Atoms

We study the planar repulsive two-center Coulomb system in the presence of a uniform magnetic field perpendicular to the plane, taking the inter-center separation a and the magnetic field strength B as independent control parameters. The free-field system $B=0$ is Liouville integrable and the motion is unbounded. The magnetic confinement introduces nonlinear coupling that breaks integrability and gives rise to chaotic bounded dynamics. Using Poincaré sections and maximal Lyapunov exponents, we characterize the transition from regular motion at $aB=0$ to mixed regular–chaotic dynamics for $aB\ne 0$. To probe the recoverability of the dynamics, we apply sparse regression techniques to numerical trajectories and assess their ability to capture the equations of motion across mixed dynamical regimes. Our results clarify how magnetic confinement competes with two-center repulsive interactions in governing the emergence of chaos and delineate fundamental limitations of data-driven model discovery in nonintegrable Hamiltonian systems. We further identify an organizing mechanism whereby the repulsive two-center system exhibits locally one-center-like dynamics in the absence of any static confining barrier.

Through finite-element simulation, the axial potential distribution of the ion trap is analyzed. The effects of the central hole diameter of the end cap and the spacing between the two end caps on the axial geometric parameters of the ion trap are investigated. Based on these findings, a set of linear Paul traps is designed by selecting suitable end caps and quadrupoles. Stable trapping of calcium ions (Ca⁺) is successfully achieved, and these ions are subsequently laser-cooled into ionic Coulomb crystals. In the experiment, secular motion excitation of the Ca⁺ ion Coulomb crystal is performed, yielding an axial geometric parameter of 0.115(1) for the ion trap. This value aligns well with the simulation result of 0.114(2). The precise determination of the axial geometric parameter provides a solid foundation for subsequent high-precision optical or mass spectrometry measurements.

In this work, the He and Ar triplet autoionizing states have been studied using a non-monochromatic electron beam and a high-resolution electrostatic analyzer at low incident electron energies and three ejection angles: 40°, 90°, and 130°. Low-energy electrons have been used because they have a high probability of exciting triplet states regardless of whether they are discrete isolate states or are embedded in the ionization continuum. Additionally, the He ejected electron spectra have been measured at several ejection angles between 20° and 130° and two incident energies, namely 60.5 eV and 101 eV. The anisotropic angular distributions indicate that orbital angular momentum exchange between the ejected and scattered electrons occurred. The energies of the first triplets 3s3p⁶4s(³S) and 3s3p⁶4p(³P) states of argon are found to be (24.985 ± 0.020) eV and (26.52 ± 0.02) eV, respectively.