecules in their respective crystal lattices was calculated with X-ray crystallographic data. The calculations reveal significantly stronger steric interactions for the aromatic meso compounds than for their racemic forms, in agreement with the absence of PAP u* configurations in the first. X irradiation of diphosphine disulfides in a frozen THF matrix almost invariably results in a single radical product, being the PAP u* configuration, and differences between meso and racemic isomers disappear. This is a consequence of the fact that in a randomly oriented solid matrix the molecular packing is less tight than in a molecular crystal, making more sp...

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