Detection of the 5p – 4f orbital crossing and its optical clock transition in Pr9+

Recent theoretical works have proposed atomic clocks based on narrow optical transitions in highly charged ions. The most interesting candidates for searches of physics beyond the Standard Model are those which occur at rare orbital crossings where the shell structure of the periodic table is reordered. There are only three such crossings expected to be accessible in highly charged ions, and hitherto none have been observed as both experiment and theory have proven difficult. In this work we observe an orbital crossing in a system chosen to be tractable from both sides: Pr$${}^{9+}$$9+. We present electron beam ion trap measurements of its spectra, including the inter-configuration lines that reveal the sought-after crossing. With state-of-the-art calculations we show that the proposed nHz-wide clock line has a very high sensitivity to variation of the fine-structure constant, $$\alpha$$α, and violation of local Lorentz invariance; and has extremely low sensitivity to external perturbations.

Aero-resonant migration

ABSTRACT The process of planet conglomeration, which primarily unfolds in a geometrically thin disc of gas and dust, is often accompanied by dynamical excitation of the forming planets and planetesimals. The ensuing orbital crossing can lead to large-scale collisional fragmentation, populating the system with icy and rocky debris. In a gaseous nebula, such leftover solid matter tends to spiral down towards the host star due to aerodynamic drag. Along the way, the inward drifting debris can encounter planets and gravitationally couple to them via mean-motion resonances, sapping them of their orbital energy and causing them to migrate. Here, we develop a simple theory for this migration mechanism, which we call ‘aero-resonant migration’ (ARM), in which small planetesimals (10 m ≲ s ≲ 10 km) undergo orbital decay due to aerodynamic drag and resonantly shepherd planets ahead of them. Using a combination of analytical calculations and numerical experiments, we show that ARM is a robust migration mechanism, able to significantly transport planets on time-scales ≲1 Myr, and present simple formulae for the ARM rate.

DO N-PLANET SYSTEMS HAVE A BOUNDARY BETWEEN CHAOTIC AND REGULAR MOTIONS?

Planetary systems consisting of one star and n planets with equal planet masses μ and scaled orbital separation are referred as EMS systems. They represent an ideal model for planetary systems during the post-oligarchic evolution. Through the calculation of Lyapunov exponents, we study the boundary between chaotic and regular regions of EMS systems. We find that for n ≥ 3, there does not exist a transition region in the initial separation space, whereas for n = 2, a clear borderline occurs with relative separation ∼ μ2/7 due to overlap of resonances (Wisdom, 1980). This phenomenon is caused by the slow diffusion of velocity dispersion (∼ t1/2, t is the time) in planetary systems with n ≥ 3, which leads to chaotic motions at the time of roughly two orders of magnitude before the orbital crossing occurs. This result does not conflict with the existence of transition boundary in the full phase space of N -body systems.

Fragmentation Rates of Aromatic Radical Anions and the π*— σ* Orbital Crossing Point

The reaction coordinate of the fragmentation of aromatic radical anions with nucleofugal groups was studied by the INDO and MNDO techniques. The reaction coordinate turned out as the stretching between the nucleofugal group bonded to the carbon atom of the aryl moiety. It was found that to fragment a π* radical anion, the odd electron has to be transferred to the σ* molecular orbital of the aryl-nucleofugal bond by an orbital crossing, which is reached by the lengthening of this bond. There is a qualitative agreement between the length of the bond to reach the orbital crossing point and the experimental fragmentation rates of the aromatic radical anions. Finally, some considerations about the σ-π coupling are made, since it is defining the possibility of a transfer from the π* to the σ* molecular orbital.