Rotational energy relaxation quantum dynamics of a diatomic molecule in a superfluid helium nanodroplet and study of the hydrogen isotopes case

Abstract

The rotational energy relaxation (RER) of a molecule X₂(j,m_j) in a ⁴He superfluid nanodroplet [HeND or (⁴He)_N; T = 0.37 K] has been investigated using a hybrid quantum dynamics approach recently proposed by us. As far as we know, this is the first theoretical study about rotational relaxation inside HeNDs, and here several (real and hypothetical) isotopes of H₂ have been examined, in order to analyze the influence of the rotational constant B_e of these fast rotors on the dynamics. The structure of the nanodroplet practically does not change during the RER process, which approximately takes place according to a cascade mechanism j → j − 2; j − 2 → j − 4; …; 2 → 0, and m_j is conserved. The results are consistent with the very scarce estimated experimental data available. The lifetime of an excited rotational state (≈1.0–7.6 ns) increases when: (a) B_e increases; (b) j increases; and (c) N decreases (above N = 100 there is a small influence of N on the lifetime). This also applies to the global relaxation time and transition time. The analysis of the influence of the coupling between the j and j − 2 rotational states (due to the X₂–helium interaction) and the X₂ angular velocity on the lifetime and related properties has been helpful to better understand the dynamics. In contrast to the RER results, for the vibrational energy relaxation (VER) in HeNDs, when the quantum number v increases a decrease is observed in the lifetime of the excited vibrational state. This difference can be interpreted taking into account that RER and VER are associated with very different types of motion. Besides, in VER the intermediate excited states show metastability, differing from the RER case. We hope that the present study will encourage more studies to be developed on the RER dynamics in HeNDs, a basic, interesting and difficult to study physical phenomenon about which we still know very little.