Several dynamical processes involving Helium-4 nanodroplets (HNDs) are studied theoretically, in relation with experiments. HNDs are clusters of several hundred to several hundred billions of 4He atoms which exhibit remarkable properties: very low temperature, ~0.4K, superfluid properties, ability to pickup any dopant, weak interaction with any atom or molecule. The studied processes reflect the two main interests in HNDs: characterizing superfluid properties in a finite-size system (quantum vortex nucleation and detection), and using HNDs as an ideal environment to study dopant spectroscopy and dynamics (clustering, ion solvation, and Coulomb explosion). Extensive simulations are conducted using 4He-Density Functional Theory (4He-DFT) and its time-dependent version (4He-TDDFT). This approach can successfully simulate the equilibrium and dynamics of droplets of several thousand of atoms and provide detailed insight into the structural dynamics of the entire system which is not accessible experimentally: visualization of solvation shells, nature of helium droplet excitations. Rare gas (Rg) cluster formation is studied inside HeN under realistic conditions where one Rg atom collides with a solvated n-atom cluster to form the (n+1)-atom cluster. The 4He-DFT simulation results are compared to those of approximate atomistic approaches. Although quantum and superfluidity effects are better described with 4He-TDDFT, several common features are demonstrated. The most stable gas phase configuration is usually not produced, but an isomer with fewer bonds instead, and/or more dilute structures because of the rigidity of the helium solvation shell around the Rg atoms. The sinking of alkali (Ak) cations in HNDs is simulated in parallel with experimental investigations in the group of Stapelfeldt (Aarhus), in complement to earlier studies on Na+ sinking. It aims at shedding some light on the primary steps of solvation, by suddenly ionizing the alkali atom sitting in a dimple at the droplet surface. The build up of the first solvation shell around the ions is shown to be progressive, pointing to a Poissonian mechanism in which each He atom binds independently to the ion. For the lighter alkalis, the solvation shell is incomplete at the end of the dynamics, suggesting a kinetic rather than thermodynamical control of its formation. Coulomb explosion simulations of Ak2 molecules initially sitting at the droplet surface and suddenly ionized are conducted in order to understand the effect of the HNDs on Ak2++ fragmentation dynamics. The corresponding experiment in Stapelfeldt's group in Aarhus aimed at measuring the proportion of triplet to singlet state in the formation of Ak2, and at imaging the vibrational wave function. Several parameters are examined in the simulations: droplet size, zero point motion of Ak2 vibration, and orientational distribution of Ak2 on the droplet surface. The results validate the experimental approach, and evidence an unexpected curvature of the ion trajectories which could be used to measure droplet sizes individually, something that has only been possible up to now for very large sizes (by X-ray diffraction). The nucleation of quantum vortices, a characteristic of helium superfluidity, has been revealed in very large droplets (VLD) and attributed to angular momentum created by friction of the liquid in the nozzle prior to expansion and cooling. Here droplet-droplet collisions are explored as an alternative mechanism. The results show the nucleation of quantum vortices at indentations of the merged droplet, a mechanism general for all droplet sizes. However, no signature has been found to detect vortices in smaller droplets so far. In this work, fluorescence absorption or excitation spectroscopy of alkali atoms is proposed: a vortex is shown to shift and broaden the alkali spectrum. The effect could be measurable above the first excited states.

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We report electron diffraction results of xenon clusters formed in superfluid helium droplets, with droplet sizes in the range of 105–106 atoms/droplet and xenon clusters from a few to a few hundred atoms. Under four different experimental conditions, the diffraction profiles can be fitted using four atom pairs of Xe. For the two experiments performed with higher helium contributions, the fittings with one pair of Xe–He and three pairs of Xe–Xe distances are statistically preferred compared with four pairs of Xe–Xe distances, while the other two experiments exhibit the opposite preference. In addition to the shortest pair distances corresponding to the van der Waals distances of Xe–He and Xe–Xe, the longer distances are in the range of the different arrangements of Xe–He–Xe and Xe–He–He–Xe. The number of independent atom pairs is too many for the small xenon clusters and too few for the large clusters. We consider these results evidence of xenon foam structures, with helium atoms stuck between Xe atoms. This possibility is confirmed by helium time-dependent density functional calculations. When the impact parameter of the second xenon atom is a few Angstroms or longer, the second xenon atom fails to penetrate the solvation shell of the first atom, resulting in a dimer with a few He atoms in between the two Xe atoms. In addition, our results for larger droplets point toward a multi-center growth process of dopant atoms or molecules, which is in agreement with previous proposals from theoretical calculations and experimental results.

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The lifetimes of NeIBr were obtained for the vibrational levels and for the van der Waals (vdW) level . Was used the Quasi-Classical Trajectories (QCT) and the Trajectory Surface Hopping (TSH) under a diabatic representation. A kinetic mechanism was implemented to study the vibrational predissociation. For this purpose, a bunch of trajectories were taken in order to properly describe the energy transfer up to 5 quanta from the IBr diatom to vdW modes. The results obtained were generally consistent with previous experimental results for this system.

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The radiative cooling of naphthalene dimer cations, (C$_{10}$H$_8$)$_2^+$ was studied experimentally through action spectroscopy using two different electrostatic ion-beam storage rings, DESIREE in Stockholm and Mini-Ring in Lyon. The spectral characteristics of the charge resonance (CR) band were observed to vary significantly with storage time of up to 30 seconds in DESIREE. In particular, the position of the CR band shifts to the blue, with specific times (inverse of rates) of 0.64 s and 8.0 s in the 0-5 s and 5-30 s storage time ranges, respectively. Such long-time scales evoke that the internal energy distribution of the stored ions evolves by vibrational radiative cooling, which is consistent with the absence of fast radiative cooling via recurrent fluorescence for (C$_{10}$H$_8$)$_2^+$. Density Functional based Tight Binding calculations with local excitations and Configuration Interactions (DFTB-EXCI) were used to simulate the absorption spectrum for ion temperatures between 10 and 500 K. The evolution of the band width and position with temperature is in qualitative agreement with the experimental findings. Furthermore, these calculations yielded linear temperature dependencies for both the shift and the broadening. Combining the relation between the CR band position and the ion temperature with the results of the statistical model, we demonstrate that the observed blue shift can be used to determine the radiative cooling rate of (C$_{10}$H$_8$)$_2^+$.

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