Particle Dynamics in Damped Nonlinear Quadrupole Ion Traps

We examine the motions of particles in quadrupole ion traps as a function of damping and trapping forces, including cases where nonlinear damping or nonlinearities in the electric field geometry play significant roles. In the absence of nonlinearities, particles are either damped to the trap center or ejected, while their addition brings about a rich spectrum of stable closed particle trajectories. In three-dimensional (3D) quadrupole traps, the extended orbits are typically confined to the trap axis, and for this case we present a 1D analysis of the relevant equation of motion. We follow this with an analysis of 2D quadrupole traps that frequently show diamond-shaped closed orbits. For both the 1D and 2D cases we present experimental observations of the calculated trajectories in microparticle ion traps. We also report the discovery of a new collective behavior in damped 2D microparticle ion traps, where particles spontaneously assemble into a remarkable knot of overlapping, corotating diamond orbits, self-stabilized by air currents arising from the particle motion

Differential cross sections for muonic atom scattering from hydrogenic molecules

The differential cross sections for low-energy muonic hydrogen atom scattering from hydrogenic molecules are directly expressed by the corresponding amplitudes for muonic atom scattering from hydrogen-isotope nuclei. The energy and angular dependence of these three-body amplitudes is thus taken naturally into account in scattering from molecules, without involving any pseudopotentials. Effects of the internal motion of nuclei inside the target molecules are included for every initial rotational-vibrational state. These effects are very significant as the considered three-body amplitudes often vary strongly within the energy interval $\lesssim{}0.1$ eV. The differential cross sections, calculated using the presented method, have been successfully used for planning and interpreting many experiments in low-energy muon physics. Studies of $\mu^{-}$ nuclear capture in $p\mu$ and the measurement of the Lamb shift in $p\mu$ atoms created in H$_2$ gaseous targets are recent examples.Comment: 21 pages, 13 figures, submitted to Phys. Rev.