Atoms

A program package for calculating regularized classical trajectories for Coulomb n–body problem is developed. The Coulomb singularities from the equations of motion are removed by transformations of variables including the time. This effectively conserves the energy of the time-independent systems to a high accuracy for long time propagation. Sample calculations are shown for the cases of 2, 3, 4, and 5 particle systems giving comparisons with the un-regularized trajectories. The program can be used for general purposes including the classical-trajectory Monte-Carlo simulations for charged-particle collisions in free or laser environments.

The first measurements of the magnetic dipole hyperfine structure constants A in singly ionized thulium revealed substantial discrepancies with the corresponding theoretical calculations. Subsequent measurements expanded the very limited available dataset and demonstrated that two of the previously reported experimental A values were incorrect, thereby motivating new theoretical calculations. In this work, we employ the configuration interaction method to calculate the A constants for several low-lying levels in Tm ii, with the random-phase-approximation corrections also taken into account. Our results show good agreement with the new experimental data and provide reliable predictions for additional states where measurements are not yet available.

Inspired by the well-known experimental connections between $X\left(3872\right)$, $Z_{cs}\left(4220\right)$, and $Y\left(4620\right)$, we systematically study the recently reported strange partner of $T_{cc}$, the $1^{+}$$cc\overline{q}\overline{s}$ system, and its orbital excitation state $1^{-}$$cc\overline{q}\overline{s}$. A chiral quark model incorporating SU(3) symmetry is considered to study these two systems. To better investigate their spatial structure, we introduce a precise few-body calculation method, the Gaussian Expansion Method (GEM). In our calculations, we include all possible physical channels, including molecular states and diquark structures, and consider channel coupling effects. To identify the stable structures in the system (bound states and resonance states) we employ a powerful resonance search method, the Real-Scaling Method (RSM). According to our results, in the $1^{+}$$cc\overline{q}\overline{s}$ system, we obtain two bound states with energies of 3890 MeV and 3940 MeV, as well as two resonance states with energies of 3975 MeV and 4090 MeV. The decay channels of these two resonance states are $D{D}_s^{\ast }$ and $D^{\ast }{D}_s$, respectively. In the $1^{-}$$cc\overline{q}\overline{s}$ system, we obtain only one resonance state, with an energy of 4570 MeV, and two main decay channels: $D{D}_{s1}^{\ast }$ and $D^{\ast }{D}_{s1}^{\prime }$. We strongly suggest that experimental groups use our predictions to search for these stable structures.